Perry’s
Chemical
Engineers’
Handbook
ABOUT THE EDITORS
Dr. Don W. Green is Emeritus Distinguished Professor of Chemical and Petroleum Engineering at the University of Kansas
(KU). He holds a B.S. in petroleum engineering from the University of Tulsa, and M.S. and Ph.D. degrees in chemical engineering from the University of Oklahoma. He is the coeditor of the sixth edition of Perry’s Chemical Engineers’ Handbook,
and editor of the seventh and eighth editions. He has authored/coauthored 70 refereed publications, over 100 technical
meeting presentations, and is coauthor of the first and second editions of the SPE textbook Enhanced Oil Recovery.
Dr. Green has won numerous teaching awards at KU, including the Honors for Outstanding Progressive Educator (HOPE)
Award and the Chancellor’s Club Career Teaching Award, the highest teaching recognitions awarded at the University.
He has also been featured as an outstanding educator in ASEE’s Chemical Engineering Education Journal. He received the
KU School of Engineering Distinguished Engineering Service Award (DESA), and has been designated an Honorary Member
of both SPE and AIME and a Fellow of the AIChE.
Dr. Marylee Z. Southard is Associate Professor of Chemical and Petroleum Engineering at the University of Kansas.
She holds B.S., M.S., and Ph.D. degrees in chemical engineering from the University of Kansas. Dr. Southard’s research
deals with small molecule drug formulations; but her industrial background is in production and process development
of inorganic chemical intermediates. Dr. Southard’s work in inorganic chemicals production has included process
engineering, design, and product development. She has consulted for industrial and pharmaceutical chemical production
and research companies. She teaches process design and project economics, and has won several university-wide teaching
awards, including the Honors for Outstanding Progressive Educator (HOPE) Award and the Kemper Teaching Fellowship.
She has authored 1 patent, 15 refereed publications, and numerous technical presentations. Her research interests are in
biological and pharmaceutical mass transport. She is a senior member of AIChE and ASEE.
PERRY’S
CHEMICAL
ENGINEERS’
HANDBOOK
NINTH
EDITION
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Editor-in-Chief
Don W. Green
Emeritus Distinguished Professor of
Chemical and Petroleum Engineering,
University of Kansas
Associate Editor
Marylee Z. Southard
Associate Professor of Chemical & Petroleum
Engineering, University of Kansas
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Contents
For the detailed contents of any section, consult the title page of that section.
See also the alphabetical index in the back of the handbook.
Section
Unit Conversion Factors and Symbols
Marylee Z. Southard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Marylee Z. Southard, Richard L. Rowley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Physical and Chemical Data
Bruce A. Finlayson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Mathematics
J. Richard Elliott, Carl T. Lira, Timothy C. Frank, Paul M. Mathias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Thermodynamics
Geoffrey D. Silcox, James J. Noble, Phillip C. Wankat, Kent S. Knaebel . . . . . . . . . . . . . . . . . . . . . . . . 5
Heat and Mass Transfer
James N. Tilton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Fluid and Particle Dynamics
Tiberiu M. Leib, Carmo J. Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Reaction Kinetics
Thomas F. Edgar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Process Control
Process Economics
James R. Couper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Transport and Storage of Fluids
Heat-Transfer Equipment
Meherwan P. Boyce, Victor H. Edwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Richard L. Shilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Psychrometry, Evaporative Cooling, and Solids Drying
John P. Hecht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Michael F. Doherty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Distillation
Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation
Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment
Timothy C. Frank . . . . . . . . . . . . . . . . . 15
M. Douglas LeVan, Giorgio Carta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Adsorption and Ion Exchange
Gas–Solid Operations and Equipment
Liquid-Solid Operations and Equipment
Reactors
Henry Z. Kister . . . . . . . . . . . . . 14
Ted M. Knowlton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Wayne J. Genck. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Carmo J. Pereira, Tiberiu M. Leib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Bioreactions and Bioprocessing
Gregory Frank, Jeffrey Chalmers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Solids Processing and Particle Technology
Waste Management
Process Safety
Karl V. Jacob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Louis Theodore, Paul S. Farber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Daniel A. Crowl, Robert W. Johnson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Energy Resources, Conversion, and Utilization
Materials of Construction
Shabbir Ahmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Lindell R. Hurst, Jr., Edward R. Naylor, Emory A. Ford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Index follows Section 25
v
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Contributors
D. Shabbir Ahmed, Ph.D. Chemical Engineer, Chemical Sciences and Engineering Division, Argonne National
Laboratory (Section Editor, Sec. 24, Energy Resources, Conversion, and Utilization)
Brooke Albin, M.S.E. Chemical Engineer, MATRIC (Mid-Atlantic Technology, Research and Innovation Center),
Charleston, WV; Member, American Institute of Chemical Engineers, American Filtration Society (Crystallization from the
Melt) (Sec. 18, Liquid-Solid Operations and Equipment)
John Alderman, M.S., P.E., C.S.P. Managing Partner, Hazard and Risk Analysis, LLC (Electrical Area
Classification, Fire Protection Systems) (Sec. 23, Process Safety)
Paul Amyotte, Ph.D., P.Eng. Professor of Chemical Engineering and C.D. Howe Chair in Process Safety,
Dalhousie University; Fellow, Chemical Institute of Canada; Fellow, Canadian Academy of Engineering (Dust Explosions)
(Sec. 23, Process Safety)
Frank A. Baczek, B.S. Sr. Research Advisor, FLSmidth USA, Inc. (Gravity Sedimentation Operations) (Sec. 18, LiquidSolid Operations and Equipment)
Wayne E. Beimesch, Ph.D. Technical Associate Director (Retired), Corporate Engineering, The Procter & Gamble
Company (Drying Equipment, Operation and Troubleshooting) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids
Drying)
Ray Bennett, Ph.D., P.E., CEFEI Senior Principal Engineer, Baker Engineering and Risk Consultants, Inc.; Member,
American Petroleum Institute 752, 753, and 756 (Estimation of Damage Effects) (Sec. 23, Process Safety)
B. Wayne Bequette, Ph.D. Professor of Chemical and Biological Engineering, Rensselaer Polytechnic Institute
(Unit Operations Control, Advanced Control Systems) (Sec. 8, Process Control)
Patrick M. Bernhagen, P.E., B.S. Director of Sales—Fired Heater, Amec Foster Wheeler North America Corp.;
API Subcommittee on Heat Transfer Equipment API 530, 536, 560, and 561 (Compact and Nontubular Heat Exchangers)
(Sec. 11, Heat-Transfer Equipment)
Michael J. Betenbaugh, Ph.D. Professor of Chemical and Biomolecular Engineering, Johns Hopkins University;
Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and Bioprocessing Technologies and Trends)
(Sec. 20, Bioreactions and Bioprocessing)
Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member, National
Academy of Engineering (Sec. 3, Mathematics)
Meherwan P. Boyce, Ph.D., P.E. (Deceased) Chairman and Principal Consultant, The Boyce Consultancy
Group, LLC; Fellow, American Society of Mechanical Engineers (U.S.); Fellow, National Academy Forensic Engineers (U.S.);
Fellow, Institution of Mechanical Engineers (U.K.); Fellow, Institution of Diesel and Gas Turbine Engineers (U.K.); Registered
Professional Engineer (Texas), Chartered Engineer (U.K.); Sigma Xi, Tau Beta Pi, Phi Kappa Phi. (Section Coeditor,
Sec. 10, Transport and Storage of Fluids)
Jeffrey Breit, Ph.D. Principal Scientist, Capsugel; Member, American Association of Pharmaceutical Scientists
(Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing)
vii
viii
COnTRIBUTORS
Laurence G. Britton, Ph.D. Process Safety Consultant; Fellow, American Institute of Chemical Engineers; Fellow,
Energy Institute; Member, Institute of Physics (U.K.) (Flame Arresters) (Sec. 23, Process Safety)
nathan Calzadilla, M.S.E. Research Program Assistant, Johns Hopkins Medicine, Chemical and Biomolecular
Engineering, Johns Hopkins University; Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and
Bioprocessing Technologies and Trends) (Sec. 20, Bioreactions and Bioprocessing)
John W. Carson, Ph.D. President, Jenike & Johanson, Inc., Founding member and past chair of ASTM Subcommittee
D18.24, “Characterization and Handling of Powders and Bulk Solids” (Bulk Solids Flow and Hopper Design)
(Sec. 21, Solids Processing and Particle Technology)
Giorgio Carta, Ph.D. Lawrence R. Quarles Professor, Department of Chemical Engineering, University of Virginia;
Member, American Institute of Chemical Engineers, American Chemical Society (Section Coeditor, Sec. 16, Adsorption and
Ion Exchange)
Jeffrey Chalmers, Ph.D. Professor of Chemical and Biomolecular Engineering, The Ohio State University; Member,
American Institute of Chemical Engineers; American Chemical Society; Fellow, American Institute for Medical and Biological
Engineering (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing)
J. Wayne Chastain, B.S., P.E., CCPSC Engineering Associate, Eastman Chemical Company; Member, American
Institute of Chemical Engineers (Layer of Protection Analysis) (Sec. 23, Process Safety)
Wu Chen, Ph.D. Principal Research Scientist, The Dow Chemical Company; Fellow, American Filtration and
Separations Society (Expression) (Sec. 18, Liquid-Solid Operations and Equipment)
Martin P. Clouthier, M.Sc., P.Eng. Director, Jensen Hughes Consulting Canada Ltd. (Dust Explosions)
(Sec. 23, Process Safety)
James R. Couper, D.Sc. Professor Emeritus, The Ralph E. Martin Department of Chemical Engineering, University of
Arkansas—Fayetteville (Section Editor, Sec. 9, Process Economics)
Daniel A. Crowl, Ph.D., CCPSC AIChE/CCPS Staff Consultant; Adjunct Professor, University of Utah; Professor
Emeritus of Chemical Engineering, Michigan Technological University; Fellow, American Institute of Chemical Engineers;
Fellow, AIChE Center for Chemical Process Safety (Section Coeditor, Sec. 23, Process Safety)
Rita D’Aquino, M.E. Consultant, Member, American Institute of Chemical Engineers (Pollution Prevention)
(Sec. 22, Waste Management)
Michael Davies, Ph.D. President and CEO, Braunschweiger Flammenfilter GmbH (PROTEGO), Member, American
Institute of Chemical Engineers; Member, National Fire Protection Association (Flame Arresters) (Sec. 23, Process Safety)
Sheldon W. Dean, Jr., ScD, P.E. President, Dean Corrosion Technology, Inc.; Fellow, Air Products and
Chemicals, Inc., Retired; Fellow, ASTM; Fellow, NACE; Fellow, AIChE; Fellow, Materials Technology Institute
(Corrosion Fundamentals, Corrosion Prevention) (Sec. 25, Materials of Construction)
Dennis W. Dees, Ph.D. Senior Electrochemical Engineer, Chemical Sciences and Engineering Division, Argonne
National Laboratory (Electrochemical Energy Storage) (Sec. 24, Energy Resources, Conversion, and Utilization)
Vinay P. Deodeshmukh, Ph.D. Sr. Applications Development Manager—High Temperature and Corrosion
Resistant Alloys, Haynes International Inc. (Corrosion Fundamentals, High-Temperature Corrosion, Nickel Alloys)
(Sec. 25, Materials of Construction)
Shrikant Dhodapkar, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers
(Gas–Solids Separations) (Sec. 17, Gas–Solid Operations and Equipment); (Feeding, Metering, and Dosing) (Sec. 21, Solids
Processing and Particle Technology)
David S. Dickey, Ph.D. Consultant, MixTech, Inc.; Fellow, American Institute of Chemical Engineers; Member, North
American Mixing Forum (NAMF); Member, American Chemical Society; Member, American Society of Mechanical Engineers;
Member, Institute of Food Technology (Mixing and Processing of Liquids and Solids & Mixing of Viscous Fluids, Pastes, and
Doughs) (Sec. 18, Liquid-Solid Operations and Equipment)
Michael F. Doherty, Ph.D. Professor of Chemical Engineering, University of California—Santa Barbara
(Section Editor, Sec. 13, Distillation)
Arthur M. Dowell, III, P.E., B.S. President, A M Dowell III PLLC; Fellow, American Institute of Chemical Engineers;
Senior Member, Instrumentation, Systems and Automation Society (Risk Analysis) (Sec. 23, Process Safety)
Brandon Downey, B.A.Sc. Principal Engineer, R&D, Lonza; Member, American Institute of Chemical Engineers
(Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing)
Karin nordström Dyvelkov, Ph.D. GEA Process Engineering A/S Denmark (Drying Equipment, Fluidized Bed
Dryers, Spray Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying)
COnTRIBUTORS
ix
Thomas F. Edgar, Ph.D. Professor of Chemical Engineering, University of Texas—Austin (Section Editor,
Sec. 8, Process Control)
Victor H. Edwards, Ph.D., P.E. Principal, VHE Technical Analysis; Fellow and Life Member, American Institute
of Chemical Engineers; Member, American Association for the Advancement of Science, American Chemical Society,
National Society of Professional Engineers; Life Member, New York Academy of Sciences; Registered Professional Engineer
(Texas), Phi Lambda Upsilon, Sigma Tau (Section Coeditor, Sec. 10, Transport and Storage of Fluids)
J. Richard Elliott, Ph.D. Professor, Department of Chemical and Biomolecular Engineering, University of Akron;
Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of
Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics)
Dirk T. Van Essendelft, Ph.D. Chemical Engineer, National Energy Technology Laboratory, U.S. Department of
Energy (Coal) (Sec. 24, Energy Resources, Conversion, and Utilization)
James R. Fair, Ph.D., P.E. (Deceased) Professor of Chemical Engineering, University of Texas; Fellow, American
Institute of Chemical Engineers; Member, American Chemical Society, American Society for Engineering Education, National
Society of Professional Engineers (Section Editor of the 7th edition and major contributor to the 5th, 6th, and 7th editions)
(Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation)
Yi Fan, Ph.D. Associate Research Scientist, The Dow Chemical Company (Solids Mixing) (Sec. 21, Solids Processing
and Particle Technology)
Paul S. Farber, P.E., M.S. Principal, P. Farber & Associates, LLC, Willowbrook, Illinois; Member, American Institute
of Chemical Engineers, Air & Waste Management Association (Section Coeditor, Sec. 22, Waste Management)
Hans K. Fauske, D.Sc. Emeritus President and Regent Advisor, Fauske and Associates, LLC; Fellow, American
Institute of Chemical Engineers; Fellow, American Nuclear Society; Member, National Academy of Engineering
(Pressure Relief Systems) (Sec. 23, Process Safety)
Zbigniew T. Fidkowski, Ph.D.
(Sec. 13, Distillation)
Process Engineer, Evonik Industries (Distillation Systems, Batch Distillation)
Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering, University of
Washington; Member, National Academy of Engineering (Section Editor, Sec. 3, Mathematics)
Emory A. Ford, Ph.D. Associate Director, Materials Technology Institute, Chief Scientist and Director of Research,
Lyondell/Bassel Retired, Fellow Materials Technology Institute (Section Coeditor, Sec. 25, Materials of Construction)
Gregory Frank, Ph.D. Principal Engineer, Amgen Inc.; Fellow, American Institute of Chemical Engineers;
Member, Society of Biological Engineering; North American Mixing Forum; Pharmaceutical Discovery, Development, and
Manufacturing Forum (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing)
Timothy C. Frank, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers
(Section Coeditor, Sec. 4, Thermodynamics; Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and
Equipment)
Walter L. Frank, B.S., P.E., CCPSC President, Frank Risk Solutions, Inc.; AIChE/CCPS Staff Consultant; Fellow,
American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Hazards of Vacuum, Hazards
of Inerts) (Sec. 23, Process Safety)
Ben J. Freireich, Ph.D. Technical Director, Particulate Solid Research, Inc. (Solids Mixing, Size Enlargement)
(Sec. 21, Solids Processing and Particle Technology)
James D. Fritz, Ph.D. Consultant, NACE International certified Material Selection Design Specialist; Member of
the Metallic Materials and Materials Joining Subcommittees of the ASME Bioprocessing Equipment Standard, the Ferrous
Specifications Subcommittee of the ASME Boiler & Pressure Vessel Code, and ASM International (Stainless Steels)
(Sec. 25, Materials of Construction)
Kevin L. Ganschow, B.S., P.E. Senior Staff Materials Engineer, Chevron Corporation; Registered Professional
Mechanical Engineer (California) (Ferritic Steels) (Sec. 25, Materials of Construction)
Wayne J. Genck, Ph.D. President, Genck International; consultant on crystallization and precipitation; Member,
American Chemical Society, American Institute of Chemical Engineers, Association for Crystallization Technology,
International Society of Pharmaceutical Engineers (ISPE) (Section Editor, Sec. 18, Liquid-Solid Operations and Equipment)
Craig G. Gilbert, B.Sc. Global Product Manager-Paste, FLSmidth USA, Inc.; Member, Society for Mining, Metallurgy,
and Exploration; Mining and Metallurgical Society of America; Registered Professional Engineer (Gravity Sedimentation
Operations) (Sec. 18, Liquid-Solid Operations and Equipment)
x
COnTRIBUTORS
Roy A. Grichuk, P.E. Piping Director, Fluor, BSME, P.E.; Member, American Society of Mechanical Engineers,
B31 Main Committee, B31MTC Committee, and B31.3 Committee; Registered Professional Engineer (Texas) (Piping)
(Sec. 10, Transport and Storage of Fluids)
Juergen Hahn, Ph.D. Professor of Biomedical Engineering, Rensselaer Polytechnic Institute (Advanced Control
Systems, Bioprocess Control) (Sec. 8, Process Control)
Roger G. Harrison, Ph.D. Professor of Chemical, Biological, and Materials Engineering and Professor of
Biomedical Engineering, University of Oklahoma; Member, American Institute of Chemical Engineers, American Chemical
Society, American Society for Engineering Education, Oklahoma Higher Education Hall of Fame; Fellow, American Institute
for Medical and Biological Engineering (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions
and Bioprocessing)
John P. Hecht, Ph.D. Technical Section Head, Drying and Particle Processing, The Procter & Gamble Company;
Member, American Institute of Chemical Engineers (Section Editor, Sec. 12, Psychrometry, Evaporative Cooling, and
Solids Drying)
Matthew K. Heermann, P.E., B.S. Consultant—Fossil Power Environmental Technologies, Sargent & Lundy LLC,
Chicago, Illinois (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management)
Dennis C. Hendershot, M.S. Process Safety Consultant; Fellow, American Institute of Chemical Engineers
(Inherently Safer Design and Related Concepts, Hazard Analysis, Key Procedures) (Sec. 23, Process Safety)
Taryn Herrera, B.S. Process Engineer, Manager Separations Laboratory, FLSmidth USA, Inc. (Gravity Sedimentation
Operations) (Sec. 18, Liquid-Solid Operations and Equipment)
Darryl W. Hertz, B.S. Senior Manager, Value Improvement Group, KBR, Houston, Texas (Front-End Loading,
Value-Improving Practices) (Sec. 9, Process Economics)
Bruce S. Holden, M.S. Principal Research Scientist, The Dow Chemical Company; Fellow, American Institute of
Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment)
Predrag S. Hrnjak, Ph.D. Will Stoecker Res. Professor of Mechanical Science and Engineering, University of Illinois
at Urbana-Champaign; Principal Investigator—U of I Air Conditioning and Refrigeration Center; Assistant Professor,
University of Belgrade; International Institute of Chemical Engineers; American Society of Heat, Refrigerating, and Air
Conditioning Engineers (Refrigeration) (Sec. 11, Heat-Transfer Equipment)
Lindell R. Hurst, Jr., M.S., P.E. Senior Materials and Corrosion Engineer, Shell Global Solutions (US) Inc. Retired,
Registered Professional Metallurgical Engineer (Alabama, Ohio, North Dakota) (Section Coeditor, Sec. 25, Materials of
Construction)
Karl V. Jacob, B.S. Fellow, The Dow Chemical Company; Lecturer, University of Michigan; Fellow, American Institute
of Chemical Engineers (Section Editor, Sec. 21, Solids Processing and Particle Technology)
Pradeep Jain, M.S. Senior Fellow, The Dow Chemical Company (Feeding, Metering, and Dosing) (Sec. 21, Solids
Processing and Particle Technology)
David Johnson, P.E., M.Ch.E.
(Sec. 11, Heat-Transfer Equipment)
Retired (Thermal Design of Heat Exchangers, Condensers, Reboilers)
Robert W. Johnson, M.S.Ch.E. President, Unwin Company; Fellow, American Institute of Chemical Engineers
(Section Coeditor, Sec. 23, Process Safety)
Hugh D. Kaiser, P.E., B.S., M.B.A. Principal Engineer, WSP USA; Fellow, American Institute of Chemical
Engineers; Registered Professional Engineer (Indiana, Nebraska, Oklahoma, and Texas) (Storage and Process Vessels)
(Sec. 10, Transport and Storage of Fluids)
Ian C. Kemp, M.A. (Cantab) Scientific Leader, GlaxoSmithKline; Fellow, Institution of Chemical Engineers;
Associate Member, Institution of Mechanical Engineers (Psychrometry, Solids-Drying Fundamentals, Freeze Dryers)
(Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Pinch Analysis) (Sec. 24, Energy Resources, Conversion,
and Utilization)
Pradip R. Khaladkar, M.S., P.E. Principal Consultant, Materials Engineering Group, Dupont Company (Retired),
Registered Professional Engineer (Delaware), Fellow, Materials Technology Institute, St. Louis (Nonmetallic Materials)
(Sec. 25, Materials of Construction)
Henry Z. Kister, M.E., C.Eng., C.Sc. Senior Fellow and Director of Fractionation Technology, Fluor Corporation;
Member, National Academy of Engineering (NAE); Fellow, American Institute of Chemical Engineers; Fellow, Institution
of Chemical Engineers (U.K.); Member, Institute of Energy (Section Editor, Sec. 14, Equipment for Distillation, Gas
Absorption, Phase Dispersion, and Phase Separation)
Kent S. Knaebel, Ph.D. President, Adsorption Research, Inc.; Member, American Institute of Chemical Engineers,
International Adsorption Society; Professional Engineer (Ohio) (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer)
COnTRIBUTORS
xi
Ted M. Knowlton, Ph.D. Technical Consultant and Fellow, Particulate Solid Research, Inc.; Member, American
Institute of Chemical Engineers (Section Editor, Sec. 17, Gas–Solid Operations and Equipment)
James F. Koch, M.S. Senior Process Engineering Specialist, The Dow Chemical Company (Size Reduction,
Screening) (Sec. 21, Solids Processing and Particle Technology)
Tim Langrish, D. Phil. School of Chemical and Biomolecular Engineering, The University of Sydney, Australia
(Solids-Drying Fundamentals, Cascading Rotary Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying)
Tim J. Laros, M.S. Owner, Filtration Technologies, LLC, Park City, UT; Member, Society for Mining, Metallurgy, and
Exploration (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment)
Tiberiu M. Leib, Ph.D. Principal Consultant, The Chemours Company (retired); Fellow, American Institute of
Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors)
M. Douglas LeVan, Ph.D. J. Lawrence Wilson Professor of Engineering Emeritus, Department of Chemical and
Biomolecular Engineering, Vanderbilt University; Member, American Institute of Chemical Engineers, American Chemical
Society, International Adsorption Society (Section Coeditor, Sec. 16, Adsorption and Ion Exchange)
Wenping Li, Ph.D. R&D Director, Agrilectric Research Company; Member, American Filtration and Separations
Society, American Institute of Chemical Engineers (Expression) (Sec. 18, Liquid-Solid Operations and Equipment)
Eugene L. Liening, M.S., P.E. Manufacturing & Engineering Technology Fellow, The Dow Chemical Company
Retired; Fellow, Materials Technology Institute; Registered Professional Metallurgical Engineer (Michigan) (Corrosion Testing)
(Sec. 25, Materials of Construction)
Dirk Link, Ph.D. Chemist, National Energy Technology Laboratory, U.S. Department of Energy (Nonpetroleum Liquid
Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization)
Carl T. Lira, Ph.D. Associate Professor, Department of Chemical and Materials Engineering, Michigan State University;
Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of
Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics)
Peter J. Loftus, D. Phil. Chief Scientist, Primaira LLC, Member, American Society of Mechanical Engineers
(Heat Generation) (Sec. 24, Energy Resources, Conversion, and Utilization)
Michael F. Malone, Ph.D. Professor of Chemical Engineering and Vice-Chancellor for Research and Engagement,
University of Massachusetts—Amherst (Batch Distillation, Enhanced Distillation) (Sec. 13, Distillation)
Paul E. Manning, Ph.D. Director CRA Marketing and Business Development, Haynes International (Nickel Alloys)
(Sec. 25, Materials of Construction)
Chad V. Mashuga, Ph.D., P.E. Assistant Professor of Chemical Engineering, Texas A&M University
(Flammability, Combustion and Flammability Hazards, Explosions, Vapor Cloud Explosions, Boiling-Liquid
Expanding-Vapor Explosions) (Sec. 23, Process Safety)
Paul M. Mathias, Ph.D. Senior Fellow and Technical Director, Fluor Corporation; Fellow, American Institute of
Chemical Engineers (Section Coeditor, Sec. 4, Thermodynamics); (Design of Gas Absorption Systems) (Sec. 14, Equipment
for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation)
Paul McCurdie, B.S. Product Manager-Vacuum Filtration, FLSmidth USA, Inc. (Filtration) (Sec. 18, Liquid-Solid
Operations and Equipment)
James K. McGillicuddy, B.S. Product Specialist, Centrifuges, Andritz Separation Inc.; Member, American Institute of
Chemical Engineers (Centrifuges) (Sec. 18, Liquid-Solid Operations and Equipment)
John D. McKenna, Ph.D. Principal, ETS, Inc.; Member, American Institute of Chemical Engineers, Air and Waste
Management Association (Air Pollution Management of Stationary Sources) (Sec. 22, Waste Management)
Terence P. Mcnulty, Ph.D. President, T. P. McNulty and Associates, Inc.; consultants in mineral processing and
extractive metallurgy; Member, National Academy of Engineering; Member, American Institute of Mining, Metallurgical,
and Petroleum Engineers; Member, Society for Mining, Metallurgy, and Exploration; Member, The Metallurgical Society;
Member Mining and Metallurgical Society of America (Leaching) (Sec. 18, Liquid-Solid Operations and Equipment)
Greg Mehos, Ph.D., P.E. Senior Project Engineer, Jenike & Johanson, Inc. (Bulk Solids Flow and Hopper Design)
(Sec. 21, Solids Processing and Particle Technology)
Georges A. Melhem, Ph.D. President and CEO, IoMosaic; Fellow, American Institute of Chemical Engineers
(Emergency Relief Device Effluent Collection and Handling) (Sec. 23, Process Safety)
Valerie S. Monical, B.S. Fellow, Ascend Performance Materials, Inc. (Phase Separation) (Sec. 14, Equipment for
Distillation, Gas Absorption, Phase Dispersion, and Phase Separation)
xii
COnTRIBUTORS
Ronnie Montgomery Technical Manager, Process Control Systems, IHI Engineering and Construction International
Corporation; Member, Process Industries Practices, Process Controls Function Team; Member, International Society of
Automation (Flow Measurement) (Sec. 10, Transport and Storage of Fluids)
David A. Moore, B.Sc., M.B.A., P.E., C.S.P. President, AcuTech Consulting Group; Member, ASSE, ASIS, NFPA
(Security) (Sec. 23, Process Safety)
Charles G. Moyers, Ph.D. Senior Chemical Engineering Consultant, MATRIC (Mid-Atlantic Technology, Research
and Innovation Center), Charleston, WV; Fellow, American Institute of Chemical Engineers (Crystallization from the Melt)
(Sec. 18, Liquid-Solid Operations and Equipment)
William E. Murphy, Ph.D., P.E. Professor of Mechanical Engineering, University of Kentucky; American Society of
Heating, Refrigerating, and Air-Conditioning Engineers; American Society of Mechanical Engineers; International Institute
of Refrigeration (Air Conditioning) (Sec. 11, Heat-Transfer Equipment)
Edward R. naylor, B.S., M.S. Senior Materials Engineering Associate, AkzoNobel; Certified API 510, 570, 653 and
Fixed Equipment Source Inspector (Section Coeditor, Sec. 25, Materials of Construction)
James J. noble, Ph.D., P.E., Ch.E. [U.K.] Research Affiliate, Department of Chemical Engineering, Massachusetts
Institute of Technology; Fellow, American Institute of Chemical Engineers; Member, New York Academy of Sciences (Heat
Transfer Coeditor, Sec. 5, Heat and Mass Transfer)
W. Roy Penney, Ph.D., P.E. Professor Emeritus, Department of Chemical Engineering, University of Arkansas;
Fellow, American Institute of Chemical Engineers (Gas-in-Liquid Dispersions) (Sec. 14, Equipment for Distillation, Gas
Absorption, Phase Dispersion, and Phase Separation)
Clint Pepper, Ph.D. Director, Lonza; Member, American Institute of Chemical Engineers (Product Attribute Control)
(Sec. 20, Bioreactions and Bioprocessing)
Carmo J. Pereira, Ph.D., M.B.A. DuPont Fellow, E. I. du Pont de Nemours and Company; Fellow, American Institute
of Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors)
Demetri P. Petrides, Ph.D. President, Intelligen, Inc.; Member, American Institute of Chemical Engineers, American
Chemical Society (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing)
Thomas H. Pratt, Ph.D., P.E., C.S.P. Retired; Emeritus Member, NFPA 77 (Static Electricity) (Sec. 23, Process Safety)
Richard W. Prugh, M.S., P.E., C.S.P. Principal Process Safety Consultant, Chilworth Technology, Inc., a Dekra
Company; Fellow, American Institute of Chemical Engineers; Member, National Fire Protection Association (Toxicity)
(Sec. 23, Process Safety)
Massood Ramezan, Ph.D., P.E. Sr. Technical Advisor, KeyLogic Systems, Inc. (Coal Conversion) (Sec. 24, Energy
Resources, Conversion, and Utilization)
George A. Richards, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy
(Natural Gas, Liquefied Petroleum Gas, Other Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization)
John R. Richards, Ph.D. Research Fellow, E. I. du Pont de Nemours and Company (retired); Fellow, American Institute
of Chemical Engineers (Polymerization Reactions) (Sec. 7, Reaction Kinetics)
James A. Ritter, Ph.D. L. M. Weisiger Professor of Engineering and Carolina Distinguished Professor, Department
of Chemical Engineering, University of South Carolina; Member, American Institute of Chemical Engineers, American
Chemical Society, International Adsorption Society (Sorption Equilibrium, Process Cycles, Equipment) (Sec. 16, Adsorption
and Ion Exchange)
Richard L. Rowley, Ph.D. Professor Emeritus of Chemical Engineering, Brigham Young University (Section Coeditor,
Sec. 2, Physical and Chemical Data)
Scott R. Rudge, Ph.D. Chief Operating Officer and Chairman, RMC Pharmaceutical Solutions, Inc.; Adjunct Professor,
Chemical and Biological Engineering, University of Colorado; Vice President, Margaux Biologics, Scientific Advisory Board,
Sundhin Biopharma (Downstream Processing: Primary Recovery and Purification); Member, American Chemical Society,
International Society of Pharmaceutical Engineers, American Association for the Advancement of Science, Parenteral Drug
Association (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing)
Adel F. Sarofim, Sc.D. Deceased; Presidential Professor of Chemical Engineering, Combustion, and Reactors, University
of Utah; Member, American Institute of Chemical Engineers, American Chemical Society, Combustion Institute (Radiation)
(Sec. 5, Heat and Mass Transfer)
David K. Schmalzer, Ph.D., P.E. Argonne National Laboratory (Retired), Member, American Chemical Society,
American Institute of Chemical Engineers (Resources and Reserves, Liquid Petroleum Fuels) (Sec. 24, Energy Resources,
Conversion, and Utilization)
COnTRIBUTORS
xiii
Fred Schoenbrunn, B.S. Director-Sedimentation Products, Member, Society of Metallurgical and Exploration
Engineers of the American Institute of Minting, Metallurgical and Petroleum Engineers; Registered Professional Engineer
(Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment)
A. Frank Seibert, Ph.D., P.E. Technical Manager, Separations Research Program, The University of Texas at Austin;
Fellow, American Institute of Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations
and Equipment)
Yongkoo Seol, Ph.D. Geologist, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas)
(Sec. 24, Energy Resources, Conversion, and Utilization)
Lawrence J. Shadle, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of
Energy (Coke) (Sec. 24, Energy Resources, Conversion, and Utilization)
Robert R. Sharp, P.E., Ph.D. Environmental Consultant; Professor of Environmental Engineering, Manhattan
College; Member, American Water Works Association; Water Environment Federation Section Director (Wastewater
Management) (Sec. 22, Waste Management)
Dushyant Shekhawat, Ph.D., P.E. Chemical Engineer, National Energy Technology Laboratory, U.S. Department
of Energy (Natural Gas, Fuel and Energy Costs) (Sec. 24, Energy Resources, Conversion, and Utilization)
Richard L. Shilling, P.E., B.E.M.E. Senior Engineering Consultant, Heat Transfer Research, Inc.; American Society of
Mechanical Engineers (Section Editor, Sec. 11, Heat-Transfer Equipment)
nicholas S. Siefert, Ph.D., P.E. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of
Energy (Other Solid Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization)
Geoffrey D. Silcox, Ph.D. Professor of Chemical Engineering, University of Utah; Member, American Institute of
Chemical Engineers, American Chemical Society (Heat Transfer Section Coeditor, Sec. 5, Heat and Mass Transfer)
Cecil L. Smith, Ph.D. Principal, Cecil L. Smith Inc. (Batch Process Control, Telemetering and Transmission, Digital
Technology for Process Control, Process Control and Plant Safety) (Sec. 8, Process Control)
(Francis) Lee Smith, Ph.D. Principal, Wilcrest Consulting Associates, LLC, Katy, Texas; Partner and General
Manager, Albutran USA, LLC, Katy, Texas (Front-End Loading, Value-Improving Practices) (Sec. 9, Process Economics);
(Evaporative Cooling) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Energy Recovery)
(Sec. 24, Energy Resources, Conversion, and Utilization)
Joseph D. Smith, Ph.D. Professor of Chemical and Biochemical Engineering, Missouri University of Science and
Technology (Thermal Energy Conversion and Utilization) (Sec. 24, Energy Resources, Conversion, and Utilization)
Daniel J. Soeder, M.S. Director, Energy Resources Initiative, South Dakota School of Mines & Technology
(Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization)
Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas;
Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education (Section
Editor, Sec. 1, Unit Conversion Factors and Symbols); (Section Editor, Sec. 2, Physical and Chemical Data)
Thomas O. Spicer III, Ph.D., P.E. Professor; Maurice E. Barker Chair in Chemical Engineering, Chemical Hazards
Research Center Director, Ralph E. Martin Department of Chemical Engineering, University of Arkansas; Fellow, American
Institute of Chemical Engineers (Atmospheric Dispersion) (Sec. 23, Process Safety)
Jason A. Stamper, M. Eng. Technology Leader, Drying and Particle Processing, The Procter & Gamble Company;
Member, Institute for Liquid Atomization and Spray Systems (Drying Equipment, Fluidized Bed Dryers, Spray Dryers)
(Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying)
Daniel E. Steinmeyer, P.E., M.S. Distinguished Science Fellow, Monsanto Company (retired); Fellow, American
Institute of Chemical Engineers; Member, American Chemical Society (Phase Dispersion, Liquid in Gas Systems)
(Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation)
Gary J. Stiegel, P.E., M.S. Technology Manager (Retired), National Energy Technology Laboratory, U.S. Department
of Energy (Coal Conversion) (Sec. 24, Energy Resources, Conversion, and Utilization)
Angela Summers, Ph.D., P.E. President, SIS-TECH; Adjunct Professor, Department of Environmental Management,
University of Houston–Clear Lake; Fellow, International Society of Automation; Fellow, American Institute of Chemical
Engineers; Fellow, AIChE Center for Chemical Process Safety (Safety Instrumented Systems) (Sec. 23, Process Safety)
Richard C. Sutherlin, B.S., P.E. Richard Sutherlin, PE, Consulting, LLC; Registered Professional Metallurgical
Engineer (Oregon) (Reactive Metals) (Sec. 25, Materials of Construction)
Ross Taylor, Ph.D. Distinguished Professor of Chemical Engineering, Clarkson University (Simulation of
Distillation Processes) (Sec. 13, Distillation)
xiv
COnTRIBUTORS
Louis Theodore, Eng.Sc.D. Consultant, Theodore Tutorials, Professor of Chemical Engineering, Manhattan College;
Member, Air and Waste Management Association (Section Coeditor, Sec. 22, Waste Management)
Susan A. Thorneloe, M.S. U.S. EPA/Office of Research & Development, National Risk Management Research
Laboratory; Member, Air and Waste Management Association, International Waste Working Group (Sec. 22, Waste
Management)
James n. Tilton, Ph.D., P.E. DuPont Fellow, Chemical and Bioprocess Engineering, E. I. du Pont de Nemours &
Co.; Member, American Institute of Chemical Engineers; Registered Professional Engineer (Delaware) (Section Editor,
Sec. 6, Fluid and Particle Dynamics)
Paul W. Todd, Ph.D. Chief Scientist Emeritus, Techshot, Inc.; Member, American Institute of Chemical Engineers
(Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing)
Krista S. Walton, Ph.D. Professor and Robert “Bud” Moeller Faculty Fellow, School of Chemical & Biomolecular
Engineering, Georgia Institute of Technology; Member, American Institute of Chemical Engineers, American Chemical Society,
International Adsorption Society (Adsorbents) (Sec. 16, Adsorption and Ion Exchange)
Phillip C. Wankat, Ph.D. Clifton L. Lovell Distinguished Professor of Chemical Engineering Emeritus, Purdue University;
Member, American Institute of Chemical Engineers (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer)
Kenneth n. Weiss, P.E., BCEE, B.Ch.E, M.B.A. Managing Partner, ERM; Member, Air and Waste Management
Association (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management)
W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow, American Institute
of Chemical Engineers (Section Coeditor, Sec. 2, Physical and Chemical Data)
Ronald J. Willey, Ph.D., P.E. Professor, Department of Chemical Engineering, Northeastern University; Fellow,
American Institute of Chemical Engineers (Case Histories) (Sec. 23, Process Safety)
Todd W. Wisdom, M.S. Director-Separations Technology, FLSmidth USA, Inc.; Member, American Institute of
Chemical Engineers (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment)
John L. Woodward, Ph.D. Senior Principal Consultant, Baker Engineering and Risk Consultants, Inc.; Fellow,
American Institute of Chemical Engineers (Discharge Rates from Punctured Lines and Vessels) (Sec. 23, Process Safety)
Preface to the
ninth Edition
“This handbook is intended to supply both the practicing engineer and the student with an authoritative reference work
that covers comprehensively the field of chemical engineering as well as important related fields.”
—John H. Perry, 1934
Chemical engineering is generally accepted to have had its origin in the United Kingdom (U.K.) during the latter part of
the nineteenth century, largely in response to the industrial revolution and growth in the demand for industrial chemicals.
To answer this demand, chemical companies began to mass-produce their products, which meant moving from batch
processing to continuous operation. New processes and equipment, in turn, called for new methods. Initially, continuous
reactions and processing were implemented largely by plant operators, mechanical engineers, and industrial chemists.
Chemical engineering evolved from this advancement of the chemical industry, creating engineers who were trained in
chemistry as well as the fundamentals of engineering, physics, and thermodynamics.
As an academic discipline, the earliest reported chemical engineering lectures were given in the United Kingdom.
George Davis is generally recognized as the first chemical engineer, lecturing at the Manchester Technical School
(later the University of Manchester) in 1887. The first American chemical engineering courses were taught at MIT in
1888. Davis also proposed an appropriate professional society that evolved with the industrial and academic profession,
ultimately called the Society of Chemical Industry (1881). His initial proposal was for a society of chemical engineers but
the name was changed because so few chemical engineers existed at that time. From there, the American Institute of
Chemical Engineers, AIChE (1908), and the U.K.-origin Institution of Chemical Engineers, IChemE (1922), were created.
As the discipline advanced, important approaches to describing and designing chemical and physical processes
developed. George Davis is credited with an early description of what came to be termed “unit operations,” although he
did not use that specific term. Arthur D. Little coined the phrase in 1908 in a report to the president of MIT and developed
the concept and applications with William H. Walker. Walker later defined “unit operations” in his 1923 seminal textbook
published by McGraw-Hill, Principles of Chemical Engineering, coauthored with Warren K. Lewis and William H. McAdams.
Other concepts developed over time, including chemical reactor engineering, transport phenomena, and use of computers
to enhance mathematical simulation, have increased our ability to understand and design chemical/physical industrial
processes. Chemical engineering concepts and methods have been applied in increasingly diverse fields, including
environmental engineering, pharmaceutical processing, microelectronics, and biological/biosimilar engineering.
The first known handbook of chemical engineering was in two volumes, written by George Davis, and published in the
United Kingdom in 1901. A second edition followed in 1904. The emphasis was on materials and their properties; laboratory
equipment and techniques; steam production and distribution; power and its applications; moving solids, liquids, and
gases; and solids handling. In the preface, Davis acknowledged the advances in industrial chemistry made in Germany,
especially in commercial organic chemistry. He also noted the “severe competition” coming from America “in the ammoniasoda industry.” The first US handbook was edited by Donald M. Liddell and published by McGraw-Hill in 1922. It was a
two-volume book with thirty-one contributing writers. It dealt with many of the same topics as in the Davis handbook, but
also had significantly more emphasis on operations such as leaching, crystallization, evaporation, and drying.
Perry’s Chemical Engineers’ Handbook originated from a decision by McGraw-Hill in 1930 (during the Great Depression)
to develop a new handbook of chemical engineering. Receiving support for the project from DuPont Company, they
selected John H. Perry to be the editor. Perry had earned a Ph.D. from MIT in 1922 in Physical Chemistry and Chemical
Engineering. He subsequently worked for the US Bureau of Mines, next as a chemist for a DuPont subsidiary in Cleveland,
OH, then moved to Wilmington, DE, to work for DuPont as a chemist in the company’s experimental station, and back to
xv
xvi
PREFACE TO THE nInTH EDITIOn
Cleveland, still with DuPont. Family lore says that Perry was a very hard worker, dedicated to chemical engineering, and
willing to basically live two lives: one as a full-time engineer for DuPont and the other as editor of the handbook. On weekends
he would hitchhike to New York, go to the Chemist’s Club with a packet of galley proofs and a carton of cigarettes, and work
all weekend, sometimes for 24 hours at a time. His work on the book extended through 1933, leading to publication of the
first edition in January 1934. There were 63 contributors, 14 from the DuPont Company and 21 from different universities,
all experts in their respective technical areas. The first sentence in the preface was applicable then as well as for this
ninth edition: “This handbook is intended to supply both the practicing engineer and the student with an authoritative
reference work that covers comprehensively the field of chemical engineering as well as important related fields.”
Several chemical engineers, serving as editor or coeditor, have guided the preparation of the different editions over the
years. John H. Perry was editor of the first (1934), second (1941), and third (1950) editions before his untimely death in
1953. The position of editor passed to his only child, Robert H. Perry (Bob), a notable chemical engineer in his own
right. Bob had a Ph.D. in chemical engineering from the University of Delaware and was working in industry at the time
of his father’s death. In 1958, he took a position as professor and later chair of the Department of Chemical Engineering at
the University of Oklahoma. He was the editor of the fourth (1963) edition, coedited with Cecil H. Chilton and assisted by
Sidney D. Kirkpatrick, and the fifth (1973) edition, coedited with Chilton.
For the sixth edition, Bob asked Don W. Green, his first Ph.D. student and now a professor of Chemical and Petroleum
Engineering at the University of Kansas, to assist him. Tragically, Bob Perry’s work on the handbook ceased when he was killed
in an accident south of London in November 1978. Green assumed responsibility as editor and completed the sixth edition
(1984), assisted by a colleague at KU, James O. Maloney. The first five editions were titled The Chemical Engineers’ Handbook.
Beginning with the sixth edition, the book was renamed Perry’s Chemical Engineers’ Handbook in honor of the father and son.
Green was also editor of the seventh (1997) and eighth (2008) editions, with Maloney assisting on the seventh edition. Robert
H. Perry was listed as the “late editor” for the seventh and eighth editions; honoring his ideas that carried over to these recent
editions. To create the ninth edition, Green brought on Marylee Z. Southard, a colleague with industrial, consulting, and academic experience in chemical engineering.
The organization of this ninth edition replicates the logic of the eighth edition, although content changes are extensive.
The first group of sections includes comprehensive tables with unit conversions and fundamental constants, physical and
chemical data, methods to predict properties, and basics of mathematics most useful to engineers. The second group,
comprising the fourth through the ninth sections, covers fundamentals of chemical engineering. The third and largest
group of sections deals with processes, including heat transfer operations, distillation, gas–liquid processes, chemical
reactors, and liquid–liquid processes. The last group of sections covers auxiliary information, including waste management,
safety and handling of hazardous materials, energy sources, and materials of construction.
In 2012, McGraw-Hill launched Access Engineering (ACE), an electronic engineering reference tool for professionals,
academics, and students. This edition of Perry’s Chemical Engineers’ Handbook is a part of ACE, as was the eighth edition.
Beyond the complete text of the handbook, ACE provides:
• Interactive graphs
• Video tutorials for example problems given in the handbook
• Excel spreadsheets to solve guided and user-defined problems in different areas, such as heat transfer or fluid flow
• Curriculum maps for use in complementing engineering course content
All 25 sections have been updated to cover the latest advances in technology related to chemical engineering. Notable
updates and completely new materials include:
• Sec. 2 includes new and updated chemical property data produced by the Design Institute for Physical Properties
(DIPPR) of AIChE
• Sec. 4 on thermodynamics fundamentals has been redesigned to be more practical, and less theoretical than in earlier
editions, to suit the practicing engineer and student pursuing applications
• A new Sec. 20, “Bioreactions and Bioprocessing,” has been added in response to the significant, large-scale growth of
commercial processes for nonfood products since the end of the twentieth century
• Sec. 21 on solids handling operations and equipment has been rewritten by industrial experts in their field
A group of 147 professionals, serving as section editors and contributors, has worked on this ninth edition. Their
names, affiliations, and writing responsibilities are listed herein as part of the front material and on the title page of their
respective sections. These authors are known experts in their field, with many having received professional awards and
named as Fellows of their professional societies.
Since the publication of the eighth edition, we have lost two major contributors to Perry’s Chemical Engineers’ Handbook.
Dr. Adel F. Sarofim died in December 2011. He was a section coeditor/contributor in the radiation subsection from the
fifth edition (1973) through this current ninth edition. Dr. Sarofim, a Professor Emeritus at MIT, was a recognized pioneer
in the development of combustion science and radiation heat transfer. He received numerous U.S. and international prizes
for his work.
Dr. Meherwan P. Boyce died in December 2017. He was the editor for the “Transport and Storage of Fluids” section in
the seventh edition and co-section editor for the eighth and current editions. Dr. Boyce was founder of Boyce Engineering
International. He was also known for his role as the first director of the Turbomachinery Laboratory and founding member
of the Turbomachinery Symposium.
On this 85th anniversary of Perry’s Chemical Engineers’ Handbook, we celebrate the memory of its creators, Dr. John
H. Perry and Dr. Robert H. Perry. Often referred to as “the Bible of Chemical Engineering,” this handbook is the gold
standard as a source of valuable information to innumerable chemical engineers.
We dedicate this ninth edition to chemical engineers who carry on the profession, creating solutions, products, and
processes needed in the challenging world ahead. We hope this edition will provide information and focus for you—to
work for the quality and improvement of human life and the earth we inhabit.
DON W. GREEN
Editor-in-Chief
MARYLEE Z. SOUTHARD
Associate Editor
Section 1
Unit Conversion Factors and Symbols
Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of
Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering
Education
Table 1-1
Table 1-2a
Table 1-2b
Table 1-3
Table 1-4
Table 1-5
UnITS AnD SYMBOLS
Standard SI Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Common Derived Units of SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Derived Units of SI That Have Special Names . . . . . . . . . . . . . . . . . . . .
SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
United States Traditional System of Weights and Measures . . . . . .
1-2
1-2
1-2
1-2
1-2
1-3
Table 1-6
Table 1-7
COnVERSIOn FACTORS
Common Units and Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . .
Alphabetical Listing of Common Unit Conversions . . . . . . . . . . . . . .
1-4
1-5
Table 1-8
Table 1-9
Table 1-10
Table 1-11
Table 1-12
Table 1-13
Table 1-14
Conversion Factors: Commonly Used and Traditional
Units to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Conversion Factors to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Temperature Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Density Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kinematic Viscosity Conversion Formulas. . . . . . . . . . . . . . . . . . . . . . .
Values of the Ideal Gas Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-7
1-15
1-17
1-17
1-17
1-17
1-18
1-1
1-2
UnIT COnVERSIOn FACTORS AnD SYMBOLS
UnITS AnD SYMBOLS
TABLE 1-2b Derived Units of SI That Have Special names
TABLE 1-1 Standard SI Quantities and Units
Quantity or “dimension”
SI unit
SI unit symbol
(“abbreviation”)
Base quantity or “dimension”
m
length
meter
kg
kilogram
mass
s
second
time
A
ampere
electric current
K
kelvin
thermodynamic temperature
mol
mole*
amount of substance
cd
candela
luminous intensity
Supplementary quantity or “dimension”
rad
radian
plane angle
sr
steradian
solid angle
*When the mole is used, the elementary entities must be specified; they may
be atoms, molecules, ions, electrons, other particles, or specified groups of such
particles.
TABLE 1-2a
Common Derived Units of SI
Quantity
Unit
Symbol
acceleration
angular acceleration
angular velocity
area
concentration (mass)
concentration (molar)
current density
density, mass
electric charge density
electric field strength
electric flux density
energy density
entropy
heat capacity
heat flux density, irradiance
luminance
magnetic field strength
molar energy
molar entropy
molar heat capacity
moment of force
permeability
permittivity
radiance
radiant intensity
specific energy
specific entropy
specific heat capacity
specific volume
surface tension
thermal conductivity
velocity
viscosity, dynamic
viscosity, kinematic
volume
wave number
meter per second squared
radian per second squared
radian per second
square meter
kilogram per cubic meter
mole per cubic meter
ampere per square meter
kilogram per cubic meter
coulomb per cubic meter
volt per meter
coulomb per square meter
joule per cubic meter
joule per kelvin
joule per kelvin
watt per square meter
candela per square meter
ampere per meter
joule per mole
joule per mole-kelvin
joule per mole-kelvin
newton-meter
henry per meter
farad per meter
watt per square meter-steradian
watt per steradian
joule per kilogram
joule per kilogram-kelvin
joule per kilogram-kelvin
cubic meter per kilogram
newton per meter
watt per meter-kelvin
meter per second
pascal-second
square meter per second
cubic meter
reciprocal meter
m/s2
rad/s2
rad/s
m2
kg/m3
mol/m3
A/m2
kg/m3
C/m3
V/m
C/m2
J/m3
J/K
J/K
W/m2
cd/m2
A/m
J/mol
J/(mol ⋅ K)
J/(mol ⋅ K)
N⋅m
H/m
F/m
W/(m2 ⋅ sr)
W/sr
J/kg
J/(kg ⋅ K)
J/(kg ⋅ K)
m3/kg
N/m
W/(m ⋅ K)
m/s
Pa ⋅ s
m2/s
m3
1/m
Quantity
absorbed dose
activity (of radionuclides)
capacitance
conductance
electric potential, potential difference,
electromotive force
electric resistance
energy, work, quantity of heat
force
frequency (of a periodic phenomenon)
illuminance
inductance
luminous flux
magnetic flux
magnetic flux density
power, radiant flux
pressure, stress
quantity of electricity, electric charge
Unit
Symbol
gray
becquerel
farad
siemens
volt
Gy
Bq
F
S
V
J/kg
l/s
C/V
A/V
W/A
Formula
ohm
joule
newton
hertz
lux
henry
lumen
weber
tesla
watt
pascal
coulomb
Ω
J
N
Hz
lx
H
lm
Wb
T
W
Pa
C
V/A
N⋅m
(kg ⋅ m)/s2
1/s
lm/m2
Wb/A
Cd ⋅ sr
V⋅s
Wb/m2
J/s
N/m2
A⋅s
TABLE 1-3 SI Prefixes
Multiplication factor
1 000 000 000
1 000 000
1 000
1
000
000
000
000
1
000
000
000
000
000
1
18
000 = 10
000 = 1015
000 = 1012
000 = 109
000 = 106
000 = 103
100 = 102
10 = 101
0.1 = 10-1
0.01 = 10-2
0.001 = 10-3
0.000 001 = 10-6
0.000 000 001 = 10-9
0.000 000 000 001 = 10-12
0.000 000 000 000 001 = 10-15
0.000 000 000 000 000 001 = 10-18
Prefix
Symbol
exa
peta
tera
giga
mega
kilo
hecto*
deka*
deci*
centi
milli
micro
nano
pico
femto
atto
E
P
T
G
M
k
h
da
d
c
m
µ
n
p
f
a
*Generally to be avoided.
TABLE 1-4 Greek Alphabet
alpha = A, α
beta
= B, b
gamma = Γ, γ
delta = Δ, δ
epsilon = Ε, ε
zeta
= Ζ, ζ
eta
= Η, η
theta = Θ, θ
iota
= Ι, ι
kappa = Κ, κ
lambda = Λ, λ
mu
= Μ, µ
nu
xi
omicron
pi
rho
sigma
tau
upsilon
phi
chi
psi
omega
= Ν, ν
= Ξ, ξ
= Ο, ο
= Π, π
= Ρ, ρ
= Σ, σ
= Τ, τ
= Υ, υ
= Φ, φ
= Χ, χ
= Ψ, ψ
= Ω, ω
UnITS AnD SYMBOLS
TABLE 1-5
United States Traditional System of Weights and Measures
Linear Measure
12 inches (in) or (″) = 1 foot ( ft) or (′)
3 feet = 1 yard (yd)
16.5 feet
= 1 rod (rd)
5.5 yards
5280 feet
= 1 mile (mi)
320 rods
1 mil = 0.001 in
Nautical:
6080.2 feet = 1 nautical mile
6 feet = 1 fathom
120 fathoms = 1 cable length
1 knot (kn) = 1 nautical mile per hour
60 nautical miles = 1° of latitude
Square Measure
144 square inches (sq in) or (in2) = 1 sq ft ( ft2)
9 sq ft ( ft2) = 1 sq yd (yd2)
30.25 sq yd = 1 sq rod, pole, or perch
10 sq chains
160 sq rods =
= 1 acre
43.560 sq ft
640 acres = 1 sq mi = 1 section
1 circular in (area of
circle of 1-in diameter) = 0.7854 sq in
1 sq in = 1.2732 circular in
1 circular mil = area of circle of 0.001-in diameter
1,000,000 circular mils = 1 circular in
Circular Measure
60 seconds (″) = 1 minute or (′)
60 minutes (′) = 1 degree (1°)
90 degrees (90°) = 1 quadrant
360 degrees (360°) = 1 circumference
1 radian (rad)
57.29578 degrees =
57 17 ′ 44.81′′
Volume Measure
Solid:
1728 cubic in (cu in) (in3) = 1 cubic foot (cu ft) ( ft3)
27 cu ft = 1 cubic yard (cu yd) (yd3)
Dry Measure:
2 pints = 1 quart
8 quarts = 1 peck
4 pecks = 1 bushel
1 U.S. Winchester bushel = 2150.42 cubic inches (in3)
Liquid:
4 gills = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
7.4805 gallons = 1 cubic foot ( ft3)
Apothecaries’ Liquid:
60 minims (min. or ) = 1 fluid dram or drachm
8 drams ( ) = 1 fluid ounce
16 ounces (oz. ) = 1 pint
Avoirdupois Weight
16 drams = 437.5 grains (gr) = 1 ounce (oz)
16 ounces = 7000 grains = 1 pound (lb)
100 pounds = 1 hundredweight (cwt)
2000 pounds = 1 short ton; 2240 pounds = 1 long ton
Troy Weight
24 grains (gr) = 1 pennyweight (dwt)
20 pennyweights = 1 ounce (oz)
12 ounces = 1 pound (lb)
Apothecaries’ Weight
20 grains (gr) = 1 scruple ( )
3 scruples = 1 dram ( )
8 drams = 1 ounce ( )
12 ounces = 1 pound (lb)
1-3
1-4
UnIT COnVERSIOn FACTORS AnD SYMBOLS
COnVERSIOn FACTORS
TABLE 1-6 Common Units and Conversion Factors*
Mass (M)
Length (L)
Area (L2)
Volume (L3)
Time (θ)
1 pound mass = 453.5924 grams
= 0.45359 kilogram
= 7000 grains
1 slug
= 32.174 pounds mass
1 ton (short) = 2000 pounds mass
1 ton (long) = 2240 pounds mass
1 ton (metric) = 1000 kilograms
= 2204.62 pounds mass
1 pound-mole = 453.59 gram-moles
1 foot
= 30.480 centimeters
= 0.3048 meter
1 inch
= 2.54 centimeters
= 0.0254 meter
1 mile (U.S.) = 1.60935 kilometers
1 yard
= 0.9144 meter
1 square foot = 929.0304 square centimeters
= 0.09290304 square meter
1 square inch = 6.4516 square centimeters
1 square yard = 0.836127 square meter
1 cubic foot = 28,316.85 cubic centimeters
= 0.02831685 cubic meter
= 28.31685 liters
= 7.481 gallons (U.S.)
1 gallon
= 3.7853 liters
= 231 cubic inches
1 hour (h) = 60 minutes (min)
= 3600 seconds (s)
Temperature (T)
1 centigrade or Celsius degree
= 1.8 Fahrenheit degrees
Temperature, Kelvin
= T °C + 273.15
Temperature, Rankine
= T °F + 459.7
Temperature, Fahrenheit
= 9/5 T °C + 32
Temperature, Celsius or centigrade = 5/9 (T °F - 32)
Temperature, Rankine
= 1.8T K
Force (F)
1 pound force = 444,822.2 dynes
= 4.448222 newtons (N)
= 32.174 poundals
2
Pressure (F/L )
Normal atmospheric pressure
note: U.S. Customary units, or British units, on left and SI units on right.
*Adapted from Faust et al., Principles of Unit Operations, John Wiley & Sons, 1980.
1 atm = 760 millimeters of mercury at 0°C
(density 13.5951 g/cm3)
= 29.921 inches of mercury at 32°F
= 14.696 pounds force/square inch
= 33.899 feet of water at 39.1°F
= 1.01325 × 106 dynes/square centimeter
= 1.01325 × 105 newtons/square meter
Density (M/L3)
1 pound mass/cubic foot = 0.01601846 gram/cubic centimeter
= 16.01846 kilograms/cubic meter
Energy (H or FL)
1 British thermal unit = 251.98 calories
= 1054.4 joules
= 777.97 foot-pounds force
= 10.409 liter-atmospheres
= 0.2930 watthour
Diffusivity (L2/θ)
1 square foot/hour = 0.258 cm2/s
= 2.58 × 10-5 m2/s
Viscosity (M/Lθ)
1 pound mass/foot-hour = 0.00413 g/cm s
= 0.000413 kg/m s
1 centipoise (cP)
= 0.01 poise (P)
= 0.01 g/cm s
= 0.001 kg/m s
= 0.000672 lbm/ft s
= 0.0000209 lbf -s/ft2
Thermal conductivity [H/θ L2(T/L)]
1 Btu/h ft2 (°F/ft) = 0.00413 cal/s cm2 (°C/cm)
= 1.728 J/s m2 (°C/m)
Heat transfer coefficient
1 Btu/h ft2 °F = 5.678 J/s m2 °C
Heat capacity (H/MT )
1 Btu/lbm °F = 1 cal/g °C
= 4184 J/kg °C
Gas constant
1.987 Btu/lbm mol °R = 1.987 cal/mol K
= 82.057 atm cm3/mol K
= 0.7302 atm ft3/lbmol °F
= 10.73 (lbf /in2) ( ft3)/lb mol °R
= 1545 (lbf /ft2) ( ft3)/lb mol °R
= 8.314 (N/m2) (m3)/mol K
Gravitational acceleration
g = 9.8066 m/s2
= 32.174 ft/s2
COnVERSIOn FACTORS
1-5
TABLE 1-7 Alphabetical Listing of Common Unit Conversions
To Convert from
acres
acres
acres
acre-feet
ampere-hours (absolute)
angstrom units
angstrom units
angstrom units
atmospheres
atmospheres
atmospheres
atmospheres
atmospheres
atmospheres
atmospheres
atmospheres
bags (cement)
barrels (cement)
barrels (oil)
barrels (oil)
barrels (U.S. liquid)
barrels (U.S. liquid)
barrels per day
bars
bars
bars
board feet
boiler horsepower
boiler horsepower
Btu
Btu
Btu
Btu
Btu
Btu
Btu
Btu
Btu
Btu
Btu per cubic foot
Btu per hour
Btu per minute
Btu per pound
Btu per pound per degree
Fahrenheit
Btu per pound per degree
Fahrenheit
Btu per second
Btu per square foot per hour
Btu per square foot per minute
Btu per square foot per second
for a temperature gradient of
1°F per inch
Btu (60°F) per degree
Fahrenheit
Bushels (U.S. dry)
Bushels (U.S. dry)
calories, gram
calories, gram
calories, gram
calories, gram
calories, gram
calories, gram, per gram
per degree C
To
Multiply by
square feet
square meters
square miles
cubic meters
Coulombs (absolute)
inches
meters
microns or micrometers
millimeters of mercury at 32°F
dynes per square centimeter
newtons per square meter
feet of water at 39.1°F
grams per square centimeter
inches of mercury at 32°F
pounds per square foot
pounds per square inch
pounds (cement)
pounds (cement)
cubic meters
gallons
cubic meters
gallons
gallons per minute
atmospheres
newtons per square meter
pounds per square inch
cubic feet
Btu per hour
kilowatts
calories (gram)
celsius heat units (chu or pcu)
foot-pounds
horsepower-hours
joules
liter-atmospheres
pounds carbon to CO2
pounds water evaporated
from and at 212°F
cubic foot–atmospheres
kilowatt-hours
joules per cubic meter
watts
horsepower
joules per kilogram
calories per gram per degree
celsius
joules per kilogram per degree
kelvin
watts
joules per square meter per
second
kilowatts per square foot
calories, gram (15°C), per
square centimeter per second
for a temperature gradient of
1°C per centimeter
calories per degree Celsius
43,560
4074
0.001563
1233
3600
3.937 × 10-9
1 × 10-10
1 × 10-4
760
1.0133 × 106
101,325
33.90
1033.3
29.921
2116.3
14.696
94
376
0.15899
42
0.11924
31.5
0.02917
0.9869
1 × 105
14.504
1
⁄12
33,480
9.803
252
0.55556
777.9
3.929 × 10-4
1055.1
10.41
6.88 × 10-5
0.001036
cubic feet
cubic meters
Btu
foot-pounds
joules
liter-atmospheres
horsepower-hours
joules per kilogram per kelvin
1.2444
0.03524
3.968 × 10-3
3.087
4.1868
4.130 × 10-2
1.5591 × 10-6
4186.8
0.3676
2.930 × 10-4
37,260
0.29307
0.02357
2326
1
4186.8
1054.4
3.1546
0.1758
1.2405
453.6
To Convert from
To
calories, kilogram
calories, kilogram per second
candle power (spherical)
carats (metric)
centigrade heat units
centimeters
centimeters
centimeters
centimeters
centimeters
centimeters of mercury at 0°C
centimeters of mercury at 0°C
centimeters of mercury at 0°C
centimeters of mercury at 0°C
centimeters of mercury at 0°C
centimeters per second
centimeters of water at 4°C
centistokes
circular mils
circular mils
circular mils
cords
cubic centimeters
cubic centimeters
cubic centimeters
cubic centimeters
cubic feet
cubic feet
cubic feet
cubic feet
cubic feet
cubic feet
cubic foot–atmospheres
cubic foot–atmospheres
cubic feet of water (60°F)
cubic feet per minute
cubic feet per minute
cubic feet per second
cubic feet per second
cubic inches
cubic yards
curies
curies
degrees
drams (apothecaries’ or troy)
drams (avoirdupois)
dynes
ergs
Faradays
fathoms
feet
feet per minute
feet per minute
feet per (second)2
feet of water at 39.2°F
foot-poundals
foot-poundals
foot-poundals
foot-pounds
foot-pounds
foot-pounds
foot-pounds
foot-pounds
foot-pounds
foot-pounds force
foot-pounds per second
foot-pounds per second
furlongs
gallons (U.S. liquid)
kilowatt-hours
kilowatts
lumens
grams
Btu
Angstrom units
feet
inches
meters
microns or micrometers
atmospheres
feet of water at 39.1°F
newtons per square meter
pounds per square foot
pounds per square inch
feet per minute
newtons per square meter
square meters per second
square centimeters
square inches
square mils
cubic feet
cubic feet
gallons
ounces (U.S. fluid)
quarts (U.S. fluid)
Bushels (U.S.)
cubic centimeters
cubic meters
cubic yards
gallons
liters
foot-pounds
liter-atmospheres
pounds
cubic centimeters per second
gallons per second
gallons per minute
million gallons per day
cubic meters
cubic meters
disintegrations per minute
coulombs per minute
radians
grams
grams
newtons
joules
Coulombs (abs.)
feet
meters
centimeters per second
miles per hour
meters per (second)2
newtons per square meter
Btu
joules
liter-atmospheres
Btu
calories, gram
foot-poundals
horsepower-hours
kilowatt-hours
liter-atmospheres
joules
horsepower
kilowatts
miles
barrels (U.S. liquid)
Multiply by
0.0011626
4.185
12.556
0.2
1.8
1 × 108
0.03281
0.3937
0.01
10,000
0.013158
0.4460
1333.2
27.845
0.19337
1.9685
98.064
1 × 10-6
5.067 × 10-6
7.854 × 10-7
0.7854
128
3.532 × 10-5
2.6417 × 10-4
0.03381
0.0010567
0.8036
28,317
0.028317
0.03704
7.481
28.316
2116.3
28.316
62.37
472.0
0.1247
448.8
0.64632
1.6387 × 10-5
0.76456
2.2 × 1012
1.1 × 1012
0.017453
3.888
1.7719
1 × 10-5
1 × 10-7
96,500
6
0.3048
0.5080
0.011364
0.3048
2989
3.995 × 10-5
0.04214
4.159 × 10-4
0.0012856
0.3239
32.174
5.051 × 10-7
3.766 × 10-7
0.013381
1.3558
0.0018182
0.0013558
0.125
0.03175
(Continued )
1-6
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-7 Alphabetical Listing of Common Unit Conversions (Continued )
To Convert from
gallons
gallons
gallons
gallons
gallons
gallons per minute
gallons per minute
grains
grains
grains per cubic foot
grains per gallon
grams
grams
grams
grams
grams
grams
grams per cubic centimeter
grams per cubic centimeter
grams per liter
grams per liter
grams per square centimeter
grams per square centimeter
hectares
hectares
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (British)
horsepower (metric)
horsepower (metric)
hours (mean solar)
inches
inches of mercury at 60°F
inches of water at 60°F
joules (absolute)
joules (absolute)
joules (absolute)
joules (absolute)
joules (absolute)
joules (absolute)
kilocalories
kilograms
kilograms force
kilograms per square
centimeter
kilometers
kilowatt-hours
kilowatt-hours
kilowatts
knots (international)
knots (nautical miles
per hour)
lamberts
liter-atmospheres
liter-atmospheres
liters
liters
liters
lumens
micromicrons
microns
To
Multiply by
cubic meters
cubic feet
gallons (imperial)
liters
ounces (U.S. fluid)
cubic feet per hour
cubic feet per second
grams
pounds
grams per cubic meter
parts per million
drams (avoirdupois)
drams (troy)
grains
kilograms
pounds (avoirdupois)
pounds (troy)
pounds per cubic foot
pounds per gallon
grains per gallon
pounds per cubic foot
pounds per square foot
pounds per square inch
acres
square meters
btu per minute
btu per hour
foot-pounds per minute
foot-pounds per second
watts
horsepower (metric)
pounds carbon to CO2
per hour
pounds water evaporated
per hour at 212°F
foot-pounds per second
kilogram-meters per
second
seconds
meters
newtons per square
meter
newtons per square meter
Btu (mean)
calories, gram (mean)
cubic foot–atmospheres
foot-pounds
kilowatt-hours
liter-atmospheres
joules
pounds (avoirdupois)
newtons
pounds per square inch
0.003785
0.13368
0.8327
3.785
128
8.021
0.002228
0.06480
1
⁄7000
2.2884
17.118
0.5644
0.2572
15.432
0.001
0.0022046
0.002679
62.43
8.345
58.42
0.0624
2.0482
0.014223
2.471
10,000
42.42
2545
33,000
550
745.7
1.0139
0.175
miles
Btu
foot-pounds
horsepower
meters per second
miles per hour
0.6214
3414
2.6552 × 106
1.3410
0.5144
1.1516
candles per square inch
cubic foot–atmospheres
foot-pounds
cubic feet
cubic meters
gallons
watts
microns or micrometers
angstrom units
2.054
0.03532
74.74
0.03532
0.001
0.26418
0.001496
1 × 10-6
1 × 104
2.64
542.47
75.0
3600
0.0254
3376.9
248.84
9.480 × 10-4
0.2389
0.3485
0.7376
2.7778 × 10-7
0.009869
4186.8
2.2046
9.807
14.223
To Convert from
microns
miles (nautical)
miles (nautical)
miles
miles
miles per hour
miles per hour
milliliters
millimeters
millimeters of mercury at 0°C
millimicrons
mils
mils
minims (U.S.)
minutes (angle)
minutes (mean solar)
newtons
ounces (avoirdupois)
ounces (avoirdupois)
ounces (U.S. fluid)
ounces (troy)
pints (U.S. liquid)
poundals
pounds (avoirdupois)
pounds (avoirdupois)
pounds (avoirdupois)
pounds per cubic foot
pounds per cubic foot
pounds per square foot
pounds per square foot
pounds per square inch
pounds per square inch
pounds per square inch
pounds force
pounds force per square foot
pounds water evaporated
from and at 212°F
pound-celsius units (pcu)
quarts (U.S. liquid)
radians
revolutions per minute
seconds (angle)
slugs
slugs
slugs
square centimeters
square feet
square feet per hour
square inches
square inches
square yards
stokes
tons (long)
tons (long)
tons (metric)
tons (metric)
tons (metric)
tons (short)
tons (short)
tons (refrigeration)
tons (British shipping)
tons (U.S. shipping)
torr (mm mercury, 0°C)
watts
watts
watts
watthours
yards
To
Multiply by
meters
feet
miles (U.S. statute)
feet
meters
feet per second
meters per second
cubic centimeters
meters
newtons per square meter
microns
inches
meters
cubic centimeters
radians
seconds
kilograms
kilograms
ounces (troy)
cubic meters
ounces (apothecaries’)
cubic meters
newtons
grains
kilograms
pounds (troy)
grams per cubic centimeter
kilograms per cubic meter
atmospheres
kilograms per square meter
atmospheres
kilograms per square
centimeter
newtons per square meter
newtons
newtons per square meter
horsepower-hours
1 × 10-6
6080
1.1516
5280
1609.3
1.4667
0.4470
1
0.001
133.32
0.001
0.001
2.54 × 10-5
0.06161
2.909 × 10-4
60
0.10197
0.02835
0.9115
2.957 × 10-5
1.000
4.732 × 10-4
0.13826
7000
0.45359
1.2153
0.016018
16.018
4.725 × 10-4
4.882
0.06805
0.07031
Btu
cubic meters
degrees
radians per second
radians
g pounds
kilograms
pounds
square feet
square meters
square meters per second
square centimeters
square meters
square meters
square meters per second
kilograms
pounds
kilograms
pounds
tons (short)
kilograms
pounds
Btu per hour
cubic feet
cubic feet
newtons per square meter
Btu per hour
joules per second
kilogram-meters per second
joules
meters
1.8
9.464 × 10-4
57.30
0.10472
4.848 × 10-6
1
14.594
32.17
0.0010764
0.0929
2.581 × 10-5
6.452
6.452 × 10-4
0.8361
1 × 10-4
1016
2240
1000
2204.6
1.1023
907.18
2000
12,000
42.00
40.00
133.32
3.413
1
0.10197
3600
0.9144
6894.8
4.4482
47.88
0.379
COnVERSIOn FACTORS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units
The following unit symbols are used in the table:
Unit symbol
Name
A
a
Bq
C
cd
Ci
d
°C
°
dyn
F
fc
G
g
gr
Unit symbol
ampere
annum (year)
becquerel
coulomb
candela
curie
day
degree Celsius
degree
dyne
farad
footcandle
gauss
gram
grain
Name
Gy
H
h
ha
Hz
J
K
L, ℓ, l
lm
lx
m
min
′
N
naut mi
Unit symbol
gray
henry
hour
hectare
hertz
joule
kelvin
liter
lumen
lux
meter
minute
minute
newton
U.S. nautical mile
Name
Oe
Ω
Pa
rad
r
S
s
″
sr
St
T
t
V
W
Wb
oersted
ohm
pascal
radian
revolution
siemens
second
second
steradian
stokes
tesla
tonne
volt
watt
weber
note: Copyright SPE-AIME, The SI Metric System of Units and SPE’s Tentative Metric Standard, Society of Petroleum Engineers, Dallas, 1977.
Quantity
Customary or commonly
used unit
SI unit
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Space, time
Length
naut mi
mi
chain
link
fathom
yd
ft
in
in
mil
km
km
m
m
m
m
m
cm
mm
cm
µm
Length/length
ft/mi
m/km
3
1.852*
1.609 344*
2.011 68*
2.011 68*
1.828 8*
9.144*
3.048*
3.048*
2.54*
2.54
2.54*
E + 00
E + 00
E + 01
E - 01
E + 00
E - 01
E - 01
E + 01
E + 01
E + 00
E + 01
1.893 939
E - 01
Length/volume
ft/U.S. gal
ft/ft3
ft/bbl
m/m
m/m3
m/m3
8.051 964
1.076 391
1.917 134
E + 01
E + 01
E + 00
Area
mi2
section
acre
ha
yd2
ft2
in2
km2
ha
ha
m2
m2
m2
mm2
cm2
2.589 988
2.589 988
4.046 856
1.000 000*
8.361 274
9.290 304*
6.451 6*
6.451 6*
E + 00
E + 02
E - 01
E + 04
E - 01
E - 02
E + 02
E + 00
Area/volume
ft2/in3
ft2/ft3
m2/cm3
m2/m3
5.699 291
3.280 840
E - 03
E + 00
Volume
m3
acre ⋅ ft
km3
m3
ha ⋅ m
m3
m3
m3
dm3
m3
dm3
m3
dm3
dm3
dm3
dm3
cm3
cm3
cm3
4.168 182
1.233 482
1.233 482
7.645 549
1.589 873
2.831 685
2.831 685
4.546 092
4.546 092
3.785 412
3.785 412
1.136 523
9.463 529
4.731 765
2.841 307
2.957 353
1.638 706
E + 00
E + 03
E - 01
E + 01
E - 01
E - 02
E + 01
E - 03
E + 00
E - 03
E + 00
E + 00
E - 01
E - 01
E + 01
E + 01
E + 01
yd3
bbl (42 U.S. gal)
ft3
U.K. gal
U.S. gal
U.K. qt
U.S. qt
U.S. pt
U.K. fl oz
U.S. fl oz
in3
L
L
L
L
L
L
Volume/length (linear
displacement)
bbl/in
bbl/ft
ft3/ft
U.S. gal/ft
m3m
m3/m
m3/m
m3/m
L/m
6.259 342
5.216 119
9.290 304*
1.241 933
1.241 933
E + 00
E - 01
E - 02
E - 02
E + 01
Plane angle
rad
deg (°)
min (′)
sec (″)
rad
rad
rad
rad
1
1.745 329
2.908 882
4.848 137
E - 02
E - 04
E - 06
Solid angle
sr
sr
1
*An asterisk indicates that the conversion factor is exact.
(Continued )
1-7
1-8
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Quantity
Time
Customary or commonly
used unit
SI unit
Alternate
SI unit
a
d
s
min
s
h
year
week
h
min
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
1
7.0*
3.6*
6.0*
6.0*
1.666 667
E + 00
E + 03
E + 01
E + 01
E - 02
1.016 047
9.071 847
5.080 234
4.535 924
4.535 924
3.110 348
2.834 952
6.479 891
E + 00
E - 01
E + 01
E + 01
E - 01
E + 01
E + 01
E + 01
4.535 924
4.461 58
1.195 30
E - 01
E - 02
E - 03
2.326 000
2.326 000
6.461 112
4.184*
9.224 141
E - 03
E + 00
E - 04
E + 00
E + 00
4.184*
2.326 000
E + 03
E + 00
2.787 163
2.787 163
7.742 119
2.320 800
2.320 800
6.446 667
3.725 895
3.725 895
1.034 971
4.184*
3.581 692
E - 01
E + 02
E - 02
E - 01
E + 02
E - 02
E - 02
E + 01
E - 02
E + 00
E - 01
E + 03
E + 00
E + 01
E - 02
Mass, amount of substance
Mass
U.K. ton
U.S. ton
U.K. cwt
U.S. cwt
lbm
oz (troy)
oz (av)
gr
Mg
Mg
kg
kg
kg
g
g
mg
Amount of substance
lbmmol
std m3 (0°C, 1 atm)
std ft3 (60°F, 1 atm)
kmol
kmol
kmol
t
t
Enthalpy, calorific value, heat, entropy, heat capacity
cal/g
cal/lbm
MJ/kg
kJ/kg
kWh/kg
kJ/kg
J/kg
Caloric value, enthalpy
(mole basis)
kcal/(g ⋅ mol)
Btu/(lb ⋅ mol)
kJ/kmol
kJ/kmol
Caloric value (volume
basis—solids and liquids)
Btu/U.S. gal
MJ/m3
kJ/m3
kWh/m3
MJ/m3
kJ/m3
kWh/m3
MJ/m3
kJ/m3
kWh/m3
MJ/m3
kJ/m3
kJ/dm3
Caloric value, enthalpy
(mass basis)
Btu/lbm
Btu/U.K. gal
Btu/ft3
cal/mL
( ft ⋅ lbf)/U.S. gal
J/g
J/g
kJ/dm3
kJ/dm3
Caloric value (volume
basis—gases)
cal/mL
kcal/m3
Btu/ft3
kJ/m3
kJ/m3
kJ/m3
kWh/m3
J/dm3
J/dm3
J/dm3
Specific entropy
Btu/(lbm ⋅ °R)
cal/(g ⋅ K)
kcal/(kg ⋅ °C)
kJ/(kg ⋅ K)
kJ/(kg ⋅ K)
kJ/(kg ⋅ K)
J/(g ⋅ K)
J/(g ⋅ K)
J/(g ⋅ K)
4.184*
4.184*
3.725 895
1.034 971
4.186 8*
4.184*
4.184*
Specific heat capacity (mass basis)
kWh/(kg ⋅ °C)
Btu/(lbm ⋅ °F)
kcal/(kg ⋅ °C)
kJ/(kg ⋅ K)
kJ/(kg ⋅ K)
kJ/(kg ⋅ K)
J/(g ⋅ K)
J/(g ⋅ K)
J/(g ⋅ K)
3.6*
4.186 8*
4.184*
E + 03
E + 00
E + 00
Specific heat capacity (mole basis)
Btu/(lb ⋅ mol ⋅ °F)
cal/(g ⋅ mol ⋅ °C)
kJ/(kmol ⋅ K)
kJ/(kmol ⋅ K)
4.186 8*
4.184*
E + 00
E + 00
E + 00
E + 00
E + 00
Temperature, pressure, vacuum
Temperature (absolute)
°R
K
K
K
5/9
1
Temperature (traditional)
°F
°C
5/9(°F + 32)
Temperature (difference)
°F
K, °C
5/9
Pressure
atm (760 mmHg at 0°C or
14,696 psi)
MPa
kPa
bar
MPa
kPa
MPa
kPa
bar
kPa
kPa
kPa
kPa
kPa
Pa
Pa
Pa
1.013 250*
1.013 250*
1.013 250*
1.0*
1.0*
6.894 757
6.894 757
6.894 757
3.376 85
2.488 4
1.333 224
9.806 38
4.788 026
1.333 224
1.0*
1.0*
bar
mmHg (0°C) = torr
µmHg (0°C)
µ bar
mmHg = torr (0°C)
cmH2O (4°C)
lbf /ft2 (psf)
mHg (0°C)
bar
dyn/cm2
*An asterisk indicates that the conversion factor is exact.
E - 01
E + 02
E + 00
E + 01
E + 02
E - 03
E + 00
E - 02
E + 00
E - 01
E - 01
E - 02
E - 02
E - 01
E + 05
E - 01
COnVERSIOn FACTORS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Customary or commonly
used unit
SI unit
Vacuum, draft
inHg (60°F)
inH2O (39.2°F)
inH2O (60°F)
mmHg (0°C) = torr
cmH2O (4°C)
kPa
kPa
kPa
kPa
kPa
3.376 85
2.490 82
2.488 4
1.333 224
9.806 38
E + 00
E - 01
E - 01
E - 01
E -02
Liquid head
ft
in
m
mm
cm
3.048*
2.54*
2.54*
E - 01
E + 01
E + 00
psi/ft
kPa/m
2.262 059
E + 01
kg/m3
g/m3
kg/m3
g/cm3
kg/m3
kg/m3
g/cm3
kg/m3
kg/m3
1.601 846
1.601 846
1.198 264
1.198 264
9.977 633
1.601 846
1.601 846
1.0*
1.601 846
E + 01
E + 04
E + 02
E - 01
E + 01
E + 01
E - 02
E + 03
E + 01
ft /lbm
U.K. gal/lbm
U.S. gal/lbm
m3/kg
m3/g
dm3/kg
dm3/kg
dm3/kg
6.242 796
6.242 796
6.242 796
1.002 242
8.345 404
E - 02
E - 05
E + 01
E + 01
E + 00
Specific volume (mole basis)
L/(gmol)
ft3/(lbmol)
m3/kmol
m3/kmol
1
6.242 796
E - 02
Specific volume
bbl/U.S. ton
bbl/U.K. ton
m3/t
m3/t
1.752 535
1.564 763
E - 01
E - 01
Yield
bbl/U.S. ton
bbl/U.K. ton
U.S. gal/U.S. ton
U.S. gal/U.K. ton
dm3/t
dm3/t
dm3/t
dm3/t
1.752 535
1.564 763
4.172 702
3.725 627
E + 02
E + 02
E + 00
E + 00
Concentration (mass/mass)
wt %
wt ppm
kg/kg
g/kg
mg/kg
1.0*
1.0*
1
E - 02
E + 01
lbm/bbl
g/U.S. gal
g/U.K. gal
lbm/1000 U.S. gal
lbm/1000 U.K. gal
gr/U.S. gal
gr/ft3
lbm/1000 bbl
mg/U.S. gal
gr/100 ft3
kg/m3
kg/m3
kg/m3
g/m3
g/m3
g/m3
mg/m3
g/m3
g/m3
mg/m3
2.853 010
2.641 720
2.199 692
1.198 264
9.977 633
1.711 806
2.288 351
2.853 010
2.641 720
2.288 351
E + 00
E - 01
E - 01
E + 02
E + 01
E + 01
E + 03
E + 00
E - 01
E + 01
ft3/ft3
bbl/(acreft)
vol %
U.K. gal/ft3
U.S. gal/ft3
mL/U.S. gal
mL/U.K. gal
vol ppm
U.K. gal/1000 bbl
U.S. gal/1000 bbl
U.K. pt/1000 bbl
m3/m3
m3/m3
m3/m3
dm3/m3
dm3/m3
dm3/m3
dm3/m3
cm3/m3
dm3/m3
cm3/m3
cm3/m3
cm3/m3
Concentration (mole/volume)
(lbmol)/U.S. gal
(lbmol)/U.K. gal
(lbmol)/ft3
std ft3 (60°F, 1 atm)/bbl
kmol/m3
kmol/m3
kmol/m3
kmol/m3
Concentration (volume/mole)
U.S. gal/1000 std ft3
(60°F/60°F)
bbl/million std ft3
(60°F/60°F)
dm3/kmol
Quantity
Pressure drop/length
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Density, specific volume, concentration, dosage
Density
lbm/ft3
lbm/U.S. gal
lbm/U.K. gal
lbm/ft3
g/cm3
lbm/ft3
Specific volume
ft3/lbm
3
Concentration (mass/volume)
Concentration (volume/volume)
*An asterisk indicates that the conversion factor is exact.
3
dm /kmol
cm3/g
cm3/g
L/t
L/t
L/t
L/t
g/dm3
g/L
mg/dm3
mg/dm3
mg/dm3
mg/dm3
mg/dm3
3
L/m
L/m3
L/m3
L/m3
L/m3
1
1.288 931
1.0*
1.605 437
1.336 806
2.641 720
2.199 692
1
1.0*
2.859 403
2.380 952
3.574 253
E - 04
E - 02
E + 02
E + 02
E - 01
E - 01
E - 03
E + 01
E + 01
E + 00
1.198 264
9.977 644
1.601 846
7.518 21
E + 02
E + 01
E + 01
E - 03
L/kmol
3.166 91
E + 00
L/kmol
1.330 10
E - 01
(Continued )
1-9
1-10
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Quantity
Customary or commonly
used unit
SI unit
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Facility throughput, capacity
Throughput (mass basis)
U.K. ton/yr
U.S. ton/yr
U.K. ton/day
U.S. ton/day
U.K. ton/h
U.S. ton/h
lbm/h
Throughput (volume basis)
bbl/day
ft3/day
bbl/h
ft3/h
U.K. gal/h
U.S. gal/h
U.K. gal/min
U.S. gal/min
t/a
t/a
t/d
t/h
t/d
t/h
t/h
t/h
kg/h
1.016 047
9.071 847
1.016 047
4.233 529
9.071 847
3.779 936
1.016 047
9.071 847
4.535 924
E + 00
E - 01
E + 00
E - 02
E - 01
E - 02
E + 00
E - 01
E - 01
t/a
m3/d
m3/h
m3/h
m3/h
m3/h
L/s
m3/h
L/s
m3/h
L/s
m3/h
L/s
5.803 036
1.589 873
1.179 869
1.589 873
2.831 685
4.546 092
1.262 803
3.785 412
1.051 503
2.727 655
7.576 819
2.271 247
6.309 020
E + 01
E - 01
E - 03
E - 01
E - 02
E - 03
E - 03
E - 03
E - 03
E - 01
E - 02
E - 01
E - 02
kmol/h
kmol/s
4.535 924
1.259 979
E - 01
E - 04
Throughput (mole basis)
(lbmmol)/h
Flow rate (mass basis)
U.K. ton/min
U.S. ton/min
U.K. ton/h
U.S. ton/h
U.K. ton/day
U.S. ton/day
million lbm/yr
U.K. ton/yr
U.S. ton/yr
lbm/s
lbm/min
lbm/h
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
kg/s
1.693 412
1.511 974
2.822 353
2.519 958
1.175 980
1.049 982
5.249 912
3.221 864
2.876 664
4.535 924
7.559 873
1.259 979
E + 01
E + 01
E - 01
E - 01
E - 02
E - 02
E + 00
E - 05
E - 05
E - 01
E - 03
E - 04
Flow rate (volume basis)
bbl/day
U.K. gal/h
U.S. gal/h
U.K. gal/min
U.S. gal/min
ft3/min
ft3/s
m3/d
L/s
m3/d
L/s
m3/s
L/s
m3/s
L/s
dm3/s
dm3/s
dm3/s
dm3/s
dm3/s
dm3/s
1.589 873
1.840 131
2.831 685
3.277 413
4.416 314
4.416 314
7.865 791
7.865 791
1.262 803
1.051 503
7.576 820
6.309 020
4.719 474
2.831 685
E - 01
E - 03
E - 02
E - 04
E - 05
E - 02
E - 06
E - 03
E - 03
E - 03
E - 02
E - 02
E - 01
E + 01
Flow rate (mole basis)
(lbmol)/s
(lbmol)/h
million scf/D
kmol/s
kmol/s
kmol/s
4.535 924
1.259 979
1.383 45
E - 01
E - 04
E - 02
Flow rate/length (mass basis)
lbm/(sft)
lbm/(hft)
kg/(sm)
kg/(sm)
1.488 164
4.133 789
E + 00
E - 04
Flow rate/length (volume basis)
U.K. gal/(min ⋅ ft)
U.S. gal/(min ⋅ ft)
U.K. gal/(h ⋅ in)
U.S. gal/(h ⋅ in)
U.K. gal/(h ⋅ ft)
U.S. gal/(h ⋅ ft)
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
2.485 833
2.069 888
4.971 667
4.139 776
4.143 055
3.449 814
E - 04
E - 04
E - 05
E - 05
E - 06
E - 06
Flow rate/area (mass basis)
lbm/(s ⋅ ft2)
lbm/(h ⋅ ft2)
kg/(s ⋅ m2)
kg/(s ⋅ m2)
4.882 428
1.356 230
E + 00
E - 03
Flow rate/area (volume basis)
ft3/(s ⋅ ft2)
ft3/(min ⋅ ft2)
U.K. gal/(h ⋅ in2)
U.S. gal/(h ⋅ in2)
U.K. gal/(min ⋅ ft2)
U.S. gal/(min ⋅ ft2)
U.K. gal/(h ⋅ ft2)
U.S. gal/(h ⋅ ft2)
m/s
m/s
m/s
m/s
m/s
m/s
m/s
m/s
3.048*
5.08*
1.957 349
1.629 833
8.155 621
6.790 972
1.359 270
1.131 829
E - 01
E - 03
E - 03
E - 03
E - 04
E - 04
E - 05
E - 05
Flow rate
3
ft /day
bbl/h
ft3/h
*An asterisk indicates that the conversion factor is exact.
L/s
L/s
L/s
L/s
L/s
L/s
m3/(s ⋅ m)
m3/(s ⋅ m)
m3/(s ⋅ m)
m3/(s ⋅ m)
m3/(s ⋅ m)
m3/(s ⋅ m)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
m3/(s ⋅ m2)
COnVERSIOn FACTORS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Quantity
Customary or commonly
used unit
SI unit
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Energy, work, power
kcal
cal
ft ⋅ lbf
lbf ⋅ ft
J
(lbf ⋅ ft2)/s2
erg
MJ
kJ
kWh
MJ
MJ
kJ
kWh
MJ
kJ
kWh
MJ
kJ
kJ
kWh
kJ
kWh
kJ
kJ
kJ
kJ
kJ
kJ
J
1.055 056
1.055 056
2.930 711
1.431 744
2.684 520
2.684 520
7.456 999
2.647 780
2.647 780
7.354 999
3.6*
3.6*
1.899 101
5.275 280
1.055 056
2.930 711
4.184*
4.184*
1.355 818
1.355 818
1.0*
4.214 011
1.0*
E + 02
E + 05
E + 01
E + 01
E + 00
E + 03
E - 01
E + 00
E + 03
E - 01
E + 00
E + 03
E + 00
E - 04
E + 00
E - 04
E + 00
E - 03
E - 03
E - 03
E - 03
E - 05
E - 07
Impact energy
kgf ⋅ m
lbf ⋅ ft
J
J
9.806 650*
1.355 818
E + 00
E + 00
Surface energy
erg/cm2
mJ/m2
1.0*
E + 00
J/cm2
J/cm2
9.806 650*
2.101 522
E - 02
E - 03
Energy, work
therm
U.S. tonf ⋅ mi
hp ⋅ h
ch ⋅ h or CV ⋅ h
kWh
Chu
Btu
Specific-impact energy
(kgf ⋅ m)/cm
(lbf ⋅ ft)/in2
Power
million Btu/h
tons of refrigeration
Btu/s
kW
hydraulic horsepower (hhp)
hp (electric)
hp [(550 ft ⋅ lbf)/s]
ch or CV
Btu/min
( ft ⋅ lbf)/s
kcal/h
Btu/h
( ft ⋅ lbf)/min
MW
kW
kW
kW
kW
kW
kW
kW
kW
kW
W
W
W
2.930 711
3.516 853
1.055 056
1
7.460 43
7.46*
7.456 999
7.354 999
1.758 427
1.355 818
1.162 222
2.930 711
2.259 697
E - 01
E + 00
E + 00
Power/area
Btu/(s ⋅ ft2)
cal/(h ⋅ cm2)
Btu/(h ⋅ ft2)
kW/m2
kW/m2
kW/m2
1.135 653
1.162 222
3.154 591
E + 01
E - 02
E - 03
Heat-release rate, mixing power
hp/ft3
cal/(h ⋅ cm3)
Btu/(s ⋅ ft3)
Btu/(h ⋅ ft3)
kW/m3
kW/m3
kW/m3
kW/m3
2.633 414
1.162 222
3.725 895
1.034 971
E + 01
E + 00
E + 01
E - 02
Cooling duty (machinery)
Btu/(bhp ⋅ h)
W/kW
3.930 148
E - 01
Specific fuel consumption (mass
basis)
lbm/(hp ⋅ h)
mg/J
kg/kWh
kg/MJ
1.689 659
6.082 774
E - 01
E - 01
Specific fuel consumption (volume
basis)
m3/kWh
U.S. gal/(hp ⋅ h)
U.K. pt/(hp ⋅ h)
dm3/MJ
dm3/MJ
dm3/MJ
mm3/J
mm3/J
mm3/J
2.777 778
1.410 089
2.116 806
E + 02
E + 00
E - 01
Fuel consumption
U.K. gal/mi
U.S. gal/mi
mi/U.S. gal
mi/U.K. gal
dm3/100 km
dm3/100 km
km/dm3
km/dm3
L/100 km
L/100 km
km/L
km/L
2.824 807
2.352 146
4.251 437
3.540 064
E + 02
E + 02
E - 01
E - 01
Velocity (linear), speed
knot
mi/h
ft/s
km/h
km/h
m/s
cm/s
m/s
mm/s
mm/s
m/d
mm/s
mm/s
1.852*
1.609 344*
3.048*
3.048*
5.08*
8.466 667
3.527 778
3.048*
2.54*
4.233 333
E + 00
E + 00
E - 01
E + 01
E - 03
E - 02
E - 03
E - 01
E + 01
E - 01
ft/min
ft/h
ft/day
in/s
in/min
*An asterisk indicates that the conversion factor is exact.
2
E - 01
E - 01
E - 01
E - 01
E - 02
E - 03
E + 00
E - 01
E - 02
(Continued )
1-11
1-12
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Customary or commonly
used unit
SI unit
Corrosion rate
in/yr (ipy)
mil/yr
mm/a
mm/a
2.54*
2.54*
E + 01
E - 02
Rotational frequency
r/min
r/s
rad/s
1.666 667
1.047 198
E + 02
E - 01
Acceleration (linear)
ft/s2
m/s2
cm/s2
3.048*
3.048*
E - 01
E + 01
Acceleration (rotational)
rpm/s
rad/s2
1.047 198
E - 01
Momentum
(lbm ⋅ ft)/s
(kg ⋅ m)/s
1.382 550
E - 01
Force
U.K. tonf
U.S. tonf
kgf
lbf
dyn
kN
kN
N
N
mN
9.964 016
8.896 443
9.806 650*
4.448 222
1.0
E + 00
E + 00
E + 00
E + 00
E - 02
Bending moment, torque
U.S. tonf ⋅ ft
kgf ⋅ m
lbf ⋅ ft
lbf ⋅ in
kN ⋅ m
N⋅m
N⋅m
N⋅m
2.711 636
9.806 650*
1.355 818
1.129 848
E + 00
E + 00
E + 00
E - 01
Bending moment/length
(lbf ⋅ ft)/in
(lbf ⋅ in)/in
(N ⋅ m)/m
(N ⋅ m)/m
5.337 866
4.448 222
E + 01
E + 00
Moment of inertia
lbm ⋅ ft2
kg ⋅ m2
4.214 011
E - 02
Stress
U.S. tonf/in2
kgf/mm2
U.S. tonf/ft2
lbf/in2 (psi)
lbf/ft2 (psf)
dyn/cm2
MPa
MPa
MPa
MPa
kPa
Pa
1.378 951
9.806 650*
9.576 052
6.894 757
4.788 026
1.0*
E + 01
E + 00
E - 02
E - 03
E - 02
E - 01
Quantity
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
N/mm2
N/mm2
N/mm2
N/mm2
Mass/length
lbm/ft
kg/m
1.488 164
E + 00
Mass/area structural loading,
bearing capacity (mass basis)
U.S. ton/ft2
lbm/ft2
Mg/m2
kg/m2
9.764 855
4.882 428
E + 00
E + 00
Diffusivity
ft2/s
m2/s
ft2/h
m2/s
mm2/s
m2/s
9.290 304*
1.0*
2.580 64*
E - 02
E + 06
E - 05
Thermal resistance
(°C ⋅ m2 ⋅ h)/kcal
(°F ⋅ ft2 ⋅ h)/Btu
(K ⋅ m2)/kW
(K ⋅ m2)/kW
8.604 208
1.761 102
E + 02
E + 02
Heat flux
Btu/(h ⋅ ft2)
kW/m2
3.154 591
E - 03
W/(m ⋅ K)
W/(m ⋅ K)
(kJ ⋅ m)/(h ⋅ m2 ⋅ K)
W/(m ⋅ K)
W/(m ⋅ K)
W/(m ⋅ K)
4.184*
1.730 735
6.230 646
1.162 222
1.442 279
1.162 222
E + 02
E + 00
E + 00
E + 00
E - 01
E - 01
Btu/(h ⋅ ft2 ⋅ °R)
kcal/(h ⋅ m2 ⋅ °C)
kW/(m2 ⋅ K)
kW/(m2 ⋅ K)
kW/(m2 ⋅ K)
kW/(m2 ⋅ K)
kJ/(h ⋅ m2 ⋅ K)
kW/(m2 ⋅ K)
kW/(m2 ⋅ K)
4.184*
2.044 175
1.162 222
5.678 263
2.044 175
5.678 263
1.162 222
E + 01
E + 01
E - 02
E - 03
E + 01
E - 03
E - 03
Volumetric heat-transfer
coefficient
Btu/(s ⋅ ft3 ⋅ °F)
Btu/(h ⋅ ft3 ⋅ °F)
kW/(m3 ⋅ K)
kW/(m3 ⋅ K)
6.706 611
1.862 947
E + 01
E - 02
Surface tension
dyn/cm
mN/m
Miscellaneous transport properties
Thermal conductivity
2
(cal ⋅ cm)/(s ⋅ cm ⋅ °C)
(Btu ⋅ ft)/(h ⋅ ft2 ⋅ °F)
(kcal ⋅ m)/(h ⋅ m2 ⋅ °C)
(Btu ⋅ in)/(h ⋅ ft2 ⋅ °F)
(cal ⋅ cm)/(h ⋅ cm2 ⋅ °C)
Heat-transfer coefficient
Viscosity (dynamic)
cal/(s ⋅ cm2 ⋅ °C)
Btu/(s ⋅ ft2 ⋅ °F)
cal/(h ⋅ cm2 ⋅ °C)
Btu/(h ⋅ ft2 ⋅ °F)
2
(lbf ⋅ s)/in
(lbf ⋅ s)/ft2
(kgf ⋅ s)/m2
lbm/( ft ⋅ s)
(dyn ⋅ s)/cm2
cP
lbm/( ft ⋅ h)
*An asterisk indicates that the conversion factor is exact.
Pa ⋅ s
Pa ⋅ s
Pa ⋅ s
Pa ⋅ s
Pa ⋅ s
Pa ⋅ s
Pa ⋅ s
1
2
(N ⋅ s)/m
(N ⋅ s)/m2
(N ⋅ s)/m2
(N ⋅ s)/m2
(N ⋅ s)/m2
(N ⋅ s)/m2
(N ⋅ s)/m2
6.894 757
4.788 026
9.806 650*
1.488 164
1.0*
1.0*
4.133 789
E + 03
E + 01
E + 00
E + 00
E - 01
E - 03
E - 04
COnVERSIOn FACTORS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Customary or commonly
used unit
SI unit
Viscosity (kinematic)
ft2/s
in2/s
m2/h
ft2/h
cSt
m2/s
mm2/s
mm2/s
m2/s
mm2/s
9.290 304*
6.451 6*
2.777 778
2.580 64*
1
E - 02
E + 02
E + 02
E - 05
Permeability
darcy
millidarcy
µm2
µm2
9.869 233
9.869 233
E - 01
E - 04
Thermal flux
Btu/(h ⋅ ft2)
Btu/(s ⋅ ft2)
cal/(s ⋅ cm2)
W/m2
W/m2
W/m2
3.152
1.135
4.184
E + 00
E + 04
E + 04
Mass-transfer coefficient
(lbmol)/[h ⋅ ft2(lbmol/ft3)]
(gmol)/[s ⋅ m2(gmol/L)]
m/s
m/s
8.467
1.0
E - 05
E + 01
Quantity
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Electricity, magnetism
Admittance
S
S
1
Capacitance
µF
µF
1
Charge density
C/mm3
C/mm3
1
Conductance
S
S
S
1
1
(mho)
Ω
Conductivity
S/m
/m
m /m
S/m
S/m
mS/m
1
1
1
Current density
A/mm2
A/mm2
1
1
Ω
Ω
2
Displacement
C/cm
C/cm2
Electric charge
C
C
1
Electric current
A
A
1
Electric-dipole moment
C⋅m
C⋅m
1
Electric-field strength
V/m
V/m
1
Electric flux
C
C
1
Electric polarization
C/cm2
C/cm2
1
Electric potential
V
mV
V
mV
1
1
Electromagnetic moment
A ⋅ m2
A ⋅ m2
1
Electromotive force
V
V
1
Flux of displacement
C
C
1
Frequency
cycles/s
Hz
1
Impedance
Ω
Ω
1
Linear-current density
A/mm
A/mm
1
Magnetic-dipole moment
Wb ⋅ m
Wb ⋅ m
1
Magnetic-field strength
A/mm
Oe
gamma
A/mm
A/m
A/m
1
7.957 747
7.957 747
Magnetic flux
mWb
mWb
1
Magnetic-flux density
mT
G
gamma
mT
T
nT
1
1.0*
1
Magnetic induction
mT
mT
1
Magnetic moment
A ⋅ m2
A ⋅ m2
1
Magnetic polarization
mT
mT
1
Magnetic potential difference
A
A
1
Magnetic-vector potential
Wb/mm
Wb/mm
1
Magnetization
A/mm
A/mm
1
Modulus of admittance
S
S
1
*An asterisk indicates that the conversion factor is exact.
E + 01
E + 04
E - 04
(Continued )
1-13
1-14
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued )
Customary or commonly
used unit
SI unit
Modulus of impedance
Ω
Ω
1
Mutual inductance
H
H
1
Permeability
µH/m
µH/m
1
Permeance
H
H
1
Permittivity
µF/m
µF/m
1
Potential difference
V
V
1
Quantity
Alternate
SI unit
Conversion factor;
multiply
customary unit by
factor to
obtain SI unit
Quantity of electricity
C
C
1
Reactance
Ω
Ω
1
Reluctance
H-1
H-1
1
Resistance
Ω
Ω
1
Resistivity
Ω ⋅ cm
Ω⋅m
Ω ⋅ cm
Ω⋅m
1
1
Self-inductance
mH
mH
1
Surface density of change
mC/m2
mC/m2
1
Susceptance
S
S
1
Volume density of charge
C/mm3
C/mm3
1
Absorbed dose
rad
Gy
1.0*
Acoustical energy
J
J
1
Acoustical intensity
W/cm2
W/m2
1.0*
Acoustical power
W
W
1
Sound pressure
N/m2
N/m2
1.0*
Illuminance
fc
lx
1.076 391
E + 01
Illumination
fc
lx
1.076 391
E + 01
Acoustics, light, radiation
2
2
Irradiance
W/m
W/m
1
Light exposure
fc ⋅ s
lx ⋅ s
1.076 391
Luminance
cd/m2
cd/m2
1
Luminous efficacy
lm/W
lm/W
1
2
2
E - 02
E + 04
E + 01
Luminous exitance
lm/m
lm/m
1
Luminous flux
lm
lm
1
Luminous intensity
cd
cd
1
Radiance
W/m2 ⋅ sr
W/m2 ⋅ sr
1
Radiant energy
J
J
1
Radiant flux
W
W
1
Radiant intensity
W/sr
W/sr
1
Radiant power
W
W
1
Wavelength
Å
nm
1.0*
E - 01
Capture unit
10 cm
m
E + 01
m
m
1.0*
1
1
Ci
Bq
3.7*
E + 10
-3
-1
Radioactivity
*An asterisk indicates that the conversion factor is exact.
-1
-1
-1
10-3 cm-1
COnVERSIOn FACTORS
TABLE 1-9 Other Conversion Factors to SI Units
The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m.
To Convert from
abampere
abcoulomb
abfarad
abhenry
abmho
abohm
abvolt
acre
ampere (international of
1948)
angstrom
are
astronomical unit
atmosphere
bar
barn
barrel (petroleum 42 gal)
barye
British thermal unit
(ISO/TC 12)
British thermal unit
(International Steam Table)
British thermal unit (mean)
British thermal unit
(thermochemical)
British thermal unit (39°F)
British thermal unit (60°F)
bushel (U.S.)
cable
caliber
calorie (International Steam Table)
calorie (mean)
calorie (thermochemical)
calorie (15°C)
calorie (20°C)
calorie (kilogram,
International Steam Table)
calorie (kilogram, mean)
calorie (kilogram,
thermochemical)
carat (metric)
Celsius (temperature)
centimeter of mercury (0°C)
centimeter of water (4°C)
chain (engineer’s)
chain (surveyor’s or
Gunter’s)
circular mil
cord
coulomb (international of
1948)
cubit
cup
curie
day (mean solar)
day (sidereal)
degree (angle)
denier (international)
dram (avoirdupois)
dram (troy or apothecary)
dram (U.S. fluid)
dyne
electron volt
erg
Fahrenheit (temperature)
Fahrenheit (temperature)
farad (international of 1948)
faraday (based on carbon 12)
faraday (chemical)
faraday (physical)
fathom
fermi ( femtometer)
fluid ounce (U.S.)
foot
To
Multiply by
ampere
coulomb
farad
henry
mho
ohm
volt
meter2
ampere
+01 1.00
+01 1.00
+09 1.00
-09 1.00
+09 1.00
-09 1.00
-08 1.00
+03 4.046 856
-01 9.998 35
meter
meter2
meter
newton/meter2
newton/meter2
meter2
meter3
newton/meter2
joule
-10 1.00
+02 1.00
+11 1.495 978
+05 1.013 25
+05 1.00
-28 1.00
-01 1.589 873
-01 1.00
+03 1.055 06
joule
+03 1.055 04
joule
joule
+03 1.055 87
+03 1.054 350
joule
joule
meter3
meter
meter
joule
joule
joule
joule
joule
joule
+03 1.059 67
+03 1.054 68
-02 3.523 907
+02 2.194 56
-04 2.54
+00 4.1868
+00 4.190 02
+00 4.184
+00 4.185 80
+00 4.181 90
+03 4.186 8
joule
joule
+03 4.190 02
+03 4.184
kilogram
kelvin
newton/meter2
newton/meter2
meter
meter
-04 2.00
tK = tC + 273.15
+03 1.333 22
+01 9.806 38
+01 3.048
+01 2.011 68
meter2
meter3
coulomb
-10 5.067 074
+00 3.624 556
-01 9.998 35
meter
meter3
disintegration/second
second (mean solar)
second (mean solar)
radian
kilogram/meter
kilogram
kilogram
meter3
newton
joule
joule
kelvin
Celsius
farad
coulomb
coulomb
coulomb
meter
meter
meter3
meter
-01 4.572
-04 2.365 882
+10 3.70
+04 8.64
+04 8.616 409
-02 1.745 329
-07 1.111 111
-03 1.771 845
-03 3.887 934
-06 3.696 691
-05 1.00
-19 1.602 10
-07 1.00
tK = (5/9)(tF + 459.67)
tC = (5/9)(tF - 32)
-01 9.995 05
+04 9.648 70
+04 9.649 57
+04 9.652 19
+00 1.828 8
-15 1.00
-05 2.957 352
-01 3.048
To Convert from
foot (U.S. survey)
foot of water (39.2°F)
footcandle
footlambert
furlong
galileo
gallon (U.K. liquid)
gallon (U.S. dry)
gallon (U.S. liquid)
gamma
gauss
gilbert
gill (U.K.)
gill (U.S.)
grad
grad
grain
gram
hand
hectare
henry (international of 1948)
hogshead (U.S.)
horsepower (550 ft lbf/s)
horsepower (boiler)
horsepower (electric)
horsepower (metric)
horsepower (U.K.)
horsepower (water)
hour (mean solar)
hour (sidereal)
hundredweight (long)
hundredweight (short)
inch
inch of mercury (32°F)
inch of mercury (60°F)
inch of water (39.2°F)
inch of water (60°F)
joule (international of 1948)
kayser
kilocalorie (International
Steam Table)
kilocalorie (mean)
kilocalorie (thermochemical)
kilogram mass
kilogram-force (kgf)
kilopound-force
kip
knot (international)
lambert
lambert
langley
lbf (pound-force,
avoirdupois)
lbm (pound-mass,
avoirdupois)
league (British nautical)
league (international
nautical)
league (statute)
light-year
link (engineer’s)
link (surveyor’s or Gunter’s)
liter
lux
maxwell
meter
micrometer
mil
mile (U.S. statute)
mile (U.K. nautical)
mile (international nautical)
mile (U.S. nautical)
millibar
millimeter of mercury (0°C)
To
Multiply by
meter
newton/meter2
lumen/meter2
candela/meter2
meter
meter/second2
meter3
meter3
meter3
tesla
tesla
ampere turn
meter3
meter3
degree (angular)
radian
kilogram
kilogram
meter
meter2
henry
meter3
watt
watt
watt
watt
watt
watt
second (mean solar)
second (mean solar)
kilogram
kilogram
meter
newton/meter2
newton/meter2
newton/meter2
newton/meter2
joule
1/meter
joule
-01 3.048 006
+03 2.988 98
+01 1.076 391
+00 3.426 259
+02 2.011 68
-02 1.00
-03 4.546 087
-03 4.404 883
-03 3.785 411
-09 1.00
-04 1.00
-01 7.957 747
-04 1.420 652
-04 1.182 941
-01 9.00
-02 1.570 796
-05 6.479 891
-03 1.00
-01 1.016
+04 1.00
+00 1.000 495
-01 2.384 809
+02 7.456 998
+03 9.809 50
+02 7.46
+02 7.354 99
+02 7.457
+02 7.460 43
+03 3.60
+03 3.590 170
+01 5.080 234
+01 4.535 923
-02 2.54
+03 3.386 389
+03 3.376 85
+02 2.490 82
+02 2.4884
+00 1.000 165
+02 1.00
+03 4.186 74
joule
joule
kilogram
newton
newton
newton
meter/second
candela/meter2
candela/meter2
joule/meter2
newton
+03 4.190 02
+03 4.184
+00 1.00
+00 9.806 65
+00 9.806 65
+03 4.448 221
-01 5.144 444
+04 1/π
+03 3.183 098
+04 4.184
+00 4.448 221
kilogram
-01 4.535 923
meter
meter
+03 5.559 552
+03 5.556
meter
meter
meter
meter
meter3
lumen/meter2
weber
wavelengths Kr 86
meter
meter
meter
meter
meter
meter
newton/meter2
newton/meter2
+03 4.828 032
+15 9.460 55
-01 3.048
-01 2.011 68
-03 1.00
+00 1.00
-08 1.00
+06 1.650 763
-06 1.00
-05 2.54
+03 1.609 344
+03 1.853 184
+03 1.852
+03 1.852
+02 1.00
+02 1.333 224
(Continued )
1-15
1-16
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-9 Other Conversion Factors to SI Units (Continued )
The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m.
To Convert from
minute (angle)
minute (mean solar)
minute (sidereal)
month (mean calendar)
nautical mile (international)
nautical mile (U.S.)
nautical mile (U.K.)
oersted
ohm (international of 1948)
ounce-force (avoirdupois)
ounce-mass (avoirdupois)
ounce-mass (troy or apothecary)
ounce (U.S. fluid)
pace
parsec
pascal
peck (U.S.)
pennyweight
perch
phot
pica (printer’s)
pint (U.S. dry)
pint (U.S. liquid)
point (printer’s)
poise
pole
pound-force (lbf
avoirdupois)
pound-mass (lbm
avoirdupois)
pound-mass (troy or
apothecary)
poundal
quart (U.S. dry)
quart (U.S. liquid)
rad (radiation dose
absorbed)
Rankine (temperature)
rayleigh (rate of photon
emission)
rhe
rod
roentgen
rutherford
second (angle)
To
Multiply by
radian
second (mean solar)
second (mean solar)
second (mean solar)
meter
meter
meter
ampere/meter
ohm
newton
kilogram
kilogram
meter3
meter
meter
newton/meter2
meter3
kilogram
meter
lumen/meter2
meter
meter3
meter3
meter
(newton-second)/meter2
meter
newton
-04 2.908 882
+01 6.00
+01 5.983 617
+06 2.628
+03 1.852
+03 1.852
+03 1.853 184
+01 7.957 747
+00 1.000 495
-01 2.780 138
-02 2.834 952
-02 3.110 347
-05 2.957 352
-01 7.62
+16 3.083 74
+00 1.00
-03 8.809 767
-03 1.555 173
+00 5.0292
+04 1.00
-03 4.217 517
-04 5.506 104
-04 4.731 764
-04 3.514 598
-01 1.00
+00 5.0292
+00 4.448 221
kilogram
-01 4.535 923
kilogram
-01 3.732 417
newton
meter3
meter3
joule/kilogram
-01 1.382 549
-03 1.101 220
-04 9.463 529
-02 1.00
kelvin
1/second-meter2
tK = (5/9)tR
+10 1.00
meter2/(newtonsecond)
meter
coulomb/kilogram
disintegration/second
radian
+01 1.00
+00 5.0292
-04 2.579 76
+06 1.00
-06 4.848 136
To Convert from
To
Multiply by
second (ephemeris)
second (mean solar)
second
second (ephemeris)
second (sidereal)
section
scruple (apothecary)
shake
skein
slug
span
statampere
statcoulomb
statfarad
stathenry
statmho
statohm
statute mile (U.S.)
statvolt
stere
stilb
stoke
tablespoon
teaspoon
ton (assay)
ton (long)
ton (metric)
ton (nuclear equivalent of TNT)
ton (register)
ton (short, 2000 lb)
tonne
torr (0°C)
township
unit pole
volt (international of 1948)
watt (international of 1948)
yard
year (calendar)
year (sidereal)
year (tropical)
year 1900, tropical, Jan., day
0, hour 12
year 1900, tropical, Jan., day
0, hour 12
second (mean solar)
meter2
kilogram
second
meter
kilogram
meter
ampere
coulomb
farad
henry
mho
ohm
meter
volt
meter3
candela/meter2
meter2/second
meter3
meter3
kilogram
kilogram
kilogram
joule
meter3
kilogram
kilogram
newton/meter2
meter2
weber
volt
watt
meter
second (mean solar)
second (mean solar)
second (mean solar)
second (ephemeris)
+00 1.000 000
Consult
American
Ephemeris
and Nautical
Almanac
-01 9.972 695
+06 2.589 988
-03 1.295 978
-08 1.00
+02 1.097 28
+01 1.459 390
-01 2.286
-10 3.335 640
-10 3.335 640
-12 1.112 650
+11 8.987 554
-12 1.112 650
+11 8.987 554
+03 1.609 344
+02 2.997 925
+00 1.00
+04 1.00
-04 1.00
-05 1.478 676
-06 4.928 921
-02 2.916 666
+03 1.016 046
+03 1.00
+09 4.20
+00 2.831 684
+02 9.071 847
+03 1.00
+02 1.333 22
+07 9.323 957
-07 1.256 637
+00 1.000 330
+00 1.000 165
-01 9.144
+07 3.1536
+07 3.155 815
+07 3.155 692
+07 3.155 692
second
+07 3.155 692
COnVERSIOn FACTORS
TABLE 1-10 Temperature Conversion Formulas
°F = (°C × 5/9) + 32
°C = (°F - 32) × 5/9
°R = °F + 459.67
K = °C + 273.15
K = °R × 5/9
TABLE 1-13 Values of the Ideal Gas Constant
Temp.
scale
Temperature difference ΔT:
°F = °C × 9/5
atm
atm
mmHg
bar
kg/cm2
atm
mmHg
TABLE 1-11 Density Conversion Formulas
lb
gal
T,P
lb
ft 3
T,P
= sp gr
= sp gr
T,P
T,P
Pressure
units
Volume
units
Kelvin
Bé = 145 − 145 (heavier than H O)
2
sp gr
Tw = sp gr 60 /60 F − 1
0.005
API = 141.5 − 131.5
sp gr
Bé = 140 − 130 (lighter than H O)
2
sp gr
cm3
liters
liters
liters
liters
ft3
ft3
Rankine
atm
in Hg
mmHg
lb/in2 abs
lb/ft2 abs
× 8.345406
× 62.42797
ft3
ft3
ft3
ft3
ft3
Kinematic Viscosity Conversion Formulas
Viscosity scale
Saybolt Universal
Saybolt Furol
Redwood No. 1
Range of t, s
Kinematic viscosity, stokes*
32 < t < 100
t > 100
25 < t < 40
t > 40
34 < t < 100
t > 100
0.00226t - 1.95/t
0.00220t - 1.35/t
0.0224t - 1.84/t
0.0216t - 0.60/t
0.00260t - 1.79/t
0.00247t - 0.50/t
0.027t - 20/t
0.00147t - 3.74/t
Redwood Admiralty
Engler
*1 stoke (St) = 1 cm2/s = 10-4 m2/s
R
Energy /
(Weight ⋅ Temp)
Weight
units
Energy
units*
g mol
g mol
g mol
g mol
g mol
g mol
g mol
g mol
lb mol
lb mol
lb mol
calories
joules (abs)
joules (int)
atm ⋅ cm3
atm ⋅ liters
mmHg ⋅ liters
bar ⋅ liters
kg/(cm2)(liters)
atm ⋅ ft3
mmHg ⋅ ft3
chu or pcu
1.9872
8.3144
8.3130
82.057
0.08205
62.361
0.08314
0.08478
1.314
998.9
1.9872
lb mol
lb mol
lb mol
lb mol
lb mol
lb mol
lb mol
lb mol
Btu
hph
kWh
atm ⋅ ft3
in Hg ⋅ ft3
mmHg ⋅ ft3
(lb)( ft3)/in2
ft ⋅ lbf
1.9872
0.0007805
0.0005819
0.7302
21.85
555.0
10.73
1545.0
*Energy units are the product of pressure units and volume units.
TABLE 1-12
1-17
1-18
UnIT COnVERSIOn FACTORS AnD SYMBOLS
TABLE 1-14 Fundamental Physical Constants
1 sec = 1.00273791 sidereal seconds
g0 = 9.80665 m/s2
1 liter = 0.001 cu m
1 atm = 101,325 newtons/sq m
1 mmHg (pressure) = (1⁄760) atm
= 133.3224 newtons/sq m
1 int ohm = 1.000495 ± 0.000015 abs ohm
1 int amp = 0.999835 ± 0.000025 abs amp
1 int coul = 0.999835 ± 0.000025 abs coul
1 int volt = 1.000330 ± 0.000029 abs volt
1 int watt = 1.000165 ± 0.000052 abs watt
1 int joule = 1.000165 ± 0.000052 abs joule
T0°C = 273.150 ± 0.010 K
(PV)0°CP=0 = (RT)0°C = 2271.16 ± 0.04 abs joule/mole
= 22,414.6 ± 0.4 cu cm atm/mole
= 22.4146 ± 0.0004 liter atm/mole
R = 8.31439 ± 0.00034 abs joule/deg mole
= 1.98719 ± 0.00013 cal/deg mole
= 82.0567 ± 0.0034 cu cm atm/deg mole
= 0.0820567 ± 0.0000034 liter atm/deg mole
ln 10 = 2.302585
R ln 10 = 19.14460 ± 0.00078 abs joule/deg mole
= 4.57567 ± 0.00030 cal/deg mole
N = (6.02283 ± 0.0022) × 1023/mole
h = (6.6242 ± 0.0044) × 10-34 joule s
c = (2.99776 ± 0.00008) × 108 m/s
(h2/8 π2k) = (4.0258 ± 0.0037) × 10-39 g sq cm deg
(h/8 π2c) = (2.7986 ± 0.0018) × 10-39 g cm
Z = Nhc = 11.9600 ± 0.0036 abs joule cm/mole
= 2.85851 ± 0.0009 cal cm/mole
Z/R = hc/k = c2 = 1.43847 ± 0.00045 cm deg
f = 96,501.2 ± 10.0 int coul/g-equiv or int joule/int volt g-equiv
= 96,485.3 ± 10.0 abs coul/g-equiv or abs joule/abs volt g-equiv
= 23,068.1 ± 2.4 cal/int volt g-equiv
= 23,060.5 ± 2.4 cal/abs volt g-equiv
e = (1.60199 ± 0.00060) × 10-19 abs coul
= (1.60199 ± 0.00060) × 10-20 abs emu
= (4.80239 ± 0.00180) × 10-10 abs esu
1 int electron-volt/molecule = 96,501.2 ± 10 int joule/mole
= 23,068.1 ± 2.4 cal/mole
1 abs electron-volt/molecule = 96,485.3 ± 10. abs joule/mole
= 23,060.5 ± 2.4 cal/mole
1 int electron-volt = (1.60252 ± 0.00060) × 10-12 erg
1 abs electron-volt = (1.60199 ± 0.00060) × 10-12 erg
hc = (1.23916 ± 0.00032) × 10-4 int electron-volt cm
= (1.23957 ± 0.00032) × 10-4 abs electron-volt cm
k = (8.61442 ± 0.00100) × 10-5 int electron-volt/deg
= (8.61727 ± 0.00100) × 10-5 abs electron-volt/deg
= R/N = (1.38048 ± 0.00050) × 10-23 joule/deg
1 IT cal = (1⁄860) = 0.00116279 int watt-h
= 4.18605 int joule
= 4.18674 abs joule
= 1.000654 cal
1 cal = 4.1840 abs joule
= 4.1833 int joule
= 41.2929 ± 0.0020 cu cm atm
= 0.0412929 ± 0.0000020 liter atm
1 IT cal/g = 1.8 Btu/lb
1 Btu = 251.996 IT cal
= 0.293018 int watt-h
= 1054.866 int joule
= 1055.040 abs joule
= 252.161 cal
1 horsepower = 550 ft-lbf (wt)/s
= 745.578 int watt
= 745.70 abs watt
1 in = (1/0.3937) = 2.54 cm
1 ft = 0.304800610 m
1 lb = 453.5924277 g
1 gal = 231 cu in
= 0.133680555 cu ft
= 3.785412 × 10-3 cu m
= 3.785412 liter
sec = mean solar second
Definition: g0 = standard gravity
Definition: atm = standard atmosphere
mmHg (pressure) = standard millimeter mercury
int = international; abs = absolute
amp = ampere
coul = coulomb
Absolute temperature of the ice point, 0°C
PV = product for ideal gas at 0°C
R = gas constant per mole
ln = natural logarithm (base e)
N = Avogadro number
h = Planck constant
c = velocity of light
Constant in rotational partition function of gases
Constant relating wave number and moment of inertia
Z = constant relating wave number and energy per mole
c2 = second radiation constant
ℱ = Faraday constant
e = electronic charge
emu = electromagnetic unit of charge
esu = electrostatic unit of charge
Constant relating wave number and energy per molecule
k = Boltzmann constant
Definition of IT cal: IT = International steam tables
cal = thermochemical calorie
Definition: cal = thermochemical calorie
Definition of Btu: Btu = IT British thermal unit
cal = thermochemical calorie
Definition of horsepower (mechanical): lb (wt) = weight of 1 lb
at standard gravity
Definition of inch: in = U.S. inch
ft = U.S. foot (1 ft = 12 in)
Definition: lb = avoirdupois pound
Definition: gal = U.S. gallon
Section 2
Physical and Chemical Data
Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University
of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering
Education (Section Coeditor, Physical and Chemical Data)
Richard L. Rowley, Ph.D. Department of Chemical Engineering, Emeritus, Brigham Young University
(Section Coeditor, Prediction and Correlation of Physical Properties)
W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow,
American Institute of Chemical Engineers (Section Coeditor, Prediction and Correlation of Physical Properties)
GEnERAL REFEREnCES
PHYSICAL PROPERTIES OF PURE SUBSTAnCES
Tables
2-1
2-2
Physical Properties of the Elements and Inorganic Compounds . . . . .
Physical Properties of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . .
2-5
2-26
VAPOR PRESSURES
Tables
2-3 Vapor Pressure of Water Ice from 0 to −40°C . . . . . . . . . . . . . . . . . . . . . . . .
2-4 Vapor Pressure of Supercooled Liquid Water from 0 to −40°C . . . . . . .
Vapor Pressures of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-5 Vapor Pressure (MPa) of Liquid Water from 0 to 100°C . . . . . . . . . . . . . .
2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106,
2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family . . . . . . . . . . .
2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72,
2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 . . . . . . . . . . . . . . .
2-8 Vapor Pressure of Inorganic and Organic Liquids,
ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K . . . . . . . . . . . . . . . . . . .
2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm . . . . . . . . . . . . . .
2-10 Vapor Pressures of Organic Compounds, up to 1 atm . . . . . . . . . . . . . . . .
VAPOR PRESSURES OF SOLUTIOnS
Tables
2-11 Partial Pressures of Water over Aqueous Solutions of HCl . . . . . . . . . . .
Vapor Pressures of H3PO4 Aqueous: Partial Pressure of
H2O Vapor (Fig. 2-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions . . .
2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg . . . . . . . . .
2-14 Partial Pressures of HNO3 and H2O over Aqueous
Solutions of HNO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-15 Total Vapor Pressures of Aqueous Solutions
of CH3COOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-16 Partial Pressure of H2O over Aqueous Solutions of NH3 (psia) . . . . . . . .
2-17 Partial Pressures of H2O over Aqueous Solutions of Sodium
Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-46
2-46
2-46
2-46
2-46
2-46
2-47
2-50
2-53
2-59
2-63
2-78
2-78
2-79
2-80
2-80
2-81
2-82
2-83
2-18 Partial Pressures of H2O and CH3OH over Aqueous Solutions of
Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium
Hydroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Water Vapor Content in Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Water Content in Air at Pressures over Atmospheric (Fig. 2-2) . . . . . . .
SOLUBILITIES
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-20 Solubilities of Inorganic Compounds in Water at Various
Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-21 Solubility as a Function of Temperature and Henry’s Constant
at 25°C for Gases in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-22 Henry’s Constant H for Various Compounds in Water at 25°C . . . . . . .
2-23 Henry’s Constant H for Various Compounds in Water at 25°C
from Infinite Dilution Activity Coefficients . . . . . . . . . . . . . . . . . . . . . . . .
2-24 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-25 Ammonia-Water at 10 and 20°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-26 Carbon Dioxide (CO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-27 Chlorine (Cl2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-28 Chlorine Dioxide (ClO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-29 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-30 Hydrogen Sulfide (H2S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DEnSITIES
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References and Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Densities of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point
to the Critical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-32 Densities of Inorganic and Organic Liquids (mol/dm3) . . . . . . . . . . . . . .
2-83
2-83
2-84
2-84
2-84
2-84
2-85
2-89
2-89
2-90
2-90
2-90
2-90
2-91
2-91
2-91
2-91
2-92
2-92
2-92
2-92
2-93
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
Tables
2-33 Ammonia (NH3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100
2-34 Ammonium Chloride (NH4Cl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100
2-1
2-2
PHYSICAL AnD CHEMICAL DATA
2-35 Calcium Chloride (CaCl2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-36 Ferric Chloride (FeCl3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-37 Ferric Sulfate [Fe2(SO4)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-38 Ferric Nitrate [Fe(NO3)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-39 Ferrous Sulfate (FeSO4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-40 Hydrogen Cyanide (HCN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-41 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-42 Hydrogen Peroxide (H2O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-43 Nitric Acid (HNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-44 Perchloric Acid (HClO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-45 Phosphoric Acid (H3PO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-46 Potassium Bicarbonate (KHCO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-47 Potassium Carbonate (K2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-48 Potassium Chloride (KCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-49 Potassium Hydroxide (KOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-50 Potassium Nitrate (KNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-51 Sodium Acetate (NaC2H3O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-52 Sodium Carbonate (Na2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-53 Sodium Chloride (NaCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-54 Sodium Hydroxide (NaOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-55 Sulfuric Acid (H2SO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Densities of Aqueous Organic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-56 Acetic Acid (CH3COOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-57 Methyl Alcohol (CH3OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-58 Ethyl Alcohol (C2H5OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-59 n-Propyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-60 Isopropyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-61 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-62 Hydrazine (N2H4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-63 Densities of Aqueous Solutions of Miscellaneous
Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DEnSITIES OF MISCELLAnEOUS MATERIALS
Tables
2-64 Approximate Specific Gravities and Densities of Miscellaneous
Solids and Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-65 Density (kg/m3) of Selected Elements as a Function of
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LATEnT HEATS
.......................................................
Unit Conversions
Tables
2-66 Heats of Fusion and Vaporization of the Elements and
Inorganic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-67 Heats of Fusion of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . .
2-68 Heats of Fusion of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-69 Heats of Vaporization of Inorganic and Organic Liquids
(J/kmol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SPECIFIC HEATS
Specific Heats of Pure Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-70 Heat Capacities of the Elements and Inorganic Compounds . . . . . . . . .
2-71 Specific Heat [kJ/(kg ⋅ K)] of Selected Elements. . . . . . . . . . . . . . . . . . . . . .
2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol ⋅ K)] . . . . .
2-73 Specific Heats of Organic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-74 Heat Capacity at Constant Pressure of Inorganic and Organic
Compounds in the Ideal Gas State Fit to a Polynomial
Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-75 Heat Capacity at Constant Pressure of Inorganic and Organic
Compounds in the Ideal Gas State Fit to Hyperbolic Functions
Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-76 Cp/Cv : Ratios of Specific Heats of Gases at 1 atm Pressure. . . . . . . . . . . .
Specific Heats of Aqueous Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-77 Acetic Acid (at 38°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-78 Ammonia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-79 Ethyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-80 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-81 Hydrochloric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-82 Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-83 Nitric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-84 Phosphoric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-85 Potassium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-86 Potassium Hydroxide (at 19°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-87 Normal Propyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-88 Sodium Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-89 Sodium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-90 Sodium Hydroxide (at 20°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-91 Sulfuric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specific Heats of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-92 Specific Heats of Miscellaneous Liquids and Solids. . . . . . . . . . . . . . . . . .
2-93 Oils (Animal, Vegetable, Mineral Oils) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-100
2-100
2-100
2-100
2-100
2-100
2-100
2-100
2-101
2-102
2-102
2-102
2-102
2-103
2-103
2-103
2-103
2-103
2-103
2-103
2-104
2-106
2-106
2-107
2-108
2-109
2-109
2-110
2-110
2-111
2-113
2-114
2-114
2-115
2-117
2-118
2-120
2-128
2-128
2-128
2-128
2-136
2-137
2-144
2-147
2-149
2-156
2-156
2-156
2-156
2-156
2-156
2-156
2-157
2-157
2-157
2-157
2-157
2-157
2-157
2-157
2-157
2-157
2-157
2-158
2-158
2-158
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-158
Tables
2-94 Heats and Free Energies of Formation of Inorganic Compounds . . . . . 2-159
2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and
Net Enthalpies of Combustion of Inorganic and Organic
Compounds at 298.15 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-167
2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol),
of Combustion Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-174
2-97 Ideal Gas Entropies s°, kJ/(kmol ⋅ K), of Combustion Products . . . . . . . 2-175
HEATS OF SOLUTIOn
Tables
2-98 Heats of Solution of Inorganic Compounds in Water . . . . . . . . . . . . . . . .
2-99 Heats of Solution of Organic Compounds in Water (at Infinite
Dilution and Approximately Room Temperature) . . . . . . . . . . . . . . . . . .
THERMAL EXPAnSIOn AnD COMPRESSIBILITY
Unit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermal Expansion of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-100 Linear Expansion of the Solid Elements . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-101 Linear Expansion of Miscellaneous Substances . . . . . . . . . . . . . . . . . . . .
2-102 Volume Expansion of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-103 Volume Expansion of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gas Expansion: Joule-Thomson Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-104 Additional References Available for the Joule-Thomson
Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-105 Approximate Inversion-Curve Locus in Reduced Coordinates
(Tr = T/Tc ; Pr = P/Pc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Critical Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-106 Critical Constants and Acentric Factors of Inorganic and
Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compressibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-107 Compressibilities of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-108 Compressibilities of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
THERMODYnAMIC PROPERTIES
Explanation of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-109 Thermodynamic Properties of Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-110 Thermodynamic Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Dry Air (Fig. 2-3) . . . . . . . . . . . . . . . . . .
2-111 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Air, Moist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-112 Thermodynamic Properties of Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . .
2-113 Thermodynamic Properties of Carbon Dioxide . . . . . . . . . . . . . . . . . . . .
2-114 Thermodynamic Properties of Carbon Monoxide . . . . . . . . . . . . . . . . . .
Temperature-Entropy Diagram for Carbon Monoxide (Fig. 2-4) . . . .
2-115 Thermodynamic Properties of Ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalpy-Concentration Diagram for Aqueous Ethyl Alcohol
(Fig. 2-5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-116 Thermodynamic Properties of Normal Hydrogen . . . . . . . . . . . . . . . . . .
2-117 Saturated Hydrogen Peroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-118 Thermodynamic Properties of Hydrogen Sulfide . . . . . . . . . . . . . . . . . . .
Enthalpy-Concentration Diagram for Aqueous Hydrogen Chloride
at 1 atm (Fig. 2-6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-119 Thermodynamic Properties of Methane . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-120 Thermodynamic Properties of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . .
2-121 Thermodynamic Properties of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Nitrogen (Fig. 2-7) . . . . . . . . . . . . . . . . .
2-122 Thermodynamic Properties of Oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Oxygen (Fig. 2-8) . . . . . . . . . . . . . . . . . . .
Enthalpy-Concentration Diagram for Oxygen-Nitrogen Mixture
at 1 atm (Fig. 2-9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
K Values (K = y/x) in Light-Hydrocarbon Systems (Fig. 2-10) . . . . . . .
2-123 Composition of Selected Refrigerant Mixtures . . . . . . . . . . . . . . . . . . . . .
2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane . . . . . . .
Pressure-Enthalpy Diagram for Refrigerant 22. (Fig. 2-11) . . . . . . . . . .
2-125 Thermodynamic Properties of R-32, Difluoromethane . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Refrigerant 32. (Fig. 2-12) . . . . . . . . . .
2-126 Thermodynamic Properties of R-125, Pentafluoroethane. . . . . . . . . . .
Pressure-Enthalpy Diagram for Refrigerant 125 (Fig. 2-13) . . . . . . . . .
2-127 Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane . . .
Pressure-Enthalpy Diagram for Refrigerant 134a. (Fig. 2-14). . . . . . . .
2-176
2-178
2-179
2-179
2-179
2-179
2-180
2-181
2-181
2-182
2-182
2-182
2-182
2-182
2-182
2-182
2-183
2-190
2-190
2-190
2-190
2-190
2-191
2-191
2-191
2-191
2-192
2-194
2-198
2-199
2-199
2-200
2-202
2-204
2-206
2-207
2-209
2-210
2-212
2-213
2-215
2-216
2-218
2-220
2-222
2-223
2-225
2-226
2-226
2-227
2-228
2-230
2-231
2-233
2-234
2-236
2-237
2-239
PHYSICAL AnD CHEMICAL DATA
2-128 Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane . . . . . . .
2-129 Thermodynamic Properties of R-404A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-130 Thermodynamic Properties of R-407C . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Refrigerant 407C (Fig. 2-15) . . . . . . . .
2-131 Thermodynamic Properties of R-410A . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-132 Opteon YF (R-1234yf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pressure-Enthalpy Diagram for Refrigerant 1234yf (Fig. 2-16) . . . . . .
2-133 Thermophysical Properties of Saturated Seawater . . . . . . . . . . . . . . . . .
Enthalpy-Concentration Diagram for Aqueous Sodium Hydroxide
at 1 atm (Fig. 2-17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalpy-Concentration Diagram for Aqueous Sulfuric Acid
at 1 atm (Fig. 2-18) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-134 Saturated Solid/Vapor Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-135 Thermodynamic Properties of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-136 Thermodynamic Properties of Water Substance along
the Melting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TRAnSPORT PROPERTIES
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mass Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-137 Surface Tension σ (dyn/cm) of Various Liquids . . . . . . . . . . . . . . . . . . . .
2-138 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) . . . . . . . .
2-139 Viscosity of Inorganic and Organic Liquids (Pa∙s) . . . . . . . . . . . . . . . . . .
2-140 Viscosities of Liquids: Coordinates for Use with Fig . 2-19 . . . . . . . . . . .
Nomograph for Viscosities of Liquids at 1 atm (Fig . 2-19) . . . . . . . . .
2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) . . . . . . . . . . . . . . . . . .
2-142 Diffusivities in Liquids (25°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermal Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-143 Transport Properties of Selected Gases at Atmospheric Pressure . . .
2-144 Prandtl Number of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-145 Vapor Thermal Conductivity of Inorganic and Organic
Substances [W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-146 Thermophysical Properties of Miscellaneous Saturated Liquids . . . .
2-147 Thermal Conductivity of Inorganic and Organic Liquids
[W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-148 Nomograph for Thermal Conductivity of Organic Liquids
(Fig . 2-20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-149 Thermal-Conductivity-Temperature Table for Metals
and Nonmetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-150 Thermal Conductivity of Chromium Alloys . . . . . . . . . . . . . . . . . . . . . . . .
2-151 Thermal Conductivity of Some Alloys at High Temperature . . . . . . . .
2-152 Thermophysical Properties of Selected Nonmetallic
Solid Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-153 Lower and Upper Flammability Limits, Flash Points, and
Autoignition Temperatures for Selected Hydrocarbons . . . . . . . . . . .
PREDICTIOn AnD CORRELATIOn OF
PHYSICAL PROPERTIES
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prediction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Property Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Classification of Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theory and Empirical Extension of Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Corresponding States (CS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Group Contributions (GCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Computational Chemistry (CC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Empirical QSPR Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Molecular Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Critical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-154 Ambrose Group Contributions for Critical Constants . . . . . . . . . . . . . .
2-155 Group Contributions for the Nannoolal et al . Method for
Critical Constants and Normal Boiling Point . . . . . . . . . . . . . . . . . . . . .
2-156 Intermolecular Interaction Corrections for the Nannoolal et al .
Method for Critical Constants and Normal Boiling Point . . . . . . . . . .
2-157 Wilson-Jasperson First- and Second-Order Contributions
for Critical Temperature and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normal Melting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-158 First-Order Groups and Their Contributions for Melting Point . . . . .
2-159 Second-Order Groups and Their Contributions for Melting Point . . .
Characterizing and Correlating Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acentric Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radius of Gyration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dipole Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-240
2-242
2-244
2-246
2-247
2-249
2-258
2-259
2-260
2-260
2-261
2-262
2-265
2-266
2-266
2-266
2-266
2-266
2-267
2-274
2-281
2-282
2-283
2-285
2-288
2-288
2-288
2-289
2-296
2-298
2-305
2-306
2-307
2-307
2-307
2-308
2-311
2-311
2-311
2-314
2-314
2-314
2-314
2-315
2-315
2-315
2-315
2-315
2-315
2-315
2-315
2-317
2-318
2-320
2-321
2-321
2-321
2-322
2-322
2-323
2-323
2-324
2-324
Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dielectric Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-160 Wildman-Crippen Contributions for Refractive Index . . . . . . . . . . . . . .
Vapor Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalpy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-161 Domalski-Hearing Group Contribution Values for Standard
State Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gibbs Energy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Latent Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalpy of Vaporization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enthalpy of Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-162 Cs (C—H) Group Values for Chickos Estimation of ∆Hfus . . . . . . . . . . .
2-163 Ct (Functional) Group Values for Chickos Estimation of ∆H fus . . . . . .
Enthalpy of Sublimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-164 Group Contributions and Corrections for ∆Hsub . . . . . . . . . . . . . . . . . . . .
Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-165 Benson and CHETAH Group Contributions for Ideal
Gas Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-166 Liquid Heat Capacity Group Parameters for Ruzicka-Domalski
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-167 Group Values and Nonlinear Correction Terms for Estimation
of Solid Heat Capacity with the Goodman et al . Method . . . . . . . . . . .
2-168 Element Contributions to Solid Heat Capacity for the
Modified Kopp’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-169 Simple Fluid Compressibility Factors Z (0) . . . . . . . . . . . . . . . . . . . . . . . . . .
2-170 Acentric Deviations Z (1) from the Simple Fluid Compressibility
Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-171 Constants for the Two Reference Fluids Used in Lee-Kesler Method . . .
Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-172 Relationships for Eq . (2-70) for Common Cubic EoS . . . . . . . . . . . . . . . .
Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-173 Reichenberg Group Contribution Values . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-174 Group Contributions for the Hsu et al . Method . . . . . . . . . . . . . . . . . . . .
Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-175 UNIFAC-VISCO Group Interaction Parameters αmn . . . . . . . . . . . . . . . .
Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-176 Correlation Parameters for Baroncini et al . Method for
Estimation of Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pure Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-177 Knotts Group Contributions for the Parachor in Estimating
Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flammability Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flash Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flammability Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tables
2-178 Group Contributions for Quantities Used to Estimate
Flammability Limits By Rowley et al . Method for Organic
Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-179 Ideal Gas Enthalpies of Formation and Average Heat Capacities
of Combustion Gases for Use in Eq . (2-125) . . . . . . . . . . . . . . . . . . . . . . .
Autoignition Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2-180 Group Contributions for Pintar Autoignition Temperature
Method for Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-3
2-324
2-325
2-325
2-326
2-326
2-327
2-327
2-327
2-328
2-334
2-334
2-334
2-334
2-335
2-336
2-336
2-336
2-337
2-337
2-337
2-338
2-339
2-343
2-344
2-345
2-345
2-345
2-345
2-345
2-347
2-348
2-349
2-349
2-349
2-350
2-350
2-351
2-351
2-351
2-352
2-353
2-354
2-354
2-355
2-356
2-356
2-357
2-357
2-358
2-358
2-358
2-359
2-360
2-360
2-360
2-361
2-361
2-361
2-362
GEnERAL REFEREnCES
Considerations of reader interest, space availability, the system or systems of units
employed, copyright issues, etc., have all influenced the revision of material in previous
editions for the present edition. Reference is made at numerous places to various specialized works and, when appropriate, to more general works. A listing of general works may
be useful to readers in need of further information.
ASHRAE Handbook—Fundamentals, SI edition, ASHRAE, Atlanta, 2005;
Benedek, P., and F. Olti, Computer-Aided Chemical Thermodynamics of Gases
and Liquids, Wiley, New York, 1985; Brule, M. R., L. L. Lee, and K. E. Starling,
Chem. Eng., 86, 25, Nov. 19, 1979, pp. 155–164; Cox, J. D., and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press,
New York, 1970; Cox, J. D., D. D. Wagman, and V. A. Medvedev, CODATA Key
Values for Thermodynamics, Hemisphere Publishing Corp., New York, 1989;
Daubert, T. E., R. P. Danner, H. M. Sibel, and C. C. Stebbins, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Taylor & Francis,
Washington, 1997; Domalski, E. S., and E. D. Hearing, Heat capacities and
entropies of organic compounds in the condensed phase, vol. 3, J. Phys.
Chem. Ref. Data 25(1):1–525, Jan-Feb 1996; Dykyj, J., and M. Repas, Saturated
vapor pressures of organic compounds, Veda, Bratislava, 1979 (Slovak);
Dykyj, J., M. Repas, and J. Svoboda, Saturated vapor pressures of organic
compounds, Veda, Bratislava, 1984 (Slovak); Glushko, V. P., ed., Thermal
Constants of Compounds, Issues I–X, Moscow, 1965–1982 (Russian only);
Gmehling, J., Azeotropic Data, 2 vols., VCH Weinheim, Germany, 1994;
Gmehling, J., and U. Onken, Vapor-Liquid Equilibrium Data Collection,
Dechema Chemistry Data Series, Frankfurt, 1977–1978; International Data
Series, Selected Data on Mixtures, Series A: Thermodynamics Research
Center, National Institute of Standards and Technology, Boulder, Colo.;
Kaye, S. M., Encyclopedia of Explosives and Related Items, U.S. Army R&D command, Dover, N.J., 1980; King, M. B., Phase Equilibrium in Mixtures, Pergamon,
Oxford, 1969; Landolt-Boernstein, Numerical Data and Functional Relationships in Science and Technology (New Series), http://www.springeronline
.com/sgw/cda/frontpage/0,11855,4-10113-2-95859-0,00.html; Lide, D. R.,
CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, Boca Raton,
Fla., 2005; Lyman, W. J., W. F. Reehl, and D. H. Rosenblatt, Handbook of Chemical Property Estimation Methods, McGraw-Hill, New York, 1990; Majer, V.,
and V. Svoboda, Enthalpies of Vaporization of Organic Compounds: A Critical
Review and Data Compilation, Blackwell Science, 1985; Majer V., V. Svoboda,
and J. Pick, Heats of Vaporization of Fluids, Elsevier, Amsterdam, 1989 (general discussion); Marsh, K. N., Recommended Reference Materials for the Realization of Physicochemical Properties, Blackwell Science, 1987; NIST-IUPAC
Solubility Data Series, Pergamon Press, http://www.iupac.org/publications/
ci/1999/march/solubility.html; Ohse, R. W., and H. von Tippelskirch, High
Temp.—High Press., 9:367–385, 1977; Ohse, R. W., Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell Science Pubs.,
Oxford, England, 1985; Pedley, J. B., R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Compounds, Chapman and Hall, New York, 1986; Physical Property Data for the Design Engineer, Hemisphere, New York, 1989;
Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and
2-4
Liquids, 5th ed., McGraw-Hill, New York, 2001; Rothman, D., et al., Max
Planck Inst. f. Stromungsforschung, Ber 6, 1978; Smith, B. D., and R. Srivastava,
Thermodynamic Data for Pure Compounds, Part A: Hydrocarbons and
Ketones, Elsevier, Amsterdam, 1986, Physical sciences data 25, http://www
.elsevier.com/wps/find/bookseriesdescription.librarians/BS_PSD/description; Sterbacek, Z., B. Biskup, and P. Tausk, Calculation of Properties Using
Corresponding States Methods, Elsevier, Amsterdam, 1979; Stull, D. R., E. F.
Westrum, and G. C. Sink, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969; TRC Thermodynamic Tables—Hydrocarbons,
Thermodynamics Research Center, National Institute of Standards and
Technology, Boulder, Colo.; TRC Thermodynamic Tables—Non-Hydrocarbons,
Thermodynamics Research Center, National Institute of Standards and
Technology, Boulder, Colo.; Young, D. A., “Phase Diagrams of the Elements,”
UCRL Rep. 51902, 1975 republished in expanded form by the University of
California Press, 1991; Zabransky, M., V. Ruzicka, Jr., V. Majer, and E. S. Domalski,
Heat Capacity of Liquids: Critical Review and Recommended Values, J. Phys.
Chem. Ref. Data, Monograph No. 6, 1996.
Critical Data Sources
Ambrose, D., “Vapor-Liquid Critical Properties,” N. P. L. Teddington, Middlesex, Rep. 107, 1980; Kudchaker, A. P., G. H. Alani, and B. J. Zwolinski, Chem.
Revs. 68: 659–735, 1968; Matthews, J. F., Chem. Revs. 72: 71–100, 1972;
Simmrock, K., R. Janowsky, and A. Ohnsorge, Critical Data of Pure Substances, Parts 1 and 2, Dechema Chemistry Data Series, 1986. Other recent
references for critical data can be found in Lide, D. R., CRC Handbook of
Chemistry and Physics, 86th ed., CRC Press, Boca Raton, Fla., 2005.
Publications on Thermochemistry
Pedley, J. B., Thermochemical Data and Structures of Organic Compounds, 1,
Thermodynamic Research Center, Texas A&M Univ., 1994 (976 pp., 3000
cpds.); Frenkel, M., et al., Thermodynamics of Organic Compounds in the
Gas State, 2 vols., Thermodynamic Research Center, Texas A&M Univ.,
1994 (1825 pp., 2000 cpds.); Barin, I., Thermochemical Data of Pure Substances, 2nd ed., 2 vols., VCH Weinheim, Germany, 1993 (1834 pp., 2400
substances); Gurvich, L. V., et al., Thermodynamic Properties of Individual
Substances, 4th ed., 3 vols., Hemisphere, New York, 1989, 1990, and 1993
(2520 pp.); Lide, D. R., and G. W. A. Milne, Handbook of Data on Organic
Compounds, 3rd ed., 7 vols., Chemical Rubber, Miami, 1993 (7000 pp.);
Daubert, T. E., et al., Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, extant 1995, Taylor & Francis, Bristol, Pa., 1995;
Database 11, NIST, Gaithersburg, Md. U.S. Bureau of Mines publications
include Bulletins 584, 1960 (232 pp.); 592, 1961 (149 pp.); 595, 1961 (68 pp.);
654, 1970 (26 pp.); Chase, M. W., et al., JANAF Thermochemical Tables,
3d ed., J. Phys. Chem. Ref. Data 14 suppl. 1, 1986 (1896 pp.); Journal of Physical and Chemical Reference Data is available online at http://listserv.nd
.edu/cgi-bin/wa?×A2=ind0501&L=pamnet&F=&S=&P=8490 and at http://
www.nist.gov/srd/reprints.htm
PHYSICAL PROPERTIES OF PURE SUBSTAnCES
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds*
Abbreviations Used in the Table
a., acid
A., specific gravity with reference
to air = 1
abs., absolute
ac., acetic acid
act., acetone
al., 95 percent ethyl alcohol
alk, alkali (i.e., aq. NaOH or KOH)
am., amyl (C5H11)
amor., amorphous
anh., anhydrous
aq., aqueous or water
aq. reg., aqua regia
atm., atmosphere or 760 mm. of
mercury pressure
bk., black
brn., brown
bz., benzene
c., cold
cb., cubic
cc, cubic centimeter
chl., chloroform
col., colorless or white
conc., concentrated
cr., crystals or crystalline
d., decomposes
D., specific gravity with reference
to hydrogen = 1
hyg., hygroscopic
i., insoluble
ign., ignites
lq., liquid
lt., light
m. al., methyl alcohol
mn., monoclinic
nd., needles
NH3, liquid ammonia
NH4OH, ammonium hydroxide
solution
oct., octahedral
or., orange
pd., powder
d. 50, decomposes at 50°C; 50 d.,
melts at 50°C with
decomposition
delq., deliquescent
dil., dilute
dk., dark
eff., effloresces or efflorescent
et., ethyl ether
expl., explodes
gel., gelatinous
gly., glycerol (glycerin)
gn., green
h., hot
hex., hexagonal
Formula weights are based upon the International Atomic Weights in “Atomic Weights of the Elements 2001,”
Pure Appl. Chem., 75, 1107, 2003, and are computed to the nearest hundredth .
Refractive index, where given for a uniaxial crystal, is for the ordinary (ω) ray; where given for a biaxial crystal, the index given is for the median (β) value . Unless otherwise specified, the index is given for the sodium D-line
(λ = 589 .3 µm) .
Specific gravity values are given at room temperatures (15 to 20°C) unless otherwise indicated by the small
figures which follow the value: thus, 5.6 184° indicates a specific gravity of 5 .6 for the substance at 18°C referred to
water at 4°C . In this table the values for the specific gravity of gases are given with reference to air (A) = 1, or
hydrogen (D) = 1 .
Melting point is recorded in a certain case as 82 d . and in some other case as d . 82, the distinction being made
in this manner to indicate that the former is a melting point with decomposition at 82°C, while in the latter
decomposition only occurs at 82°C . Where a value such as −2H2O, 82 is given, it indicates loss of 2 moles of water
per formula weight of the compound at a temperature of 82°C .
Boiling point is given at atmospheric pressure (760 mm of mercury) unless otherwise indicated; thus,
8215 mm indicates the boiling point is 82°C when the pressure is 15 mm .
Name
Aluminum
acetate, normal
acetate, basic
bromide
bromide
carbide
chloride
Formula
Al
Al(C2H3O2)3
Al(OH)(C2H3O2)2
AlBr3
AlBr3⋅6H2O
Al4C3
AlCl3
Formula
weight
26 .98
204 .11
162 .08
266 .69
374 .78
143 .96
133 .34
Color, crystalline form,
and refractive index
silv ., cb .
wh . pd .
wh ., amor .
trig .
col ., delq . cr .
yel ., hex ., 2 .70
wh ., delq ., hex .
Specific
gravity
2 .7020°
3 .01 254°
2 .95
2 .44
25 °
4
pl., plates
pr., prisms or prismatic
pyr., pyridine
rhb., rhombic (orthorhombic)
s., soluble
satd., saturated
sl., slightly
soln., solution
subl., sublimes
sulf., sulfides
tart. a., tartaric acid
tet., tetragonal
tr., transition
tri., triclinic
trig., trigonal
v., very
vac., in vacuo
vl., violet
volt., volatile or volatilizes
wh., white
yel., yellow
∞, soluble in all proportions
<, less than
>, greater than
42±, about or near 42
−3H2O, 100, loses 3 moles of water
per formula weight at 100°C
Solubility is given in parts by weight (of the formula shown at the extreme left) per 100 parts by weight of the
solvent; the small superscript indicates the temperature . In the case of gases the solubility is often expressed in
some manner as 510° cc which indicates that at 10°C, 5 cc of the gas are soluble in 100 g of the solvent . The symbols
of the common mineral acids: H2SO4, HNO3, HCl, etc ., represent dilute aqueous solutions of these acids . See also
special tables on Solubility .
references: The information given in this table has been collected mainly from the following sources: Mellor,
A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Longmans, New York, 1922 . Abegg, Handbuch der
anorganischen Chemie, S . Hirzel, Leipzig, 1905 . Gmelin-Kraut, Handbuch der anorganischen Chemie, 7th ed ., Carl
Winter, Heidelberg; 8th ed ., Verlag Chemie, Berlin, 1924 . Friend, Textbook of Inorganic Chemistry, Griffin, London,
1914 . Winchell, Microscopic Character of Artificial Inorganic Solid Substances or Artificial Minerals, Wiley, New York,
1931 . International Critical Tables, McGraw-Hill, New York, 1926 . Tables annuelles internationales de constants et
donnes numeriques, McGraw-Hill, New York . Annual Tables of Physical Constants and Numerical Data, National
Research Council, Princeton, N .J ., 1943 . Comey and Hahn, A Dictionary of Chemical Solubilities, Macmillan,
New York, 1921 . Seidell, Solubilities of Inorganic and Metal Organic Compounds, Van Nostrand, New York, 1940 .
Melting
point, °C
660
d . 200
d .
97 .5
d . 100
d . >2200
1945 .2atm .
Boiling
point, °C
2056
268
752mm
182 .7
;
subl . 178
Solubility in 100 parts
Cold water
i .
s .
i .
s .
s .
d . to CH4
69 .8715°
chloride
AlCl3⋅6H2O
col ., delq ., trig ., 1 .560
400
241 .43
fluoride (fluellite)
AlF3⋅H2O
col ., rhb ., 1 .490
2 .17
d .
sl . s .
101 .99
fluoride
Al2F6⋅7H2O
wh ., cr . pd .
−4H2O, 120
−6H2O, 250
i .
294 .06
hydroxide
Al(OH)3
wh ., mn .
2 .42
−2H2O, 300
0 .00010418°
78 .00
nitrate
Al(NO3)3⋅9H2O
rhb ., delq .
73
d . 134
v . s .
375 .13
4atm .
25 °
nitride
Al2N2
yel ., hex .
3 .05 4
2150
d . >1400
d . slowly
81 .98
oxide
Al2O3
col ., hex ., 1 .67–8
3 .99
1999 to 2032
i .
101 .96
oxide (corundum)
Al2O3
wh ., trig ., 1 .768
4 .00
1999 to 2032
2210
i .
101 .96
phosphate
AlPO4
col ., hex .
2 .59
i .
121 .95
∗By N . A . Lange, Ph .D ., Handbook Publishers, Inc ., Sandusky, Ohio . Abridged from table of Physical Constants of Inorganic Compounds in Lange’s Handbook of Chemistry.
Hot water
i .
d .
Other reagents
s . HCl, H2SO4, alk .
s . d .
s .a .; i . NH4 salts
s .al ., act ., CS2
s . al ., CS2
s . a .; i . act .
s . et ., chl ., CCl4; i . bz .
v . s .
50 al .; s . et .
s .
sl . s .
i .
v . s . d .
i .
i .
i .
s . a ., alk .; i . a .
s . al ., CS2
s . alk . d .
v . sl . s . a ., alk .
v . sl . s . a ., alk .
s . a ., alk .; i . ac .
(Continued )
2-5
2-6
TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Aluminum (Cont.)
potassium silicate (muscovite)
potassium silicate (orthoclase)
Aluminum potassium tartrate
sodium fluoride (cryolite)
sodium silicate
sulfate
Alum, ammonium (tschermigite)
ammonium chrome
Formula
Formula
weight
3Al2O3⋅K2O⋅6SiO2⋅2H2O
Al2O3⋅K2O⋅6SiO2
AlK(C4H4O6)2
AlF3⋅3NaF
Al2O3⋅Na2O⋅6SiO2
Al2(SO4)3
Al2(SO4)3⋅(NH4)2SO4⋅
24H2O
Cr2(SO4)3⋅(NH4)2SO4⋅
24H2O
Fe2(SO4)3⋅(NH4)2SO4⋅
24H2O
Al2(SO4)3⋅K2SO4⋅24H2O
Cr2(SO4)3⋅K2SO4⋅24H2O
Al2(SO4)3⋅Na2SO4⋅24H2O
NH3
796 .61
556 .66
362 .22
209 .94
524 .44
342 .15
906 .66
956 .69
Color, crystalline form,
and refractive index
mn., 1.590
col., mn., 1.524
col.
wh., mn., 1.3389
col., tri., 1.529
wh. cr.
col., oct., 1.4594
gn . or vl ., oct ., 1 .4842
Specific
gravity
Melting
point, °C
2.9
2.56
d.
1450 (1150)
2.90
2.61
2.71
1.64 204°
1000
1100
d. 770
93.5
1 .72
Boiling
point, °C
−20H2O, 120;
−24H2O, 200
100 d .
vl ., oct ., 1 .485
1 .71
40
948 .78
998 .81
916 .56
17 .03
col ., mn ., 1 .4564
red or gn ., cb ., 1 .4814
col ., oct ., 1 .4388
col . gas, 1 .325 (lq .)
92
89
61
−77 .7
−18H2O, 64 .5
77 .08
337 .09
79 .06
97 .94
114 .10
157 .13
wh ., hyg . cr .
pl .
mn . or rhb ., 1 .5358
col ., cb ., 1 .7108
col . pl .
wh . cr .
114
d . 200
d . 35–60
subl . 542
d . 58
subl .
d .
272 .21
wh .
chloride (salammoniac)
chloroplatinate
chloroplatinite
chlorostannate
chromate
cyanide
dichromate
ferrocyanide
fluoride
fluoride, acid
formate
NH4C2H3O2
NH4CN⋅Au(CN)3⋅H2O
NH4HCO3
NH4Br
(NH4)2CO3⋅H2O
NH4HCO3⋅
NH2CO2NH4‡
(NH4)2CO3⋅
2NH4HCO3⋅H2O
NH4Cl
(NH4)2PtCl6
(NH4)2PtCl4
(NH4)2SnCl6
(NH4)2CrO4
NH4CN
(NH4)2Cr2O7
(NH4)4Fe(CN)6⋅6H2O
NH4F
NH4F⋅HF
HCO2NH4
1 .76 264°
1 .83
1 .675 204°
0 .817−79°
0 .5971 (A)
1 .073
53 .49
443 .87
372 .97
367 .50
152 .07
44 .06
252 .06
392 .19
37 .04
57 .04
63 .06
wh ., cb ., 1 .639, 1 .6426
yel ., cb .
tet .
pink ., cb .
yel ., mn .
col ., cb .
or ., mn .
mn .
wh ., hex .
wh ., rhb ., 1 .390
col ., mn ., delq .
hydrosulfide
hydroxide
molybdate
molybdate, heptanitrate (α), stable −16° to 32°
nitrate (β), stable 32° to 84°
NH4HS
NH4OH
(NH4)2MoO4
(NH4)6Mo7O24⋅4H2O‡
NH4NO3
NH4NO3
51 .11
35 .05
196 .01
1235 .86
80 .04
80 .04
col ., rhb .
in soln . only
mn .
col ., mn .
col ., tet ., 1 .611
col ., rhb . or mn .
nitrite
osmochloride
oxalate
oxalate, acid
perchlorate
persulfate
phosphate, monobasic
phosphate, dibasic
phosphate, meta-
NH4NO2
(NH4)2OsCl6
(NH4)2C2O4⋅H2O
NH4HC2O4⋅H2O
NH4ClO4
(NH4)2S2O8
NH4H2PO4
(NH4)2HPO4
(NH4)4P4O12
64 .04
439 .02
142 .11
125 .08
117 .49
228 .20
115 .03
132 .06
388 .04
wh . nd .
cb .
col ., rhb .
col ., trimetric
col ., rhb ., 1 .4833
wh ., mn ., 1 .5016
col ., tet ., 1 .5246
col ., mn ., 1 .53
col ., mn .
potassium (kalinite)
potassium chrome
sodium
Ammonia†
Ammonium acetate
auricyanide
bicarbonate
bromide
carbonate
carbonate, carbamate
carbonate, sesqui-
1 .573
2 .327 154°
124
−33 .4
d .
1 .5317°
3 .065
2 .4
1 .91712°
0 .79100° (A)
2 .15
2 .21 1212°
1 .266
d . 350
d .
d .
d .
2 .27
subl . 520
d . 180
36
d . 185
d .
114–116
d . 180; subl .
in vac .
subl . 120
d .
25 °
4
25 °
4
1 .66
1 .725
169 .6
1 .69
2 .93 204°
1 .501
1 .556
1 .95
1 .98
1 .803 194°
1 .619
2 .21
expl .
i.
i.
s.
sl. s.
i.
31.30°
3.90°
21 .2
964 .38
ammonium iron
Solubility in 100 parts
Cold water
d . 210
d . 210
s.
i.
89100°
∞ 100°
25°
Other reagents
i. HCl
d. a.
i . al .
s . al .
25°
i . al .
5 .70°
20
106 .40°
89 .90°
∞93°
50
121 .745°
7 .496°
1484°
s .
11 .90°
6810°
10015°
2515°
v . s .
2730°
145 .6100°
2015°
5049°
29 .40°
0 .715°
s .
33 .315°
40 .530°
s .
47 .230°
s .
v . s .
v . s .
1020°
77 .3100°
1 .25100°
v . s .
s . NH3; sl . s . al ., m . al .
0 .005 al .
d .
v . s .
v . s .
d .
sl . s . act ., NH3; i . al .
s . al .
s . al .; i . act .
i . al .
s . al .; i . NH3
53180°
s . al .
v . s .
s .
d .
4425°
118 .30°
365 .835°
s .
6765°
2 .5
s .
10 .90°
58 .20°
22 .70°
13115°
s .
i . al .
i . al .
14 .820° al .; s . et .
s . al .; sl . s . act .
i . al .
i . al .
s . al ., et ., act .
i . al ., CS2, NH3
s . al .
d .
i . al ., NH3
i . al .
30°
241 .8
58080°
d .
0°
d .
d .
d . 120
Hot water
11 .850°
100°
46 .9
d .
173 .2100°
3 .820° al ., 17 .120° m . al .;
v . s . NH3
s . al .
sl . s . al .; i . NH3
220° al .; s . act .; i . et .
i . ac .
i . act .
Ammonium phosphomolybdate
silicofluoride
sulfamate
sulfate (mascagnite)
sulfate, acid
sulfide
sulfide, pentasulfite
sulfite, acid
tartrate
thiocyanate
vanadate, metaAntimony
chloride, tri- (butter of
antimony)∗
oxide, tri- (valentinite)
oxide, tri- (senarmontite)
sulfide, tri- (stibnite)
(NH4)3PO4⋅12MoO3⋅
3H2O (?)
(NH4)2SiF6
NH4⋅SO3NH2
(NH4)2SO4
NH4HSO4
(NH4)2S
(NH4)2S5
(NH4)2SO3⋅H2O
NH4HSO3
(NH4)2C4H4O6
NH4CNS
NH4VO3
Sb
1930 .39
178 .15
114 .12
132 .14
115 .11
68 .14
196 .40
134 .16
99 .11
184 .15
76 .12
116 .98
121 .76
yel.
cb., 1.3696
col. pl.
col., rhb., 1.5230
col., rhb., 1.480
yel.-wh.
or.-red pr.
col., mn.
rhb.
col., mn.
col., mn., 1.685±
col. cr.
tin wh., trig.
d.
0.0315°
i.
s. alk.; i. al., HNO3
55.5
35750°
103.3100°
s. al.; i. act.
8760°
17020°
3.0570°
i.
1.769 204°
1.78
132
235 d.
146.9
d.
1.41
2.03 124°
1.60
1.305
2.326
6.68425°
d.
d.
d.
149.6
d.
630.5
1380
18.517.5°
1340°
70.60°
100
v. s.
s.
10012°
s.
450°
1200°
0.4418°
i.
73.4
220.2
601.60°
∞72°
656
652
550
1570
2.01
SbCl3
228 .12
col., rhb., delq.
3.14
Sb2O3
Sb2O3
Sb2S3
291 .52
291 .52
339 .72
rhb ., 2 .35
cb ., 2 .087
bk ., rhb ., 4 .046
5 .67
5 .2
4 .64
20 °
4
0°
subl.
d. 160
490
d. 170
i. al., act., CS2
v. sl. s. al.; i. act.
12025° NH3
i. al., act.
sl. s. al.
s. al., act., NH3, SO2
i. al., NH4Cl
s. aq. reg., h. conc.
H2SO4
s . al ., HCl, HBr,
H2C4H4O6
s . HCl, KOH, H2C4H4O6
v . sl . s .
sl . s .
0 .0001718°
d .
−2S, 135
629
i .
i .
5 .268 .7°
d .
i .
5 .60° cc
35 .7100°
d .
d .
2 .2350° cc
s . gly .; i . al .
s . HCl; alk ., NH4HS,
K2S; i . ac .
s . HCl, alk ., NH4HS
sulfide, pentatelluride, triAntimonyl potassium tartrate
(tartar emetic)
sulfate, normal
sulfate, basic
Argon
Sb2S5
Sb2Te3
403 .85
626 .32
golden
gray
4 .120
(SbO)KC4H4O6⋅½H2O
(SbO)2SO4
(SbO)2SO4⋅Sb2(OH)4
Ar
333 .94
371 .58
683 .20
39 .95
wh ., rhb .
wh . pd .
wh . pd .
col . gas
2 .60
4 .89
−½H2O, 100
−189 .2
−185 .7
Arsenic (crystalline) (α)
Arsenic (black) (β)
As4
As4
299 .69
299 .69
met ., hex .
bk ., amor .
1 .65−288°;
1 .402−185 .7°;
1 .38 (A)
5 .72714°
4 .720°
81436atm .
subl . 615
i .
i .
i .
i .
s . HNO3
s . HNO3, aq . reg .,
aq . Cl2, h . alk .
Arsenic (yellow) (γ)
acid, orthoacid, metaacid, pyropentoxide
sulfide, di- (realgar)
As4
H3AsO4⋅½H2O
HAsO3
H4As2O7
As2O5
As2S2
299 .69
150 .95
123 .93
265 .87
229 .84
213 .97
yel ., cb .
col ., hyg .
wh ., hyg .
col .
wh ., amor .
red, mn ., 2 .68
−H2O, 160
50
H3AsO4
H3AsO4
76 .7100°
d .
s . alk .
d .
565
16 .7
d . to form
d . to form
59 .50°
i .
s . alk ., al .
s . K2S, NaHCO3
sulfide, pentaArsenious chloride (butter of
arsenic)
hydride (arsine)
oxide (arsenolite)
oxide (claudetite)
oxide
As2S5
AsCl3
310 .17
181 .28
d . 500
130
0 .0001360°
d .
i .
d .
s . HNO3, alk .
s . HCl, HBr, PCl3
AsH3
As2O3
As2O3
As2O3
−55; d . 230
20 cc
sl . s .
sl . s .
1 .210°
sl . s .
sl . s .
sl . s .
2 .9340°
Auric chloride
cyanide
Aurous chloride
cyanide
Cf. also under Gold
Barium
acetate
acetate
bromide
∗Usually the solution .
†
See special tables .
‡
Usual commercial form .
sl . s . alk .
i . al ., et .
i . al ., et .
s . HCl, alk ., Na2CO3;
i . al ., et .
s . HCl, al ., et .; sl . s .
NH3
s . al .
s . HCl, HBr; d . al .
s . KCN; i . al ., et .
Ba
Ba(C2H3O2)2
Ba(C2H3O2)2⋅H2O
BaBr2
2 .020°
2 .0–2 .5
d . 358
35 .5
d .
d . 206
4 .086
(α)3 .50619°;
(β)3 .25419°
(α)tr . 267;
(β)307
yel .
oily lq .
lq . 2 .163
−18
77 .95
197 .84
197 .84
197 .84
col . gas
col ., cb ., fibrous, 1 .755
col ., mn ., 1 .92
amor . or vitreous
2 .695 (A)
3 .865 254°
3 .85
3 .738
−113 .5
subl .
subl .
315
AuCl3⋅2H2O
339 .36
or . cr .
d .
v . s .
v . s .
Au(CN)3⋅6H2O
AuCl
AuCN
383 .11
232 .42
222 .98
yel . cr .
yel . cr .
7 .4
d . 50
AuCl3, 170
d .
d . 290
v . s .
d .
i .
v . s .
d .
i .
137 .33
255 .42
273 .43
297 .14
silv . met .
col .
wh ., tri . pr ., 1 .517
col .
3 .5
2 .468
2 .19
4 .781 244°
850
1140
−H2O, 41
847
d .
d .
58 .80°
7530°(anh .)
980°
d .
75 .0100°
7940°(anh .)
149100°
5 .1515° gly .
2425° cc al .
s . a .; d . al .
i . al .
v . s . m . al .; v . sl . s . act .
(Continued )
2-7
2-8
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Barium (Cont.)
bromide
carbonate (witherite)
carbonate (α)
carbonate (β)
Barium chlorate
chlorate
chloride
chloride
chloride
hydroxide
hydroxide
nitrate (nitrobarite)
oxalate
oxide
peroxide
peroxide
phosphate, monobasic
phosphate, dibasic
phosphate, tribasic
phosphate, pyrosilicofluoride
sulfate (barite, barytes)
sulfide, monosulfide, trisulfide, tetraBeryllium (glucinum)
Bismuth
carbonate, subchloride, dichloride, trinitrate
nitrate, suboxide, trioxide, trioxide, trioxychloride
Formula
Formula
weight
Color, crystalline form,
and refractive index
333.17
197.34
197.34
197.34
304.23
322.24
208.23
208.23
244.26
171.34
315.46
261.34
225.35
153.33
col., mn., 1.7266
wh., rhb., 1.676
wh., hex.
wh.
col.
col., mn., 1.577
col., mn., 1.7361
col., cb.
col., mn., 1.646
col., mn.
col., mn., 1.5017
col., cb., 1.572
wh. cr.
col., cb., 1.98
BaO2∗
BaO2⋅8H2O
BaH4(PO4)2
BaHPO4
Ba3(PO4)2
Ba2P2O7
BaSiF6
BaSO4
169.33
313.45
331.30
233.31
601.92
448.60
279.40
233.39
gray or wh. pd.
pearly sc.
tri.
wh., rhb. nd., 1.635
wh., cb.
wh., rhb.
pr.
col., rhb., 1.636
BaS
BaS3
BaS4⋅2H2O
Be(Gl)
Bi
169.39
233.52
301.62
9.01
208.98
Bi2O3⋅CO2⋅H2O
BiCl2
BiCl3∗
Bi(NO3)3⋅5H2O
BiONO3⋅H2O
Bi2O3
Bi2O3
Bi2O3
BiOCl
527.98
279.89
315.34
485.07
305.00
465.96
465.96
465.96
260.43
col., cb., 2.155
yel.-gn.
red, rhb.
gray, met., hex.
silv. wh. or reddish,
hex.
wh. pd.
bk. nd.
wh. cr.
col., tri.
hex. pl.
yel., rhb.
yel., tet.
yel., cb.
wh., amor.
6.86
4.86
4.75
2.82
4.92815°
8.9
8.55
8.20
7.7215°
d.
163
230
d. 30
d. 260
820
860
tr. 704
wh., tri.
1.43515°
185 d.
2.32
2.54
1.85
1.49
2300
2450
577
d.
d. 100
−7.2
61.83
H3BO3
Boron
carbide
oxide
oxide (sassolite)
Bromic acid
Bromine
B
B4C
B2O3
B2O3⋅3H2O
HBrO3
Br2
10.81
55.25
69.62
123.67
128.91
159.81
gray or bk., amor. or mn.
bk. cr.
col. glass, 1.459
tri., 1.456
col.; in soln. only
rhb., or red lq.
Br2⋅10H2O
Cd
Cd(C2H3O2)2
Cd(C2H3O2)2⋅2H2O∗
CdCO3
339.96
112.41
230.50
266.53
172.42
red, oct.
silv. met., hex.
col.
col., mn.
wh., trig.
chloride
Melting
point, °C
BaBr2⋅2H2O
BaCO3
BaCO3
BaCO3
Ba(ClO3)2
Ba(ClO3)2⋅H2O∗
BaCl2
BaCl2
BaCl2⋅2H2O†
Ba(OH)2
Ba(OH)2⋅8H2O
Ba(NO3)2
BaC2O4
BaO
Boric acid
hydrate
Cadmium
acetate
acetate
carbonate
Specific
gravity
CdCl2
183.32
wh., cb.
3.69
4.29
3.179
3.856 244°
3.097 244°
4.495
2.18816°
3.24428°
2.658
5.72
4.958
4°
2.9
4.16515°
4.116°
3.920°
4.27915°
4.49915°
4.2515°
2.98820°
1.816
9.8020°
3.11920°;
5.87 (A)
8.6520°
2.341
2.01
4.2584°
4.047
25 °
4
Boiling
point, °C
−2H2O, 100
tr. 811 to α
tr. 982 to β
174090 atm.
414
d. 120
tr. 925
962
−2H2O, 100
d.
d. 1450
77.9
592
−8H2O, 550
d.
1923
d. 400
d. 200
1284
271
d. 6.8
320.9
256
−H2O, 130
d. <500
568
Hot water
Other reagents
v. s.
0.002218°
v. s.
0.0065100°
s. al.
s. a.; i. al.
0.002218°
20.350°
s.
310°
0.0065100°
84.880°
s.
59100°
s. a.; i. al.
76.8100°
101.480°
2000±
39.30°
1.670°
5.615°
5.00°
0.00168°
1.50°
d.
d.
d.
tr. to mn. 1149
v. sl. s.
0.168
d.
0.015
i.
0.01
0.02617°
0.0001150°
2767
1450
d.
s.
4115°
i.
i.
d.
s.
v. s.
sl. s. d.
i.
i.
d.
d.
d.
i.
i.
i.
i.
sl. s.
i.
i.
i.
i.
i.
sl. s.
2.660°
40.2100°
i.
i.
1.10°
sl. s.
v. s.
4.220°
i.
i.
15.7100°
s.
d.
3.1330°
1560
1560
−O, 800
−8H2O, 100
1580 d.
Solubility in 100 parts
Cold water
d. 300
447
−5H2O, 80
1900±
2550
>3500
>1500
58.78
767
d.
960
s.
i.
v. s.
v. s.
i.
90
0°
34.2100°
0.002424°
90.880°
0.09100°
0.00028530°
i.
i.
147100°
sl. s. al., act.
sl. s. HCl, HNO3; i. al.
sl. s. HCl, HNO3; i. al.
v. sl. s. al.; i. et.
sl. s. a.; i. al.
s. a., NH4Cl; i. al.
s. HCl, HNO3, abs. al.;
i. NH3, act.
s. dil. a.; i. act.
s. dil. a.; i. al., et., act.
s. a.
s. a., NH4 salts
s. a.
s. a., NH4 salts
sl. s. HCl, NH4Cl; i. al.
s. conc. H2SO4; 0.006,
3% HCl
d. HCl; i. al.
i. al., CS2
s. dil. a., alk.
s. aq. reg., conc. H2SO4,
HNO3
s. a.
s. al.
4219° act.; s. a.; i. al.
s. a.
s. a.
s. a.
s. a.
s. a.; i. act., NH3,
H2C4H4O6
22.220° gly., 0.2425° et.;
s. al.
s. HNO3; i. al.
i. a.
s. a., al., gly.
s. al., et., alk., CS2
s. a., NH4NO3
s. m. al.
s. al.
s. a., KCN, NH4 salts;
i. NH3
1.5215° al.; i. et., act.
CdCl2 ⋅2½H2O
Cd(CN)2
Cd(OH)2
Cd(NO3)2
Cd(NO3)2⋅4H2O∗
CdO
CdO
Cd2O
CdSO4
CdSO4⋅H2O
3CdSO4⋅8H2O∗
CdSO4⋅4H2O
CdSO4⋅7H2O
CdS
Ca
Ca(C2H2O2)2⋅H2O
Ca(AlO2)2
CaO⋅Al2O3⋅2SiO2
Ca3(AsO4)2
CaBr2
CaCO3
CaCO3
CaCl2∗
CaCl2⋅H2O
CaCl2⋅6H2O
Ca3(C6H5O7)2⋅4H2O
CaCN2
Ca2Fe(CN)6⋅12H2O
CaF2
Ca(HCO2)2
CaH2
Ca(OH)2
Ca(ClO)2⋅4H2O
Ca2P2O6⋅2H2O
Ca(C3H5O3)2⋅5H2O
228 .36
164 .45
146 .43
236 .42
308 .48
128 .41
128 .41
240 .82
208 .47
226 .49
769 .54
280 .53
334 .58
144 .48
40 .08
176 .18
158 .04
278 .21
398 .07
199 .89
100 .09
100 .09
110 .98
129 .00
219 .08
570 .49
80 .10
508 .29
78 .07
130 .11
42 .09
74 .09
215 .04
274 .13
308 .29
col., mn., 1.6513
3.327
wh., trig.
col.
col. nd.
brn., cb.
brn., amor, 2.49
gn., amor.
rhb.
mn.
col., mn., 1.565
col.
mn.
yel.-or., hex., 2.506
silv. met., cb.
wh. nd.
col., rhb. or mn.
tri., 1.5832
wh. pd.
delq. nd.
col., rhb., 1.6809
col., hex., 1.550
wh., delq., cb, 1.52
col., delq.
col., trig., 1.417
col. nd.
col., rhombohedral
yel., tri., 1.5818
wh., cb., 1.4339
col., rhb.
wh. cr. or pd.
col., hex., 1.574
wh., feathery cr.
granular
col., eff.
4.79 154°
CaO⋅MgO⋅2CO2
CaO⋅MgO⋅2SiO2
Ca(NO3)2
Ca(NO3)2⋅4H2O∗
Ca3N2
Ca(NO2)2⋅H2O
CaC2O4
CaC2O4⋅H2O
CaO
184 .40
216 .55
164 .09
236 .15
148 .25
150 .10
128 .10
146 .11
56 .08
trig ., 1 .68174
wh ., mn .
col ., cb .
col ., mn ., 1 .498
brn . cr .
delq ., hex .
col ., cb .
col .
col ., cb ., 1 .837
peroxide
phosphate, monobasic
phosphate, dibasic
phosphate, tribasic
phosphate, metaphosphate, pyrophosphate, pyro- (brushite)
phosphide
silicate (α) (pseudowollastonite)
CaO2⋅8H2O
CaH4(PO4)2⋅H2O
CaHPO4⋅2H2O
Ca3(PO4)2
Ca(PO3)2
Ca2P2O7
Ca2P2O7⋅5H2O
Ca3P2
CaSiO3
216 .20
252 .07
172 .09
310 .18
198 .02
254 .10
344 .18
182 .18
116 .16
silicate (β) (wollastonite)
sulfate (anhydrite)
CaSiO3
CaSO4
116 .16
136 .14
pearly, tet .
wh ., tri .
wh ., mn . pl .
wh ., amor .
wh ., tet ., 1 .588
col ., biaxial, 1 .60
wh ., mn .
red cr .
col ., pseudo hex .,
1 .6150 or mn .
col ., mn ., 1 .610
col ., rhb ., 1 .576, or
mn ., 1 .50
chloride
cyanide
hydroxide
nitrate
nitrate
oxide
oxide
oxide, subCadmium sulfate
sulfate
sulfate
sulfate
sulfate
sulfide (greenockite)
Calcium
acetate
aluminate
aluminum silicate (anorthite)
arsenate
bromide
carbonate (aragonite)
carbonate (calcite)
chloride (hydrophilite)
chloride
chloride
citrate
cyanamide
ferrocyanide
fluoride ( fluorite)
formate
hydride
hydroxide
hypochlorite
hypophosphate
lactate
magnesium carbonate
(dolomite)
magnesium silicate (diopside)
nitrate (nitrocalcite)
nitrate
nitride
nitrite
oxalate
oxalate
oxide
∗Usual commercial form .
†
The solubility of CaCO3 in H2O is greatly increased by increasing the amount of CO2 in the H2O .
2.455 174°
8.15
6.95
8.192 184°
4.691 244°
3.78620°
3.09
3.05
2.48 204°
4.58
1.5520°
tr. 34
d. >200
d. 300
350
59.4
132
d. 900–1000
d.
1000
tr. 108
tr. 41.5
3.6720°
2.765
tr. 4
1750100atm.
810
d.
1600
1551
3.353 254°
2.93
2.711 254°
2.152 154°
760
d. 825
1339103atm.
772
>1600
29.92
−2H2O, 130
−6H2O, 200
−4H2O, 185
17°
1.68
1.7
3.18020°
2.015
1.7
2.2
2 .872
3 .3
2 .36
1 .82
2 .6317°
2 .2334°
2 .24°
2 .2
3 .32
2 .220 164°
2 .306 164°
3 .14
2 .82
3 .09
2 .25
2 .5115°
2 .905
2 .915
2 .96
subl. in N2, 980
1200 ± 30
1810
1330
d.
d. 675
−H2O, 580
d.
−2H2O, 200
−3H2O, 100
d . 730–760
1391
561
42 .7
900
d .
−H2O, 200
2570
−8H2O, 100
−H2O, 100
d .
1670
975
1230
2850
expl . 275
d . 200
32659.5°
i.
i.
60.8100°
s.
127.660°
s.
0.01325°
1250°
0.001220°†
0.001425°
59.50°
s.
v. s.
0.08518°
s. d.
s.
0.001618°
16.10°
d.
0.1850°
delq.; d.
i.
10.5
i.
312105°
0.002100°
0.002100°
347260°
s.
v. s.
0.09626°
d.
15090°
0.001726°
18.4100
0 .03218°
i .
1020°
2660°
d .
770°
0 .0006713°
i .
Forms
Ca(OH)2
sl . s .
0 .02
0 .0025
i .
i .
sl . s .
d .
0 .009517°
tr . 1193 to rhb .
180100°
76.50°
s.
114.20°
s.
350−5°
0.000001
d.
520°
d.
24 .5°
>1600
1540
tr . 1190 to α
1450(mn .)
16820°
0.024718°
0.0002625°
109.70°
2150°
i.
i.
0 .29820°
Colloidal
d.
45.580°
0.077100°
d.
∞
i .
376151°
v . s .
d .
41790°
0 .001495°
i .
d .
d .
0 .075100°
d .
i .
0 .1619100°
2.0515° m. al.
s. a.; NH4OH, KCN
s. a., NH4 salts; i. alk.
v. s. a.
s. al., NH3; i. HNO3
s. a., NH4 salts; i. alk.
s. a., NH4 salts; i. alk.
d. a., alk.
i.act., NH3
i. al.
i. al.
i. al.
s. a.; v. s. NH4OH
s, a.; sl. s. al.
sl. s. al.
s. HCl
s. dil. a.
s. al., act.; sl. s. NH3
s. a., NH4Cl
s. a., NH4Cl
s. al.
s. al.
s. al.
0.006518° al.
i. al.
sl. s. a.
i. al., et.
d. a.; i. bz.
s. NH4Cl
d. a.
s. HCl, H4P2O6
∞h . al .; i . et .
1415° al .; s . amyl al ., NH3
s . dil . a .; i . abs . al .
s . 90% al .
s . a .; i . ac .
s . a .; i . ac
s . a .; i . al .
s . a . d .; i . al ., et .
s . a .; i . al ., ac .
i . a .
s . a .
s . a .; i . NH4Cl
s . dil . a .; i . al ., et .
s . HCl
s . a ., Na2S2O3, NH4 salts
(Continued )
2-9
2-10
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Calcium (Cont.)
sulfate (gypsum)
Formula
Formula
weight
Color, crystalline form,
and refractive index
CaSO4⋅2H2O
172.17
col., mn., 1.5226
Ca(SH)2⋅6H2O
CaS
CaSO3⋅2H2O
CaC4H4O6⋅4H2O
Ca(CNS)2⋅3H2O
CaS2O3⋅6H2O
CaWO4
214.32
72.14
156.17
260.21
210.29
260.30
287.92
col. pr.
col., cb.
wh., cr., 1.595
col., rhb.
wh., delq. cr.
col., tri., 1.56
wh., tet., 1.9200
C
C
C
CO2
12.01
12.01
12.01
44.01
bk., amor.
col., cb., 2.4195
bk., hex.
col. gas
disulfide
CS2
76.14
col. lq.
monoxide
CO
28.01
col., poisonous,
odorless gas
poisonous gas
gas
sulfhydrate
sulfide (oldhamite)
sulfite
tartrate
thiocyanate
thiosulfate
tungstate (scheelite)
Carbon, cf. table of organic
compounds
Carbon, amorphous
Carbon, diamond
Carbon, graphite
dioxide
oxychloride (phosgene)
oxysulfide
suboxide
thionyl chloride
Ceric hydroxide
hydroxynitrate
oxide
sulfate
Cerium
COCl2
COS
C3O2
CSCl2
2CeO2⋅3H2O
Ce(OH)(NO3)3⋅3H2O
CeO2
Ce(SO4)2⋅4H2O
Ce
98.92
60.08
68.03
114.98
398.28
397.18
172.11
404.30
140.12
Cerous sulfate
sulfate
Cesium
Chloric acid
Chlorine
Ce2(SO4)3
Ce2(SO4)3⋅8H2O
Cs
HClO3⋅7H2O
Cl2
568.42
712.54
132.91
210.57
70.91
hydrate
Chloroplatinic acid
Chlorostannic acid
Chlorosulfonic acid
Chromic acetate
chloride
chloride
fluoride
hydroxide
Cl2⋅8H2O
H2PtCl6⋅6H2O
H2SnCl6⋅6H2O
HO⋅SO2⋅Cl
Cr2(C2H3O2)6⋅2H2O
CrCl3
CrCl3⋅6H2O∗
CrF3
Cr(OH)3
215.03
517.90
441.54
116.52
494.29
158.36
266.45
108.99
103.02
Cr(OH)3⋅2H2O
Cr(NO3)3⋅9H2O∗
Cr(NO3)3⋅7½H2O
Cr2O3
Cr2(SO4)3
Cr2(SO4)3⋅5H2O
Cr2(SO4)3⋅15H2O
Cr2(SO4)3⋅18H2O
Cr2S3
139.05
400.15
373.13
151.99
392.18
482.26
662.41
716.46
200.19
hydroxide
nitrate
nitrate
oxide
sulfate
sulfate
sulfate
sulfate
sulfide
gas
yel.-red lq.
yel., gelatinous
red, mn.
wh. or pa. yel., cb.
yel., rhb.
steel gray, cb. or
hex.
wh., mn. or rhb.
tri.
silv. met., hex.
lq.
rhb., or gn.-yel. gas
rhb.
red-brn., delq.
delq.
col. lq.
gn.
pink, trig.
vl. or gn., hex. pl.
gn., rhb.
gn. or blue,
gelatinous
gn.
purple pr.
purple, mn.
dark gn., hex.
rose pd.
gn.
vl.
vl., cb., 1.564
brn.-bk. pd.
Specific
gravity
2.32
2.815°
Melting
point, °C
−1½H2O, 128
Boiling
point, °C
−2H2O, 163
d. 15
−2H2O, 100
d.
d. 650
Solubility in 100 parts
Cold water
Hot water
0.2230°
0.25750°
v. s.
d.
0.004318°
0.0370°
s.
71.29°
0.2
v. s.
d.
0.002790°
0.2285°
v. s.
d.
Other reagents
s. a., gly., Na2S2O3,
NH4 salts
s. al.
s. a.
s. H2SO3
sl. s. al.
v. s. al.
i. al.
s. NH4Cl; i. a.
1.87316°
6.06
d.
1.8–2.1
3.5120°
2.2620°
lq. 1.101−87°;
1.53 (A);
solid 1.56−79°
lq. 1.261 2220° ;
2.63 (A)
°
lq. 0.814 −195
4 ;
0.968 (A)
1.392 194°
lq. 1.24−87°;
2.10 (A)
lq. 1.1140°
1.50915°
>3500
>3500
>3500
−56.65.2atm.
4200
4200
4200
subl. −78.5
i.
i.
i.
179.70° cc
i.
i.
i.
90.120° cc
i. a., alk.
i. a., alk.
i. a., alk.
s. a., alk.
−108.6
46.3
0.20°
0.01450°
s. al.; et.
−207
−192
0.00440°;
3.50° cc
v. s. sl. d.
1330° cc
0.001850°
2.3220° cc
d.
40.330° cc
s. al., Cu2Cl2
7.3
3.91
6.920° cb.;
6.7 hex.
3.91
2.88617°
1.9020°
1.28214.2°
lq. 1.56−33.6°;
2.490° (A)
1.23
2.431
1.97128°
1.78725°
2.75715°
1.835 254°
3.8
5.21
3.012
1.86717°
1.722°
3.7719°
756mm
−104
−138.2
8.2
−50.2760mm
−107
7761mm
73.5
1950
645
1400
d.
s. et.
s. a.; sl. s. alk. carb.; i. alk
d.
i.
s. d.
i.
i.
0°
−8H2O, 630
28.5
<−20
−101.6
d. 9.6
60
19.2
−80
subl. 83
>1000
−2H2O, 100
36.5
100
1900
100
−S, 1350
670
d. 40
−34.6
151.5765mm
1200–1500 d.
d.
d. 100
d.
−10H2O, 100
−12H2O, 100
s. ac., CCl4, bs.; d.a.
v. s. alk., al.
18.98
250°
d.
v. s.
1.460°;
31010° cc
s.
v. s.
s.
d.
s.
i.§
v. s. d.
i.
i.
i.
s.
s.
i.
i.†
s.
s.
12020°
i.
Slowly
oxidized
0.4100°
7.640°
30°
0.57 ;
17730° cc
v. s.
sl. s.
i.
s.
s.
i.
d. 67°
d.
d.
s. H2SO4, HCl
s. dil. H2SO4
s. dil. a.; i. al.
s. a., al., NH3
s. alk.
s. alk.
s. al., et.
d. al.; i. CS2
4.7615° m. al.
i. a., act., CS2
s. al.; i. et.
sl. s. a.; i. al., NH3
s. a., alk.; sl. s. NH3
s. a., alk.
s. a., alk., al., act.
sl. s. a.
i. a.
s. al., H2SO4
sl. s. al.
s. al.
s. h. HNO3
Chromium
trioxide (chromic acid)
Chromous chloride
hydroxide
oxide
sulfate
sulfide (daubrelite)
Chromyl chloride
Cobalt
carbonyl
sulfide, diCobaltic chloride
chloride, dichro
chloride, luteo
chloride, praseo
Cobaltic chloride, purpureo
chloride, roseo
hydroxide
oxide
sulfate
sulfide
Cobalto-cobaltic oxide
Cobaltous acetate
chloride
chloride
nitrate
oxide
sulfate
sulfate
sulfate (biebeorite)
sulfide (syeporite)
Copper
Cupric
acetate
aceto-arsenite (Paris green)
ammonium chloride
Cr
52 .00
CrO3
CrCl2
Cr(OH)2
CrO
CrSO4⋅7H2O
CrS
CrO2Cl2
Co
Co(CO)4
CoS2
CoCl3
Co(NH3)3Cl3⋅H2O
Co(NH3)6Cl3
Co(NH3)4Cl3⋅H2O
Co(NH3)5Cl3
Co(NH3)5Cl3⋅H2O
Co(OH)3
Co2O3
Co2(SO4)3
Co2S3
Co3O4
Co(C2H3O2)2⋅4H2O
CoCl2
CoCl2⋅6H2O∗
Co(NO3)2⋅6H2O
99 .99
122 .90
86 .01
68 .00
274 .17
84 .06
154 .90
58 .93
170 .97
123 .06
165 .29
234 .40
267 .48
251 .43
250 .44
268 .46
109 .96
165 .86
406 .05
214 .06
240 .80
249 .08
129 .84
237 .93
291 .03
CoO
CoSO4
CoSO4⋅H2O
74 .93
155 .00
173 .01
CoSO4⋅7H2O∗
CoS
Cu
Cu(C2H3O2)2
Cu(C2H3O2)2⋅H2O
(CuOAs2O3)3⋅
Cu(C2H3O2)2∗
CuCl2⋅2NH4Cl⋅2H2O
281 .10
91 .00
63 .55
181 .63
199 .65
1013 .79
gray, met., cb.
red, rhb.
wh., delq.
yel.-brn.
bk. pd.
blue
bk. pd.
dark red lq.
silv. met., cb.
or. cr.
bk., cb.
red cr.
7.1
1615
2.70
2.75
197 d.
3.97
1.92
8.920°
1.7318°
4.269
2.94
1550
−96.5
1480
51
subl.
brn., cb.
red pd.
red pd., mn.(?),
1.639
red, mn., 1.483
brn. nd.
yel.-red met., cb.
5.18
d. 100
−1½H2O, 100
d. 900
4.8
6.07
1.705318.7°
3.356
1.924 2525°
1.883 2525°
−4H2O, 140
subl.
86
<100
5.68
3.71025°
3.13
d. 1800
d. 880
d.
1.948 2525°
5.4518°
8.9220°
1.930 204°
1.882
96.8
>1100
1083
−7H2O, 420
115
240 d.
1.98
d. 110
ammonium sulfate
carbonate, basic (azurite)
CuSO4⋅4NH3⋅H2O
2CuCO3⋅Cu(OH)2
245 .75
344 .67
blue, tet., 1.670,
1.744
blue, rhb.
blue, mn., 1.758
carbonate, basic (malachite)
chloride (eriochalcite)
CuCO3⋅Cu(OH)2
CuCl2
221 .12
134 .45
dark gn., mn., 1.875
brn.-yel. pd.
3.9
3.054
d.
498
chloride
chromate, basic
cyanide
dichromate
ferricyanide
ferrocyanide
formate
hydroxide
lactate
nitrate
nitrate
∗Usual commercial form .
†
Also a soluble modification .
CuCl2⋅2H2O
CuCrO4⋅2CuO⋅2H2O
Cu(CN)2
CuCr2O7⋅2H2O
Cu3[Fe(CN)6]2
Cu2Fe(CN)6⋅7H2O
Cu(HCO2)2
Cu(OH)2
Cu(C3H5O3)2⋅2H2O
Cu(NO3)2⋅3H2O∗
Cu(NO3)2⋅6H2O
170 .48
374 .66
115 .58
315 .56
614 .54
465 .15
153 .58
97 .56
277 .72
241 .60
295 .65
gn., rhb., 1.684
yel.-brn.
yel.-gn.
bk., tri.
yel.-gn.
red-brn.
blue, mn.
blue, gelatinous
dark blue, mn.
blue, delq.
blue, rhb.
2.3922.4°
−2H2O, 110
−2H2O, 260
d.
−2H2O, 100
277 .47
117.6
2900
d. 52
20°
1.7016
1.847
1.819 2525°
1.81
3.88
d. 150
d. 220
2.28618°
1.831
3.368
2.047
2.074
1049
−6H2O, 110
d.
114.5
−3H2O, 26.4
i.
164.9
v. s.
d.
i.
12.350°
i.
d.
i.
i.
i.
s.
s.
4.260°
v. s.
0.2320°
16.120°
i.
i.
d.
i.
i.
s.
457°
116.50°
84.030°(anh.)
i.
25.60°
s.
2300
3380°
0.0003818°
i.
s.
7.2
i.
33.80°
18.05
i.
Forms Cu2Cl2
993
d.
−H2O
3.9°
i.
0°
d.
or., mn.
gn., rhb.
rhb.
brick red
bk.
bk.
blue cr.
bk. cr.
bk., cb.
red-vl., mn., 1.542
blue cr.
red, mn.
red, mn., 1.4
dark gn., mn.
gn.
2200
−HNO3, 170
21.5°
206.7
v. s.
100°
i.
i.
d.
s.
12.7446.5°
1.03146.5°
24.8716°
i.
i.
i.
s.
10596°
17780°
334.990°
(anh.)
i.
83100°
s.
s.
i.
s. HCl, dil. H2SO4;
i. HNO3
s. H2SO4, al., et.
sl. s. al.; i. et.
s. conc. a.
i. dil. HNO3
sl. s. al.
v. s. a.
s. et.
s. a.
s. al., et., CS2
s. HNO3, aq. reg.
s. a.; al.
i. al., NH4OH
s. a.; i. al.
i. al.
sl. s. HCl
s. a.; i. al.
s. a.
s. H2SO4
d. a.
s. H2SO4; i. HCl, HNO3
s. a., al.
31 al.; 8.6 act.
v. s. et., act.
10012.5° al.; s. act.;
sl. s. NH3
s. a., NH4OH; i. al.
1.0418° m. al.; i. NH8
2.58° al.
s. a., aq. reg.
s. HNO3, h. H2SO4
20
7 al.; s. et.; gly.
s. a., NH4OH
99.380°
s. a.
d.
d.
i. al.
s. NH4OH, h. aq.
NaHCO3
s. KCN; 0.03 aq. CO
5315° al.; 6815° m. al.
i.
70.70°
d.
107.9100°
110.40°
i.
i.
sl. s.
i.
i.
12.5
i.
16.7
38140°
243.70°
192.4100°
d.
i.
d.
d.
45100°
66680°
∞
s. al.; et., NH4Cl
s. HNO3, NH4OH
s. KCN, C5H5N
s. a.; NH4OH
s. NH4OH; i. HCl
s. NH4OH; i. a., NH8
0.25 al.
s. a., NH4OH, KCN, al.
sl. s. al.
10012.5° al.
s . al .
(Continued )
2-11
2-12
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Formula
Formula
weight
Color, crystalline form,
and refractive index
Cupric (Cont.)
oxide (paramelaconite)
oxide (tenorite)
oxychloride
phosphide
sulfate (hydrocyanite)
sulfate (blue vitriol or
chalcanthite)
sulfide (covellite)
tartate
Cuprous ammonium iodide
carbonate
chloride (nantokite)
cyanide
CuO
CuO
CuCl2⋅2CuO⋅4H2O
Cu3P2
CuSO4
79 .55
79 .55
365 .60
252 .59
159 .61
CuSO4⋅5H2O∗
CuS
CuC4H4O6⋅3H2O
CuI⋅NH4I⋅H2O
Cu2CO3
Cu2Cl2
Cu2(CN)2
249 .69
95 .61
265 .66
353 .41
187 .10
198 .00
179 .13
bk., cb.
bk., tri., 2.63
blue-gn.
bk.
gn.-wh., rhb.,
1.733
blue, tri., 1.5368
blue, hex. or mn., 1.45
1 gn. pd.
rhb. pl.
yel.
wh., cb., 1.973
wh., mn.
ferricyanide
ferrocyanide
fluoride
hydroxide
oxide (cuprite)
Cuprous phosphide
sulfide (chalcocite)
sulfide
Cyanogen
Cu3Fe(CN)6
Cu4Fe(CN)6
Cu2F2
CuOH
Cu2O
Cu6P2
Cu2S
Cu2S
C2N2
402 .59
466 .13
165 .09
80 .55
143 .09
443 .22
159 .16
159 .16
52 .03
brn.-red
brn.-red
red cr.
yel.
red, cb., 2.705
gray-bk.
bk., rhb.
bk., cb.
poisonous gas
Fe(OH)(C2H3O2)2
190 .94
brn., amor.
Cyanogen compounds, cf. table
of organic compounds
Ferric acetate, basic
ammonium sulfate, cf. Alum
chloride (molysite)
chloride
ferrocyanide (Prussian blue)
hydroxide
lactate
nitrate
oxide (hematite)
sulfate
sulfate (coquimbite)
Ferroso-ferric chloride
ferricyanide (Prussian green)
oxide (magnetite;
magnetic iron oxide)
oxide, hydrated
Ferrous ammonium sulfate
FeCl3
FeCl3⋅6H2O∗
Fe4[Fe(CN)6]3
162 .20
270 .30
859 .23
bk.-brn., hex. delq.
red-yel., delq.
dark blue
Fe(OH)3
Fe(C3H5O3)3
Fe(NO3)3⋅6H2O
Fe2O3
106 .87
323 .06
349 .95
159 .69
red-brn .
brn ., amor ., delq .
rhb ., delq .
red or bk ., trig .,
3 .042
rhb ., 1 .814
yel ., trig .
yel ., delq .
gn .
bk ., cb ., 2 .42
Fe2(SO4)3
Fe2(SO4)3⋅9H2O
FeCl2⋅2FeCl3⋅18H2O
Fe4Fe3[Fe(CN)6]6
Fe3O4
399 .88
562 .02
775 .43
1662 .61
231 .53
303 .59
392 .14
chloride (lawrencite)
Fe3O4⋅4H2O
FeSO4⋅(NH4)2SO4⋅
6H2O
FeCl2
chloroplatinate
ferricyanide (Turnbull’s blue)
ferrocyanide
formate
hydroxide
nitrate
oxide
FePtCl6⋅6H2O
Fe3[Fe(CN)6]2
Fe2Fe(CN)6
Fe(HCO2)2⋅2H2O
Fe(OH)2
Fe(NO3)2⋅6H2O
FeO
571 .73
591 .43
323 .64
181 .91
89 .86
287 .95
71 .84
126 .75
bk .
blue-gn ., mn .,
1 .4915
gn .-yel ., hex .,
1 .567
yel ., hex .
dark blue
blue-wh ., amor .
Specific
gravity
6.40
6.45
6.35
3.60615°
Melting
point, °C
d. 1026
d. 1026
−3H2O, 140
d.
d. >600
°
2.286 15.6
4
4.6
−4H2O, 110
tr. 103
d.
4.4
3.53
2.9
d.
422
474.5
3.4
6.0
6.4 to 6.8
5.6
5.80
lq. 0.866−17.2°;
1.806 (A)
908
−½H2O, 360
1235
1100
1130
−34.4
Forms CuO,
650
−5H2O, 250
d. 220
1366
d.
subl. 1100
−O, 1800
−20.5
Solubility in 100 parts
Cold water
i.
i.
i.
i.
14.30°
24.30°
0.00003318°
0.0215°
d.
i.
1.5225°
i.
i.
i.
i.
i.
i.
i.
0.000518°
0.000518°
45020° cc
Hot water
i.
i.
75.4100°
205100°
0.1485°
i.
i.
i.
i.
i.
11°
2.804
282
37
d .
3 .4 to 3 .9
−1½H2O, 500
1 .68420°
5 .12
35
1560 d .
3 .09718°
2 .1
d . 480
315
280
d .
Other reagents
s. a.; KCN, NH4Cl
s. a., KCN, NH4Cl
s. a.
s. HNO3; i. HCl
i. al.
1.18° al.
s. HNO3, KCN
s. a., KOH
s. NH4I
s. a., NH4OH
s. HCl, NH4OH, al.
s. KCN, HCl, NH4OH;
sl. s. NH3
s. NH4OH; i. HCl
s. NH4OH; i. NH4Cl
s. HF, HCl, HNO3; i. al.
s. a., NH4OH
s. HCl, NH4Cl, NH4OH
s. HNO3; i. HCl
s. HNO3, NH4OH; i. act.
s. HNO3, NH4OH; i. act.
230020° cc al.; 50018° cc et.
s. a.; al.
0°
100°
74.4
2460°
i .
535.8
∞
d .
v. s. al.; et. +HCl
s . al ., act ., gly .
s . HCl, conc . H2SO4;
i . al ., et .
s . a .; i . al ., et .
i . et .
s . al ., act .
s . HCl
i .
v . s .
1500°
i .
i .
v . s .
∞
d .
d .
s .
i .
s . d . h . HCl
i . al .
5 .2
d . 50
d . 180
1538 d .
sl . s .
440
s .
i .
i .
1 .864
d .
d .
i .
180°
i .
10075°
s . a .
i . al .
64 .410°
105 .7100°
100 al .; s . act .; i . et .
v . s .
i .
i .
sl . s .
0 .00067
2000°
i .
v . s .
2 .7
delq .
2 .714
d .
d .
lt . gn .
cr .
bk .
Boiling
point, °C
3 .4
5 .7
60 .5
1420
i . H2SO4, NH3
s . abs . al .
i . dil . a ., al .
30025°
i .
s . a ., NH4Cl
s . a .; i . alk .
phosphate (vivianite)
Fe3(PO4)2⋅8H2O
501 .60
silicate
sulfate (siderotilate)
sulfate (copperas)
sulfide
cf. also under iron
Fluoboric acid
Fluorine
FeSiO3
FeSO4⋅5H2O
FeSO4⋅7H2O∗
FeS
131 .93
241 .98
278 .01
87 .91
HBF4
F2
87 .81
38 .00
Fluosilicic acid
Gadolinium
Gallium bromide
Glucinum cf. Beryllium
Gold
Gold, colloidal
Gold salts cf. under Auric
and Aurous
Hafnium
Helium
Hydrazine
formate
hydrate
hydrochloride
hydrochloride, dinitrate
nitrate, disulfate
sulfate
Hydrazoic acid (azoimide)
Hydriodic acid
Hydriodic acid
Hydriodic acid
Hydriodic acid
Hydriodic acid
Hydrobromic acid
Hydrobromic acid
H2SiF6
Gd
GaBr3
144 .09
157 .25
309 .44
delq . cr .
Au
Au
196 .97
196 .97
yel . met ., cb .
blue to vl .
19 .320°
1063
2600
Hf
He
N2H4
N2H4⋅2HCO2H
N2H4⋅H2O
N2H4⋅HCl
N2H4⋅2HCl
N2H4⋅HNO3
N2H4⋅2HNO3
N2H4⋅½H2SO4
N2H4⋅H2SO4
HN3
HI
HI⋅H2O
HI⋅2H2O
HI⋅3H2O
HI⋅4H2O
HBr
HBr⋅H2O
178 .49
4 .00
32 .05
124 .10
50 .06
68 .51
104 .97
95 .06
158 .07
81 .08
130 .12
43 .03
127 .91
145 .93
163 .94
181 .96
199 .97
80 .91
98 .93
hex .
col . gas
col . lq .
cb .
col .
yel . lq .
wh ., cb .
cr .
nd .
delq . pl .
rhb .
col . lq .
col . gas
col . lq .
col . lq .
col . lq .
col . lq .
col . gas; 1 .325 (lq .)
col . lq .
12 .1
0 .1368 (A)
1 .011 154°
>1700
<−272 .2
1 .4
128
−40
>3200(?)
−268 .9
113 .5
Hydrobromic acid
Hydrobromic acid
Hydrochloric acid
Hydrochloric acid
Hydrochloric acid
Hydrochloric acid
Hydrocyanic acid (prussic acid)
HBr (47 .8% in H2O)
HBr⋅2H2O
HCl†
HCl (45 .2% in H2O)
HCl⋅2H2O
HCl⋅3H2O
HCN
80 .91
118 .96
36 .46
36 .46
72 .49
90 .51
27 .03
Hydrofluoric acid
Hydrofluoric acid
Hydrogen
HF
HF (35 .35% in H2O)
H2
20 .01
20 .01
2 .02
col . lq .
wh . cr .
col . gas; 1 .256 (lq .)
col . lq .
col . lq .
col . lq .
poisonous gas or
col . lq ., 1 .254
gas or col . lq .
col . lq .
col . gas or cb .
peroxide
selenide
sulfide
Hydroxylamine
hydrochloride
nitrate
sulfate
‡
H2O2
H2Se
H2S
NH2OH
NH2OH⋅HCl
NH2OH⋅HNO3
NH2OH⋅½H2SO4
∗Usual commercial form .
†
Usual commercial form about 31 percent .
‡
Usual commercial forms 3 or 30 percent .
34 .01
80 .98
34 .08
33 .03
69 .49
96 .04
82 .07
blue, mn., 1.592,
1.603
mn.
gn., tri., 1.536
blue-gn., mn.
bk., hex.
col. lq.
gn .-yel . gas
col . lq ., 1 .333
col . gas
col . gas
rhb ., delq .
col ., mn .
col . cr .
col ., mn .
2.58
3.5
2.2
1.89914.8°
4.84
lq . 1 .51−187°;
1 .3115° (A)
1 .0321°
1 .42
1 .378
4 .40° (A)
1 .715°
2 .710° (A)
1 .78
1 .486
2 .11−15°
1 .2680° (A)
1 .48
°
1 .46 −18.3
4
0 .69718°
0 .98813 .6°
1 .15
lq . 0 .0709−252 .7°
0 .06948 (A)
1 .438 204°
2 .12−42°
1 .1895 (A)
1 .3518°
1 .6717°
1550
i.
i.
s. a.; i. ac.
64
1193
−5H2O, 300
−7H2O, 300
d.
s.
32.80°
0.00061618°
s.
14950°
i. al.
i. al.
s. a.; i. NH3
130 d.
−187
∞
d .
∞
s . al .
−223
s .
s .
s .
s .
i .
s .
i .
s . aq . reg ., KCN; i . a .
s . aq . reg ., KCN; i . a .
0 .970° cc
∞
s .
∞
v . s .
s .
174 .910°
v . s .
v . s .
3 .05522°
∞
42,50010° cc
∞
∞
∞
∞
2210°
1 .0850° cc
∞
Absorbed by Pt
s . al .
∞
v . s .
v . s .
v . s .
∞ al .; i . et .
sl . s . al .
s . al .
198
70 .7
104
85
254
−80
−50 .8
−43
−48
−36 .5
−86
118 .5739 .5mm
subl . 140
d .
37
−35 .5
127774mm
−67
126
−11
−111
−15 .35
0
−24 .4
−14
−83
−35
−259 .1
−0 .89
−64
−82 .9
34
151
48
170 d .
27 .6560°
∞
v . s .
130100°
i . al .
v . sl . s . abs . al .
∞ al .
s . al .
∞ al .
s . al .
s . al .
s . al .
s . al .
Stable at −15 .5° and
1 atm ., and at −11 .3°
and 2 .5 atm .
s . al .
d .
d .
26
∞
s .
82 .30°
∞
∞
∞
∞
19 .4
120
−252 .7
∞ 0° to 19 .4°
v . s .
2 .10° cc
0 .8580° cc
sl . s . Fe, Pd, Pt
∞
3774° cc
4370° cc
s .
83 .317°
v . s .
32 .90°
27022 .5° cc
18640° cc
d .
v . s .
d .
68 .590°
s . a ., et .; i . petr . et
s . CS2, COCl2
9 .5415° cc al .; s . CS2
s . a ., al .
s . al .; i . et .
v . s . abs . al .
v . sl . s . al .; i . et ., abs . al .
−85
760mm
151 .4
−42
−59 .6
56 .522mm
d .
d . <100
s .
56 .160°
s . al ., et .
s . al .
s . al .
s . al .
∞ al ., et .
v . s .
(Continued )
2-13
2-14
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Formula
Hypobromous acid
Indium
Iodic acid
HBrO
In
HIO3
Iodine
oxide, pentaIodoplatinic acid
Iridium
Iron, cast†
pure
steel
white pig
wrought
carbide (cementite)
carbonyl
nitride
silicide
sulfide, di- (marcasite)
sulfide, di- (pyrite)
sulfide (pyrrhotite)
Cf. also under ferric and
ferrous
Krypton
Lanthanum
Lead
I2
I2O5
H2PtI6⋅9H2O
Ir
Fe
Fe
Fe
Fe
Fe
Fe3C
Fe(CO)5
Fe2N
FeSi
FeS2
FeS2
Fe7S8
Formula
weight
Color, crystalline form,
and refractive index
96.91
114.82
175.91
yel.
soft, tet. met.
col., rhb.
253.81
333.81
1120.66
192.22
55.85
55.85
55.85
55.85
55.85
179.55
195.90
125.70
83.93
119.98
119.98
647.44
blue-bk., rhb.
wh., trimetric
brn., delq. mn.
wh. met., cb.
gray
silv. met., cb.
silv. gray
gray
gray
pseudo hex.
pa. yel. lq.
gray
yel.-gray, oct.
yel., rhb.
yel., cb.
hex.
Specific
gravity
Melting
point, °C
d.
i.
576101°
0.01620°
187.412°
s. d.
i.
i.
i.
i.
i.
i.
i.
i.
d.
i.
0.00049
0.0005
i.
0.0956660°
4.9320°
4.799 254°
113.5
d. 300
184.35
22.420°
7.03
7.8620°
7.6 to 7.8
7.6 to 7.8
7.86
7.4
1.45721°
6.35
6.1 204°
4.87
5.0
4.6 204°
2350
1275
1535
1375
1075
1505
1837
−21
d. >560
>4800
tr. 450
1171
d. >700
d.
d.
−151.8
1800
1620
3000
102.5760mm
i.
i.
i.
i.
i.
i.
i.
i.
11.050° cc
d.
i.
3.5760° cc
280
−3H2O, 75
22
19.70°
45.6415°
s.
v. s.
v. s.
22150°
200100°
s.
5.55
18.2
d. 140
d. >200
d.
i.
d.
i.
i.
0.45540°
d.
0.05100°
4.75100°
0.0001120°
i.
d.
i.
d. 190
−H2O, 130
d. 470
0.6730°
0.00000720°
i.
1.616°
0.014
38.80°
3.34100°
i.
i.
18100° d.
d. red heat
888
i.
0.006818°
i.
col. gas
lead gray
silv. met., cb.
2.818 (A)
6.1520°
11.337 2020°
−169
826
327.5
Pb(C2H3O2)2
Pb(C2H3O2)2⋅3H2O†
Pb(C2H3O2)2⋅10H2O
Pb2(C2H3O2)3OH
Pb(C2H3O2)2⋅
Pb(OH)2⋅H2O
Pb(C2H3O2)2⋅
2Pb(OH)2
PbH4(AsO4)2
PbHAsO4
Pb(AsO3)2
Pb2As2O7
PbN6
PbBr2
325.29
379.33
505.44
608.54
584.52
wh. cr.
wh., mn.
wh., rhb.
wh.
wh. nd.
3.251 204°
2.55
1.689
807.72
wh. nd.
489.07
347.13
453.04
676.24
291.24
367.01
tri., 1.82
wh., mn., 1.9097
hex.
rhb., 2.03
col. nd.
col., rhb.
4.4615°
5.94
6.4215°
6.85 1515°
6.66
802
expl. 350
373
carbonate (cerussite)
carbonate, basic
(hydrocerussite; white lead)
chloride (cotunnite)
chromate (crocoite)
chromate, basic
formate
hydroxide
nitrate
PbCO3
2PbCO3⋅Pb(OH)2†
267.21
775.63
wh., rhb., 2.0763
wh., hex.
6.6
6.14
d. 315
d. 400
PbCl2
PbCrO4
PbCrO4⋅PbO
Pb(HCO2)2
3PbO⋅H2O
Pb(NO3)2
278.11
323.19
546.39
297.23
687.61
331.21
5.80
6.12
501
844
4.56
7.592
4.53
oxide, suboxide, mono- (litharge)
Pb2O
PbO
430.40
223.20
wh., rhb., 2.2172
yel., mn., 2.42
or.-yel. nd.
wh., rhb.
cb.
col., cb. or mn.,
1.7815
bk., amor.
yel., tet.
8.34
9.53
oxide, mono (massicotite)
PbO
223.20
yel., rhb., 2.61
8.0
arsenate, monobasic
arsenate, dibasic (schultenite)
arsenate, metaarsenate, pyroazide
bromide
Hot water
s.
i.
2860°
155
110 d.
83.80
138.91
207.20
acetate, basic
Solubility in 100 parts
Cold water
4050mm
1450
7.320°
4.6290°
Kr
La
Pb
acetate
acetate (sugar of lead)
acetate
acetate, basic
acetate, basic
Boiling
point, °C
−H2O, 280
918
954760mm
d.
i.
sl. s.
138.8100°
Other reagents
s. a.
v. s. 87% al.; i. abs. al.
et., chl.
s. al., KI, et.
i. abs. al., et., chl.
sl. s. aq. reg., aq. Cl2
s. a.; i. alk.
s. a.; i. alk.
s. a.; i. alk.
s. a.; i. alk.
s. a.; i. alk.
s. a.
s. al., H2SO4, alk.
s. HCl, H2SO4
i. aq. reg.
i. dil. a.
i. dil. a.
sl. s. al., bz.
s. a.
s. HNO3; i. c. HCl, H2SO4
s. gly.; v. sl. s. al.
s. gly.; sl. s. al.
sl. s. al.
s. al.
s. al.
s. HNO3
s. HNO3, NaOH
s. HNO3
s. HCl, HNO3; i. sc.
v. s. ac.; i. NH4OH
s. a., KBr.; sl. s. NH3;
i. al.
s. a., alk.; i. NH3, al.
s. ac.; sl. s. aq. CO2
sl. s. dil. HCl, NH3, i. al.
s. a., alk.; i. NH3, ac.
s. a., alk.
i. al.
s. a., alk.
8.822° al.
s. a., alk.
s. alk., PbAc, NH4Cl,
CaCl2
oxide, mono-
PbO
223 .20
amor.
9.2 to 9.5
oxide, red (minium)
oxide, sesquioxide, di- (plattnerite)
silicate
sulfate (anglesite)
Pb3O4
Pb2O3
PbO2
PbSiO3
PbSO4
685 .60
462 .40
239 .20
283 .28
303 .26
9.1
Pb(HSO4)2 ⋅H2O
PbSO4⋅PbO
PbS
Pb(CNS)2
Li
LiC7H5O2
LiBr
419 .36
526 .46
239 .27
323 .36
6 .94
128 .05
86 .85
LiBr⋅2H2O
Li2CO3
LiCl
122 .88
73 .89
42 .39
citrate
fluoride
formate
hydride
hydroxide
hydroxide
nitrate
nitrate
oxide
phosphate, monobasic
phosphate, tribasic
phosphate, tribasic
salicylate
sulfate
sulfate
sulfate, acid
Lutecium
Magnesium
acetate
acetate
aluminate (spinel)
Li3C6H5O7⋅4H2O
LiF
LiHCO2⋅H2O
LiH
LiOH
LiOH⋅H2O
LiNO3
LiNO3⋅3H2O
Li2O
LiH2PO4
Li3PO4
Li3PO4⋅12H2O
LiC7H5O3
Li2SO4
Li2SO4⋅H2O†
LiHSO4
Lu
Mg
Mg(C2H3O2)2
Mg(C2H3O2)2⋅4H2O†
MgO⋅Al2O3
281 .98
25 .94
69 .97
7 .95
23 .95
41 .96
68 .95
122 .99
29 .88
103 .93
115 .79
331 .98
144 .05
109 .94
127 .96
104 .01
174 .97
24 .31
142 .39
214 .45
142 .26
red, amor.
red-yel., amor.
brn., tet., 2.229
col., mn., 1.961
wh., mn. or rhb.,
1.8823
cr.
col., mn.
lead gray, cb., 3.912
col., mn.
silv. met. cb.
wh. leaflets
wh., delq., cb.,
1.784
wh. pr.
col., mn., 1.567
wh., delq., cb.,
1.662
wh. cr.
wh., cb., 1.3915
col., rhb.
wh., cb.
wh. cr.
col., mn.
col., trig., 1.735
col.
col ., 1 .644
col .
wh ., rhb .
wh ., trig .
col .
col ., mn ., 1 .465
col ., mn ., 1 .477
pr .
ammonium chloride
ammonium phosphate
(struvite)
ammonium sulfate
(boussingaultite)
benzoate
carbonate (magnesite)
carbonate (nesquehonite)
carbonate, basic
(hydromagnesite)
Magnesium chloride
(chloromagnesite)
chloride (bischofite)
hydroxide (brucite)
nitride
oxide (magnesia; periclase)
perchlorate
MgCl2⋅NH4Cl⋅6H2O
MgNH4PO4⋅6H2O
256 .79
245 .41
sulfate, acid
sulfate, basic (lanarkite)
sulfide (galena)
thiocyanate
Lithium
benzoate
bromide
bromide
carbonate
chloride
∗See also a table of alloys .
†
Usual commercial form .
MgSO4⋅(NH4)2SO4⋅
6H2O
Mg(C7H5O2)2⋅3H2O
MgCO3
MgCO3⋅3H2O
3MgCO3⋅Mg(OH)2⋅3H2O
MgCl2
MgCl2⋅6H2O
Mg(OH)2
Mg3N2
MgO
Mg(ClO4)2†
†
360 .60
i.
i.
9.375
6.49
6.2
d. 500
d. 360
d. 290
766
1170
i.
i.
i.
i.
0.00280°
i.
i.
i.
6.92
7.5
3.82
0.5320°
d.
977
1120
d. 190
186
1336 ± 5
25 °
4
547
1265
0.000118°
0.004418°
0.0000918°
0.0520°
d.
3325°
1430° (2H2O)
2.110°
2.068 254°
44
618
614
d.
1360
24620°
1.540°
670°
3.464
2.29521.5°
1.46
0.820
2.54
1.83
2.38
2 .013 254°
2 .461
2 .53717 .5°
1 .645
d.
870
−H2O, 94
680
445
261
29.88
2 .22
2 .06
2 .12313°
silv . met ., hex .
wh .
wh ., mn . pr ., 1 .491
col . cb ., 1 .718–23
1 .7420°
1 .42
1 .454
3 .6
651
323
80
2135
wh ., rhb ., delq .
col ., rhb ., 1 .496
1 .456
1 .715
−4H2O, 195
d . 100
1 .72
wh . pd .
wh ., trig . 1 .700
col ., rhb ., 1 .501
wh ., rhb ., 1 .530
3 .037
1 .852
2 .16
−3H2O, 110
d . 350
−H2O, 100
d .
95 .21
col ., hex ., 1 .675
2 .32525°
712
wh ., delq ., mn ., 1 .507
wh ., trig ., 1 .5617
gn .-yel ., amor .
col ., cb ., 1 .7364
wh ., delq .
1 .56
2 .4
3 .65
2 .6025°
1110
>120
320 .58
84 .31
138 .36
365 .31
203 .30
58 .32
100 .93
40 .30
223 .21
925±
d.
subl . <1000
>100
837
100
d .
860
−H2O, 130
170 .5
col ., mn .
1670
118 d .
d .
d .
2800
d .
3600
0.72100°
127.5100°
66.7100°
0.13535°
346.6104°
0 .03418°
v . sl . s .
12826°
35 .340°
43 .60°
d .
v . sl . s .
v . sl . s .
i .
v . s .
v . s .
i .
sl . s . d .
v . s .
v . s .
16 .7
0 .02310°
s .
0 .019580°
0°
25°
d .
i.
s.
d.
40100°
266100°
(1H2O)
61.215°
0.2718°
49.20°
d.
12.70°
22.310°
53.40°
v. s.
forms LiOH
16 .86
1412
0.005640°
17.5100°
26.880°
19470°
∞
29 .9100°
35100°
s. alk., PbAc, NH4Cl,
CaCl2
s. ac., h. HCl
s. a., alk.
s. ac., h. alk.; i. al.
s. a.
s. conc. a., NH4 salts; i. al.
sl. s. H2SO4
sl. s. H2SO4
s. a.; i. alk.
s. KCNS, HNO3
s. a., NH3
7.725°, 1078° al.
s. al., act.
s. al.
s. dil. a.; i. al., act., NH3
2.4815° al.; s. et.
sl. s. al., et.
s. HF; i. act.
sl. s. al., et.
i. et.
sl. s. al.
sl. s. al.
s. al., NH3
s . a ., NH4Cl; i . act .
v . s . al .
i . act ., 80% al .
i . 80% al .
s . a ., NH4 salts
5 .2515° m . al .
v . s . al .
v . sl . s . dil . HCl; i . dil .
HNO3
s . a .; i . al .
100°
130
4 .5 (anh .)
0 .0106
0 .151819°
0 .04
d .
0 .011
s . act .
s . a ., aq . CO2; i . act ., NH3
s . a ., aq . CO2
s . a ., NH4 salts; i . al .
52 .80°
73100°
50 al .
0°
281
0 .000918°
i .
0 .00062
99 .625°
s .
100°
918
d .
v . s .
50 al .
s . NH4 salts, dil . a .
s . a .; i . al .
s . a ., NH4 salts; i . al .
2425 al ., 51 .825° m . al .;
0 .29 et .
(Continued )
2-15
2-16
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Magnesium (Cont.)
peroxide
phosphate, pyrophosphate, pyropotassium chloride (carnallite)
potassium sulfate (picromerite)
silicofluoride
sodium chloride
sulfate
sulfate (epsom salt; epsomite)
Manganese
acetate
acetate
carbonate (rhodocrosite)
Formula
Formula
weight
Color, crystalline form,
and refractive index
Specific
gravity
Melting
point, °C
2.59822°
2.56
°
1.60 19.4
4
2.15
°
1.788 17.5
4
expl. 275
1383
−3H2O, 100
265
d. 72
d.
MgO2
Mg2P2O7
Mg2P2O7⋅3H2O
MgCl2⋅KCl⋅6H2O
MgSO4⋅K2SO4⋅6H2O
MgSiF6⋅6H2O
MgCl2⋅NaCl⋅H2O
MgSO4
MgSO4⋅7H2O∗
Mn
Mn(C2H3O2)2
Mn(C2H3O2)2⋅4H2O∗
MnCO3
56 .30
222 .55
276 .60
277 .85
402 .72
274 .47
171 .67
120 .37
246 .47
54 .94
173 .03
245 .09
114 .95
wh. pd.
col., mn., 1.604
wh., amor.
delq., rhb., 1.475
mn., 1.4629
col., trig., 1.3439
col.
col.
col., rhb., 1.4554
gray-pink met.
chloride (scacchite)
chloride
MnCl2
MnCl2⋅4H2O∗
125 .84
197 .91
chloride, perhydroxide (ous) (pyrochroite)
hydroxide (ic) (manganite)
nitrate
oxide (ous) (manganosite)
oxide (ic)
oxide, di- (pyrolusite;
polianite)
sulfate (ous)
sulfate (ous) (szmikite)
MnCl4
Mn(OH)2
Mn2O3⋅H2O
Mn(NO3)2⋅6H2O
MnO
Mn2O3
MnO2∗
196 .75
88 .95
175 .89
287 .04
70 .94
157 .87
86 .94
rose, delq., cb.
rose red, delq., mn.
1 .575
gn .
wh ., trig .
brn ., rhb ., 2 .24
rose red, mn .
gray-gn ., cb ., 2 .16
brn .-bk ., cb .
bk ., rhb .
MnSO4
MnSO4⋅H2O
151 .00
169 .02
red-wh .
pa . pink, mn ., 1 .595
sulfate (ous)
MnSO4⋅2H2O
187 .03
2 .52615°
15°
sulfate (ous)
MnSO4⋅3H2O
205 .05
sulfate (ous)
MnSO4⋅4H2O∗
223 .06
sulfate (ous)
MnSO4⋅5H2O
241 .08
sulfate (ous)
MnSO4⋅6H2O
259 .09
sulfate (ous)
sulfate (ic)
Mercuric acetate
bromide
carbonate, basic
chloride (corrosive sublimate)
fulminate
hydroxide
oxide (montroydite)
oxychloride (kleinite)
silicofluoride, basic
sulfate
sulfate, basic (turpeth)
Mercurous acetate
bromide
carbonate
pa. pink, mn.
rose, trig., 1.817
2.66
1.68
7.220°
1.74 204°
1.589
3.125
1185
70 d.
1260
2.977 254°
2.01
650
58.0
3 .25818°
3 .258
1 .8221°
5 .18
4 .81
5 .026
d .
d .
25 .8
1650
−0, 1080
−0, >230
3 .235
2 .87
700
Stable 57 to
117
Stable 40 to 57
2 .356
pink, rhb . or mn .,
1 .518
pink, tri ., 1 .508
2 .107
15°
2 .103
MnSO4⋅7H2O
277 .11
pink, mn . or rhb .
2 .092
Mn2(SO4)3
Hg(C2H3O2)2
HgBr2
HgCO3⋅2HgO
HgCl2
Hg(CNO)2
Hg(OH)2
HgO
HgCl2⋅3HgO
HgSiF6⋅HgO⋅3H2O
HgSO4
HgSO4⋅2HgO
HgC2H3O2
HgBr
Hg2CO3
398 .06
318 .68
360 .40
693 .78
271 .50
284 .62
234 .60
216 .59
921 .26
613 .30
296 .65
729 .83
259 .63
280 .49
461 .19
gn ., delq . cr .
wh . pl .
wh ., rhb .
brn .-red
wh ., rhb ., 1 .859
cb .
3 .24
3 .270
6 .053
yel . or red, rhb ., 2 .5
yel ., hex .
yel . nd .
wh ., rhb .
yel ., tet .
wh . sc .
wh ., tet .
yel . pd .
11 .14
7 .93
5 .44
4 .42
6 .47
6 .44
7 .307
Boiling
point, °C
Hot water
i.
i.
sl. s.
d.
81.775°
s.
s.
68.3100°
17840°
63.40°
1518°
123.8100°
∞
s. al., m. al.
s. aq. CO2, dil. a.; l.
NH3, al.
s. al.; i. et., NH3
s . al .; i . et .
129 .5
s .
0 .00220°
i .
4260°
i .
i .
i .
s .
i .
i .
∞
i .
i .
i .
s . al ., et .
s . a ., NH4 salts; i . alk .
s . h . H2SO4
v . s . al .
s . a ., NH4Cl
s . a .; i . act .
s . HCl; i . HNO3, act .
d . 850
530°
98 .4748°
7350°
79 .77100°
s . al .; i . et .
85 .2735°
106 .855°
1900
1190
−H2O, 106;
−4H2O, 200
5°
Stable 30 to 40
−4H2O, 450
s.
64.550°
74 .22
99 .3157°
13616°
16950°
5°
142
200
Stable −5 to
+8
Stable −10 to
−5; 19 d .
d . 160
d .
237
2040°
2479°
d .
d .
subl . 345
d . 130
−7H2O, 280
322
304
0°
25114°
v . s .
2510°
0 .520°
i .
3 .60°
sl . s .
i .
0 .005225°
i .
d .
d .
0 .005
0 .7513°
7 × 10−9
i .
d .
100100°
25100°
176
s. a.
s. a.; i. alk.
s. a.; i. al.
d. al.
d. HF
s. al.
s. al.
s. dil. a.
i . al .
35°
Stable 8 to 18
277
expl .
−H2O, 175
d . 100
d . 260
Other reagents
i.
i.
i.
64.519° d.
19.260°
64.817.5°
s.
26.90°
72.40°
d.
s.
s.
0.006525°
d.
Stable 18 to 30
Solubility in 100 parts
Cold water
61 .3100°
i .
0 .041100°
d .
0 .167100°
d .
i .
d .
s . HCl, dil . H2SO4; l .
s . al . sl . d .
25 .20° al .; v . sl . s . et .
s . aq . CO2, NH4Cl
3325° 99% al .; 33 et .
s . NH4OH, al .
s . a .
s . a .; i . al .
s . HCl
s . a .
s . a .; i . al ., act ., NH8
s . a .; i . al .
s . H2SO4, HNO3; i . al .
s . a .; i . al ., act .
s . NH4Cl
HgCl
236 .04
wh., tet., 1.9733
7.150
302
383.7
0.00140°
0.000743°
iodide
nitrate
Mercurous oxide
HgI
HgNO3⋅H2O
Hg2O
327 .49
280 .61
417 .18
yel., tet.
wh. mn.
bk.
7.70
4.7853.9°
9.8
290 d.
70
d. 100
subl. 140; 310d.
expl.
2 × 10−8
v. s.
i.
v. sl. s.
d.
0.0007
sulfate
Mercury†
Molybdenum
Hg2SO4
Hg
Mo
497 .24
200 .59
95 .94
wh., mn.
silv. lq. or hex.(?)
gray, cb.
7.56
13.54620°
10.2
d.
−38.87
2620 ± 10
0.05516.5°
i.
i.
0.092100°
i.
i.
MoCl2
166 .85
yel., amor.
3.714 254°
d.
i.
i.
25 °
4
d.
i.
d.
chloride (calomel)
MoCl3
202 .30
dark red pd.
chloride, tetra-
MoCl4
237 .75
brn., delq.
volt.
d.
s.
d.
chloride, penta-
MoCl5
273 .21
bk. cr.
2.928 254°
194
268
s.
d.
MoO3
MoS2
MoS3
MoS4
H2MoO4
H2MoO4⋅H2O
Nd
Ne
143 .94
160 .07
192 .14
224 .20
161 .95
161 .95
144 .24
20 .18
col., rhb.
bk., hex., 4.7
red-brn.
brn. pd.
yel-wh., hex.
yel., mn.
yellowish
col. gas
4.5019.5°
4.80114°
795
1185
d.
d.
d. 115
−H2O, 70
840
−248.67
subl.
0.10718°
i.
sl. s.
i.
v. sl. s.
0.13318°
d.
2.60° cc
2.10679°
i.
s.
i.
sl. s.
2.1370°
s. aq. reg., Hg(NO3)2;
sl. s. HNO3, HCl;
i. al., etc.
s. KI; i. al.
s. HNO3; i. al., et.
s. h. ac.; i. alk., dil. HCl,
NH3
s. H2SO4, HNO3
s. HNO3; i. HCl
s. h. conc. H2SO4; i.
HCl, HF, NH3, dil.
H2SO4, Hg
s. HCl, H2SO4, NH4OH,
al., et.
s. HNO3, H2SO4; v. sl. s.
al., et.
s. HNO3, H2SO4; sl. s.
al., et.
s. HNO3, H2SO4; i. abs.
al., et.
s. a., NH4OH
s. H2SO4, aq. reg.
s. alk. sulfides
s. alk. sulfides; i. NH3
s. NH4OH, H2SO4; i. NH
s. a., NH4OH, NH4, salts
1.145° cc
s. lq. O2, al., act., bz.
i.
s. dil. HNO3; sl. s. H2SO4,
HCl; i. NH3
i. al.
chloride, dichloride, tri-
oxide, tri- (molybdite)
sulfide, di- (molybdenite)
sulfide, trisulfide, tetraMolybdic acid
Molybdic acid
Neodymium
Neon
Neptunium
Nickel
acetate
ammonium chloride
ammonium sulfate
Np
Ni
239
239 .05
58 .69
1.798
1.645
1.923
d.
2.575
4.64 284°
carbonyl
chloride
chloride
170 .73
129 .60
237 .69
chloride, ammonia
cyanide
dimethylglyoxime
NiCl2⋅6NH3
Ni(CN)2⋅4H2O
NiC8H14O4N4
lq.
yel., delq.
gn., delq., mn.,
1.57±
231 .78
182 .79
288 .91
gn. pl.
scarlet red cr.
formate
hydroxide (ic)
hydroxide (ous)
nitrate
nitrate, ammonia
oxide, mono- (bunsenite)
Ni(HCO2)2⋅2H2O
Ni(OH)3
Ni(OH)2⋅¼H2O
Ni(NO3)2⋅6H2O
Ni(NO3)2⋅4NH3⋅2H2O
NiO
184 .76
109 .72
97 .21
290 .79
286 .86
74 .69
2-17
potassium cyanide
sulfate
∗Usual commercial form .
†
See also Tables 2-28 and 2-280 .
Ni(CN)2⋅2KCN⋅H2O
NiSO4
258 .97
154 .76
1.3117°
3.544
gn. cr.
bk.
lt. gn.
gn., mn.
4.36
2.05
gn .-bk ., cb ., 2 .37
7 .45
red yel ., mn .
yel ., cb .
2.154
11°
1 .875
3 .68
−245.9
Produced by Neutron bombardment of U
1452
2900
i.
gn. pr.
gn., delq., mn.
blue-gn., mn.,
1.5007
gn., cb.
yel., delq.
gn., delq.
vl. pd.
trig.
lt. gn., rhb.
lt. gn.
1.837
3.715
−2H2O, 200
238
8.9020
176 .78
291 .18
394 .99
422 .59
218 .50
272 .55
320 .68
841 .29
118 .70
587 .59
3.12415°
6.920°
lq. 1.204−245.9°
0.674 (A)
silv. met., cb.
Ni(C2H3O2)2
NiCl2⋅NH4Cl⋅6H2O
NiSO4⋅(NH4)2SO4⋅
6H2O
Ni(BrO3)2⋅6H2O
NiBr2
NiBr2⋅3H2O
NiBr2⋅6NH3
NiPtBr6⋅6H2O
NiCO3
2NiCO3⋅3Ni(OH)2⋅
4H2O
Ni(CO)4
NiCl2
NiCl2⋅6H2O∗
bromate
bromide
bromide
bromide, ammonia
bromoplatinate
carbonate
carbonate, basic
3.578
356.9
3700
16.6
15025°
2.53.5°
v. s.
39.288°
d.
d.
−3H2O, 200
28
112.80°
1999°
v. s.
156100°
316100°
d.
s. NH4OH
s. al., et., NH4OH
s. al., et., NH4OH
i. c. NH4OH
d.
d.
0.009325°
i.
i.
d.
s. a.
s. a., NH4 salts
0.0189.8°
53.80°
180
i.
87.6100°
v. s.
s. aq. reg., HNO3, al., et.
s. NH4OH, al.; i. NH3
v. s. al.
s.
i.
i.
d.
i.
i.
s. NH4OH; i. al.
s. KCN; i. dil. KCl
s. abs. al., a.; i. ac.,
NH4OH
i.
v. sl. s.
∞56 .7°
−25
subl.
43751mm
973
−4H2O, 200
subl. 250
d.
d.
d.
d.
56.7
Forms Ni2O3
at 400
−H2O, 100
−SO3, 840
136.7
v. sl. s. (NH4)2SO4
s.
i.
v. sl. s.
243.00°
v . s .
i .
i .
s. a., NH4OH, NH4Cl
s. a., NH4OH; i. alk.
s . NH4OH; i . abs . al .
i . al .
s . a ., NH4OH
s .
27 .20°
76 .7100°
d . a .
i . al ., et ., act .
(Continued )
2-18
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Formula
Formula
weight
Color, crystalline form,
and refractive index
Nickel (Cont.)
sulfate
NiSO4⋅6H2O∗
262 .85
sulfate (morenosite)
Nitric acid
Nitric acid
Nitric acid
Nitro acid sulfite
Nitrogen
NiSO4⋅7H2O
HNO3
HNO3⋅H2O
HNO3⋅3H2O
NO2HSO3
N2
280 .86
63 .01
81 .03
117 .06
127 .08
28 .01
Nitrogen oxide, mono- (ous)
N2O
44 .01
col . gas
oxide, di- (ic)
NO or (NO)2
col . gas
oxide, tri-
N2O3
30 .01
60 .01
76 .01
gn. mn. or blue, tet.,
1.5109
gn., rhb., 1.4893
col. lq.
col . lq .
col . lq .
col ., rhb .
col . gas or cb . cr .
red-brn . gas or blue
lq . or solid
yel . lq ., col . solid,
red-brn . gas
wh ., rhb .
oxide, tetra- (per- or di-)
NO2 or (NO2)2
oxide, penta-
N2O5
46 .01
92 .01
108 .01
oxybromide
oxychloride
NOBr
NOCl
109 .91
65 .46
brn . lq .
red-yel . lq . or gas
Nitroxyl chloride
Osmium
chloride, dichloride, trichloride, tetraOxygen
NO2Cl
Os
OsCl2
OsCl3
OsCl4
O2
81 .46
190 .23
261 .14
296 .59
332 .04
32 .00
yel .-brn . gas
blue, hex .
gn ., delq .
brn ., cb .
red-yel . nd .
col . gas or hex . solid
Ozone
O3
48 .00
Palladium
Pd
106 .42
silv . met ., cb .
PdBr2
PdCl2
PdCl2⋅2H2O
Pd(CN)2
266 .23
177 .33
213 .36
158 .45
brn .
brn ., cb .
brn . pr .
yel .
Pd2H
Pd(NH3)2Cl2
HClO4
HClO4⋅H2O
HClO4⋅2H2O∗
73 .6% anh .
HIO4
HIO4⋅2H2O
HMnO4
HMoO4⋅2H2O
H2S2O8
PONH2⋅(OH)2
H7P(Mo2O7)6⋅28H2O
PH3
213 .85
211 .39
100 .46
118 .47
136 .49
met .
red or yel ., tet .
unstable, col . lq
fairly stable nd .
stable lq ., col .
bromide (ous)
chloride
chloride
cyanide
hydride
Palladous dichlorodiammine
Perchloric acid
Perchloric acid
Perchloric acid
Periodic acid
Periodic acid
Permanganic acid
Permolybdic acid
Persulfuric acid
Phosphamic acid
Phosphatomolybdic acid
Phosphine
Phosphonium chloride
PH4Cl
191 .91
227 .94
119 .94
196 .98
194 .14
97 .01
2365 .71
34 .00
70 .46
col . gas
wh . cr .
delq ., mn .
exists only in solution
wh . cr .
hyg . cr .
cb .
yel . cb .
col . gas
wh ., cb .
Specific
gravity
Melting
point, °C
Boiling
point, °C
Solubility in 100 parts
Cold water
Hot water
Other reagents
2.07
tr. 53.3
−6H2O, 280
13150°
280100°
v. s. NH4OH, al.
1.948
1.502
98–100
−42
−38
−18 .5
73 d .
−209 .86
−6H2O, 103
86
117.830°
∞
∞
∞
−195 .8
63.50°
∞
∞
263−20°
d .
2 .350° cc
s. al.
expl . with al .
d . al .
d . al .
s . H2SO4
sl . s . al .
−102 .3
−90 .7
130 .520° cc
−161
−151
7 .340° cc
60 .8224°
cc
0 .0100°
−102
3 .5
s .
1 .026−252 .5°
0 .808−195 .8°
12 .50° (D)
lq . 1 .226−89°
1 .530 (A)
lq . 1 .269−150 .2°
1 .0367 (A)
1 .4472°
20°
1 .448
−9 .3
21 .3
d .
1 .6318°
30
47
s .
>1 .0
1 .417−12°
2 .31 (A)
lq . 1 .3214°
22 .4820°
−55 .5
−64 .5
−2
−5 .5
d .
d .
<−30
2700
5
>5300
26 .6 cc al .; 3 .5 cc H2SO4;
s . aq . FeSO4
s . a ., et .
s . HNO3, H2SO4, chl .,
CS2
Forms
HNO3
s . fuming H2SO4
−218 .4
−183
−251
−112
0 .4940° cc
060° cc
s . oil turp ., oil cinn .
1555
2200
i .
i .
i .
s .
s .
i .
i .
s .
s .
i .
s . aq . reg ., h . H2SO4;
i . NH3
s . HBr
s . HCl, act ., al .
s . HCl, act ., al .
s . HCN, KCN, NH4OH;
i . dil . a .
500 d .
d .
11 .06
2 .5
1 .768 224°
1 .88
1 .71 254°
s . H2SO4, al .
d
i .
s . d .
sl . s .
s . d .
4 .890° cc
d . 560–600
1 .14−188°
1 .426−252 .5°
1 .1053 (A)
1 .71−183°
3 .03−80°
1 .658 (A)
12 .020°
111550°
1 .5520° cc
i .
2 .630° cc
1 .7100° cc
sl . s . aq . reg ., HNO3; i . NH3
s . NaCl, al ., et .
s . a ., alk ., al .; sl . s . et .
s . HCl, al .
sl . s . al ., s . fused Ag
d .
−90°
lq . 0 .746
1 .146 (A)
−112
50
−17 .8
1618mm
d .
200
d . 138
d . 110
subl . 110
<60
d .
78
−132 .5
46atm .
28
s .
s .
s .
v . s .
−25H2O, 140
−85
s .
v . s .
v . s .
v . s .
v . s .
v . s .
s .
2617° cc
subl .
d .
s . a ., NH4OH
s . al .
v . s .
d .
v . s .
d .
v . s . d .
100°
i .
sl . s . al ., et .
d . al .
i . al .
s . HNO8
s . Cu2Cl2, al ., et .
Phosphoric acid, hypoPhosphoric acid, meta-
H4P2O6
HPO3
Phosphoric acid, orthoPhosphoric acid, pyro-
†
4
H3PO
H4P2O7
98 .00
177 .98
col., rhb.
wh. nd.
1.834
Phosphorous acid, hypoPhosphorous acid, orthoPhosphorous acid, pyroPhosphorus, black
Phosphorus, red
Phosphorus, yellow
H3PO2
H3PO3
H4P2O5
P4
P4
P4
66 .00
82 .00
145 .98
123 .90
123 .90
123 .90
syrupy
col .
nd .
rhombohedral
red, cb .
yel ., hex ., 2 .1168
1.49318.8°
1 .65121 .2°
PCl3
PCl5
137 .33
208 .24
col ., fuming lq .
delq ., tet .
chloride, trichloride, pentaoxide, pentaoxychloride
Phosphotungstic acid
Platinum
chloride (ic)
chloride (ous)
chloride (ic)
cyanide (ous)
Plutonium
Plutonium
Potassium
P2O5
POCl3
H3PO4⋅12WO3⋅xH2O
Pt
PtCl4
161 .98
79 .98
141 .94
153 .33
2880 .05
195 .08
336 .89
cr.
vitreous, delq.
wh ., delq ., amor .
col ., fuming lq .
yel .-gn . cr .
silv . met ., cb .
18.2°
2 .69
2 .2020°
1 .8220°; lq .
1 .74544 .5°
°
1 .574 20.8
4
solid 1 .6;
3 .60295° (A)
2 .387
1 .675
21 .4520°
lq . 191755°
brn .
PtCl2
265 .98
brn .
PtCl4⋅8H2O
Pt(CN)2
Pu
Pu
K
481 .01
247 .11
238 .05
239 .05
39 .10
red, mn .
yel .-brn .
acetate
KC2H3O2
98 .14
acetate, acid
KH(C2H3O2)2
158 .19
aluminate
K2(AlO2)2⋅3H2O
250 .20
amide
KNH2
55 .12
arsenate (monobasic)
KH2AsO4
180 .03
auricyanide
KAu(CN)4⋅1⋅5H2O
367 .16
aurocyanide
KAu(CN)2
288 .10
bicarbonate
KHCO3
100 .12
bisulfate
KHSO4
136 .17
bromate
KBrO3
167 .00
bromide
KBr
119 .00
carbonate
K2CO3
138 .21
carbonate
K2CO3⋅2H2O
174 .24
carbonate
2K2CO3⋅3H3O
330 .46
chlorate
KClO3
122 .55
chloride (sylvite)
KCl
74 .55
chloroplatinate
K2PtCl6
485 .99
chromate (tarapacaite)
K2CrO4
194 .19
cyanate
KCNO
81 .12
cyanide
KCN
65 .12
dichromate
K2Cr2O7
294 .18
ferricyanide
K3Fe(CN)6
329 .24
ferrocyanide
K4Fe(CN)6⋅3H2O
422 .39
formate
KHCO2
84 .12
hydride
KH
40 .11
hydrosulfide
KHS
72 .17
hydroxide
KOH
56 .11
iodate
KIO3
214 .00
iodide
KI
166 .00
∗One commercial form 70 to 72 per cent .
†
Common commercial form 85 per cent H3PO4 in aqueous solution .
2.2–2.5
silv . met ., cb .
wh . pd .
delq . nd . or pl .
cr .
yel .-grn .
col ., tet ., 1 .5674
pl .
rhb .
mn ., 1 .482
rhb ., or mn ., 1 .480
trig .
col ., cb ., 1 .5594
wh ., delq . pd ., 1 .531
rhb .
mn .
col ., mn ., 1 .5167
col ., cb ., 1 .4904
yel ., cb ., 1 .825±
yel ., rhb ., 1 .7261
wh ., tet .
wh ., cb ., delq ., 1 .410
red, tri .
red, mn . pr ., 1 .5689
yel ., mn ., 1 .5772
col ., rhb .
cb ., 1 .453
wh ., delq ., rhb .
wh ., delq ., rhb .
col ., mn .
wh ., cb ., 1 .6670
55
subl.
d. 70
s.
s.
26°
42.35
61
−½H2O, 213
2340
80028°
26.5
74
38
d.
d . 200
d . 130
ign . in air, 400
ign . in air, 725
280
∞
307 .30°
d .
i .
i .
0 .0003
−111 .8
148 under
pressure
subl . 250
2
75 .95760mm
subl . 160
d .
d .
1755
4300
59043atm .
44 .1; ign . 34
107 .2760mm
Forms H3PO4
d .
s .
i .
25°
45062°
Forms
H3PO4
v. s.
Forms
H3PO4
∞
73040°
i . CS2
s . alk .; i . CS2, NH3, et .
0 .4 al .; 100010° CS2; 1 .50°,
1081° bs .; s . NH3
s . et ., chl ., CS2
s . CS2, C6H5COCl
v . s .
s . H2SO4; i . NH3, act .
d . al .
s . al ., et .
s . aq . reg ., fused alk .
i .
140
v . s .
5 .87
d . 581
i .
i .
2 .43
−4H2O, 100
v . s .
i .
v . s .
i .
Produced by deuteron bombardment on U238
Produced by neutron bombardment on U238
0 .8620°
62 .3
760
lq . 0 .8342°
1 .8
292
148
d . 200
2 .867
2 .17
2 .35
3 .2717 .5°
2 .7525°
2 .29
2 .043
2 .13
2 .32
1 .988
3 .499
2 .73218°
2 .048
1 .5216°
2 .69
1 .84
1 .85317°
1 .91
0 .80
2 .0
2 .044
3 .89
3 .13
338
288
d . 200
d . 100–200
210
370 d .
730
891
368
790
d . 250
975
634 .5
398
d .
−3HO2, 70
167 .5
d .
455
380
560
723
subl . 400
d .
1380
d .
d . 400
1500
d .
d .
1320
1330
d .
0°
217
d .
s .
d .
18 .876°
s .
14 .3
22 .40°
36 .30°
3 .110°
53 .50°
105 .50°
1830°
129 .40°
3 .30°
27 .60°
0 .740°
58 .00°
s .
s .
4 .90°
334 .4°
27 .812 .2°
33118°
d .
s .
970°
4 .730°
127 .50°
s. al.
v. s. al., et.
i .
i .
sl . s .
d . 370
11°
i. lq. CO2
Forms
KOH
39690°
d .
v . s .
v . s .
200100°
6060°
121 .6100°
49 .75100°
104100°
156100°
331100°
268100°
57100°
56 .7100°
5 .2100°
75 .6100°
d .
122 .2108 .8°
80100°
77 .5100°
90 .696 .8°
65790°
s . d .
178100°
32 .2100°
208100°
s . al ., act .; sl . s . NH2;
i . et .
s . HCl, NH4OH; sl . s .
NH3; i . al ., et .
s . al ., et .
i . alk .
s . a ., al ., Hg
33 al .; i . et .
s . ac .
s . alk .; i al .
d . al .; 3 .625° NH3
i . al .
s . al .
sl . s . al .; i . et .
i . satd . K2CO3, al .
d . al .
sl . s . al .; i . act .
sl . s . al ., et .
i . al .
0 .83 al .; s . alk .
s . al ., alk .
i . al ., et .
i . al .
v . sl . s . al .
s . gly .; 0 .919 .5° al .; 1 .3 h . al .
i . al .
s . act .; sl . s . al .; i . NH3
s . act .; i . NH3, al ., et .
sl . s . al .; i . et .
i . et ., bz ., CS2
s . al .
v . s . al ., et .; i . NH3
s . KI; i . al ., NH3
420° al .; s . NH3; sl . s . et .
(Continued )
2-19
2-20
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Formula
Formula
weight
Color, crystalline form,
and refractive index
Potassium (Cont.)
iodide, triiodoplatinate
manganate
metabisulfite
nitrate (saltpeter)
nitrite
oxalate
oxalate, acid
oxalate, acid
oxide
perchlorate
permanganate
persulfate
phosphate, monobasic
KI3
K2PtI6
K2MnO4
K2S2O5
KNO3
KNO2
K2C2O4⋅H2O
KHC2O4∗
KHC2O4⋅½H2O
K2O
KClO4
KMnO4
K2S2O3
KH2PO4
419 .81
1034 .70
197 .13
222 .32
101 .10
85 .10
184 .23
128 .13
137 .13
94 .20
138 .55
158 .03
190 .32
136 .09
phosphate, dibasic
phosphate, tribasic
phosphate, metaphosphate, metaphosphate, pyrophthalate, acid
platinocyanide
silicate
silicate, tetrasulfate (arcanite)
sulfate, pyrosulfide, monosulfite
sulfite, acid
tartrate
tartrate, acid
thiocyanate
K2HPO4
K3PO4
KPO3
K4P4O12⋅2H2O
K4P2O7⋅3H2O
KHC8H4O4
K2Pt(CN)4⋅3H2O
K2SiO3
K2Si4O9⋅H2O
K2SO4
K2S2O7
K2S⋅5H2O
K2SO3⋅2H2O
KHSO3
K2C4H4O6⋅½H2O
KHC4H4O6∗
KCNS
174 .18
212 .27
118 .07
508 .31
384 .38
204 .22
431 .39
154 .28
352 .55
174 .26
254 .32
200 .34
194 .29
120 .17
235 .28
188 .18
97 .18
thiosulfate
thiosulfate
Praseodymium
Radium
bromide
Radon (Niton)
K2S2O3
3K2S2O3⋅H2O
Pr
Ra
RaBr2
Rn
190 .32
588 .99
140 .91
226 .03
385 .83
222 .02
dark blue, delq., mn.
cb.
gn., rhb.
mn., pl.
col., rhb., 1.5038
pr.
wh., mn.
mn., 1.545
trimetric
wh., cb.
col., rhb., 1.4737
purple, rhb.
wh., tri., 1.4669
col., delq., tet.,
1.5095
wh., delq.
wh., rhb.
wh. pd.
amor.
delq.
wh. cr.
yel., rhb., 1.62±
hyg. 1.521±
rhb., 1.530
col., rhb., 1.4947
col.
rhb., delq.
wh., rhb.
wh., mn.
col., mn., 1.526
col., rhb.
col., delq., mn.,
1.660±
col., cb.
delq., mn.
yel.
wh., met.
wh., mn.
gas
Rhenium
Re
186 .21
hex.
Rhodium
chloride
chloride
Rubidium
Rh
RhCl3
RhCl3⋅4H2O
Rb
102 .91
209 .26
281 .33
85 .47
gray-wh., cb.
red
dark red
silv. wh.
Ruthenium
Ruthenium
Samarium
Scandium
Selenic acid
Selenic acid
Selenium
Selenium
Ru
Ru
Sm (also Sa)
Sc
H2SeO4
H2SeO4⋅H2O
Se8
Se8
101 .07
101 .07
150 .36
44 .96
144 .97
162 .99
631 .68
631 .68
bk., porous
gray, hex.
hex. pr.
nd .
red pd ., amor ., 2 .92
gray, trig ., 3 .00; red,
hex .
Specific
gravity
3.498
5.18
10.6°
2.11
1.915
2.13
2.0
2.32 204°
2.524 114°
2.703
2.338
2.56417°
2.25814.5°
2.26414.5°
2.33
1.63
2.4516°
2.417
2.662
2.277
1.98
1.956
1.886
2.23
6.520°
5?
5.79
lq. 5.5; 111
(D)
Melting
point, °C
45
d. 190
d. 150
tr. 129; 333
297
d.
d.
d.
Boiling
point, °C
d. 225
d. 400
d. 350
d. 400
d. <240
d. <100
256
d.
1340
tr. 450; 798
−2H2O, 100
−2H2O, 180
d.
976
d. 400
tr. 588
300
60
d.
d. 190
172.3
d. 400
−H2O, 180
940
960
728
−71
1320
d.
−3H2O, 300
−3H2O, 150
d.
d. 500
d.
1140
subl. 900
−62
Solubility in 100 parts
Cold water
v. s.
s.
d.
250°
13.30°
2810°
28.70°
14.350°
2.20°
Forms KOH
0.750°
2.830°
1.770°
14.80°
Hot water
s. KI, al.
12094°
246100°
413100°
83.2100°
48.1100°
51.5100°
v. s.
21.8100°
32.3575°
1040°
83.590°
3325°
193.125°
s.
s.
s.
10.225°
sl. s.
s.
s.
7.350°
s.
s.
100
45.515°
12.517.5°
0.370°
1770°
v. s.
v. s.
s.
83
v. s.
36
v. s.
s.
s.
24.1100°
d.
96.10°
311.290°
d.
d. +H2
7020°
510° cc
s.
8.560° cc
>100
91.575°
278100°
6.1100°
21720°
3440
12.5
1955
d. 450
>2500
subl. 800±
lq. 1.47588.5;
1.5320°
8.6
12.220°
7.7
2.5?
2.950 154°
2 .627 154°
4 .2625°
4 .80; 4 .50
38.5
>1950
2450
>1300
1200
58
26
50
220
Other reagents
s. KOH
sl. s. al.; i. et.
0.130° al.; i. et.
v. s. NH3; sl. s. al.
s. al., et.
0.10520° m. al.; i. et.
s. H2SO4; d. al.
i. al.
i. al.
sl. s. al.
i. al.
s. a.
i. al.
s. al., et.
i. al.
i. al.
i. al., act., CS2
s. al., gly.; i. et.
sl. s. al.; i. NH3
i. abs. al.
sl. s. al.
s. a., alk.; i. al., ac.
20.822° act.; s. al.
i. al.
d. a.
s. al.
i. HF, HCl; s. H2SO4;
HNO3
sl. s. aq. reg., a.
v. sl. s. alk.; i. aq. reg., a.
s. HCl, al.; i. et.
s. a., al.
i.
i.
700
i.
i.
v. s.
d.
i.
i.
i.
i.
sl. s. aq. reg., a.
>2700
2400
260
205
688
688
130030°
v . s .
i .
i .
∞60°
s . H2SO4; d . al .; i . NH3
i .
i .
s . CS2, H2SO4, CH2I2
s . CS2, H2SO4
Selenium
Selenous acid
Silicic acid, metaSilicic acid, orthoSilicon, crystalline
Se8
H2SeO3
H2SiO3
H4SiO4
Si
Silicon, graphitic
Si
Silicon, amorphous
carbide
chloride, trichloride, tetra-
Si
SiC
Si2Cl6
SiCl4
28.09
40.10
268.89
169.90
SiF4
SiH4
SiO2⋅xH2O
SiO2
104.08
32.12
SiO2
SiO2
SiO2
Ag
AgBr
60.08
60.08
60.08
107.87
187.77
carbonate
chloride (cerargyrite)
Ag2CO3
AgCl
cyanide
nitrate (lunar caustic)
Sodium
steel gray
hex.
amor., 1.41
amor.
gray, cb., 3.736
4.825°
3.004 154°
2.1–2.3
1.57617°
2.420°
cr.
2.0–2.5
brn., amor.
blue-bk., trig., 2.654
lf. or lq.
col., fuming lq.,
1.412
gas
col. gas
iridescent, amor.
col., cb. or tet.,
1.487
2
3.17
1.580°
1.50
2600
i.
900°
i.
sl. s.
i.
i.
40090°
i.
sl. s.
i.
2600
i.
i.
>2700
−1
−70
2600
subl. 2200
144760mm
57.6
i.
i.
d.
d.
i.
i.
3.57 (A)
lq. 0.68−185°
2.2
2.32
−95.7
−185
1600–1750
1710
−651810mm
−112760mm
subl. 1750
2230
v. s. d.
i.
i.
i.
hex., 1.5442
trig., rhb., 1.469
silv. met., cb.
pa. yel., cb., 2.252
2.20
2.65020°
2.26
10.520°
6.473 254°
tr. <1425
tr. 1670
960.5
434
2230
2230
2230
1950
d. 700
i.
i.
i.
i.
0.0000220°
i.
i.
275.75
143.32
yel. pd.
wh., cb., 2.071
6.077
5.56
218 d.
455
1550
0.00320°
0.00008910°
0.05100°
0.00217100°
AgCN
AgNO3
Na
133.89
169.87
22.99
wh., 1.685±
col., rhb., 1.744
silv. met, cb.
3.95
4.352 194°
0.9720°
−(CN)2, 320
212
97.5
444 d.
880
acetate
acetate
aluminate
amide
ammonium phosphate
antimonate, metaarsenate
arsenate, acid (monobasic)
arsenate, acid (dibasic)
arsenate, acid (dibasic)
arsenite, acid
benzoate
bicarbonate
bifluoride
bisulfate
bisulfite
borate, tetraborate, tetra
NaC2H3O2
NaC2H3O2⋅3H2O
NaAlO2
NaNH2
NaNH4HPO4⋅4H2O
2NaSbO3⋅7H2O
Na3AsO4⋅12H2O
NaH2AsO4⋅H2O
Na2HAsO4⋅7H2O∗
Na2HAsO4⋅12H2O
Na2HAsO3
NaC7H5O2
NaHCO3
NaHF2
NaHSO4
NaHSO3
Na2B4O7
Na2B4O7⋅5H2O
82.03
136.08
81.97
39.01
209.07
511.60
424.07
181.94
312.01
402.09
169.91
144.10
84.01
61.99
120.06
104.06
201.22
291.30
wh., mn., 1.464
wh., mn.
amor.
olive gn.
col., mn.
cb.
hex., 1.4589
rhb., 1.5535
col., mn., 1.4658
mn., 1.4496
col.
col. cr.
wh., mn., 1.500
col. cr.
col., tri.
col., mn., 1.526
1.528
1.45
324
58
1650
210
79 d.
col., rhb., 1.461
2.742
1.48
2.367
1.815
borate, tetra- (borax)
Na2B4O7⋅10H2O∗
381.37
wh., mn., 1.4694
1.73
fluoride
hydride (silane)
oxide, di- (opal)
oxide, di- (cristobalite)
oxide, di- (lechatelierite)
oxide, di- (quartz)
oxide, di- (tridymite)
Silver
bromide (bromyrite)
631.68
128.97
78.10
96.11
28.09
28.09
60.08
1.574
217
d.
688
1420
400
1.759
2.535
1.871
1.72
1.87
86.3
d. 100
125
28
2.20
−CO2, 270
d.
>315
d.
741
d., −H2O
75
−10H2O, 200
17.5°
bromate
bromide
bromide
NaBrO3
NaBr
NaBr⋅2H2O
150.89
102.89
138.92
col., cb.
col., cb., 1.6412
col., mn.
3.339
3.20517.5°
2.176
381
755
50.7
carbonate (soda ash)
carbonate
Na2CO3
Na2CO3⋅H2O
105.99
124.00
2.533
1.55
851
−H2O, 100
carbonate
carbonate (sal soda)
Na2CO3⋅7H2O
Na2CO3⋅10H2O
232.10
286.14
wh. pd., 1.535
wh., rhb., 1.506–
1.509
rhb. or trig.
wh., mn., 1.425
1.51
1.46
d. 35.1
∗Usual commercial form.
−3H2O, 120
−7H2O, 100
−12H2O, 100
0.00002220°
1220°
d., forms
NaOH
46.520°
v. s.
s.
d.
16.7
0.03112.8°
26.717°
s.
6115°
5.590.1°
v. s.
62.525°
6.90°
3.720°
500°
sl. s.
1.30°
2262° (anh.)
d.
i.
0.00037100°
952100°
170100°
v. s.
v. s.
100
s. HNO3, al., et.
i. al., et.; d. KOH
s. HF, h. alk., fused CaCl2
s. HF; i. alk.
s. HF; i. alk.
s. HF; i. alk.
s. HF; i. alk.
s. HNO3, h. H2SO4; i. alk.
0.5118° NH4OH; s. KCN,
Na2S2O3
s. NH4OH, Na2S2O3; i. al.
s. NH4OH, KCN; sl. s.
HCl
s. NH4OH, KCN, HNO3
s. gly.; v. sl. s. al.
i. bz.; d. al.
2.118° al.
7.825° abs. al.
i. al.
d. al.
i. al.
sl. s. al., NH4 salts; i. ac.
1.67 al., 5015° gly.
v. s.
140.730°
sl. s. al.
sl. s. al.
2.325°, 8.378° al.
i. al.
7.10°
s.
76.9100°
16.460°
s.
100100°
s.
8.7940°
52.3100°
(anh.)
20.380°
(anh.)
90.9100°
121100°
118.380°
(anh.)
48.5104°
s.
i. al., et.
s. gly.; i. al., et.
s.
21.50°
s.
23830°
i. al.
1.30.5 (anh.)
0°
1390
i.
i.
i. CS2; s. H2SO4
v. s. al.; i. NH3
s. alk.; i. NH4Cl
s. alk.; i. NH4Cl
s. HNO3 + HF, Ag; sl. s.
Pb, Zn; i. HF
s. HNO3 + HF, fused
alk.; i. HF.
s. HF, KOH
s. fused alk.; i. a.
d. alk.
d. conc. H2SO4, al.
27.5
9020°
79.50° (anh.)
d. al.; i. NH3
i. al., act.
i. al.
s. gly.; i. abs. al.
i. al.
sl. s. al.
sl. s. al.
(Continued )
2-21
2-22
TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Sodium (Cont.)
carbonate, sesqui- (trona)
chlorate
Formula
Na3H(CO3)2⋅2H2O
NaClO3
Formula
weight
Color, crystalline form,
and refractive index
chloride
chromate
chromate
citrate
cyanide
dichromate
NaCl
Na2CrO4
Na2CrO4⋅10H2O
2Na3C6H5O7⋅11H2O
NaCN
Na2Cr2O7⋅2H2O
58 .44
161 .97
342 .13
714 .31
49 .01
298 .00
wh., mn., 1.5073
wh., cb., or trig.,
1.5151
col., cb., 1.5443
yel., rhb.
yel., delq., mn.
wh ., rhb .
wh ., cb ., 1 .452
red, mn ., 1 .6994
ferricyanide
ferrocyanide
Na3Fe(CN)6⋅H2O
Na4Fe(CN)6⋅10H2O
298 .93
484 .06
red, delq .
yel ., mn .
fluoride (villiaumite)
formate
hydride
NaF
NaHCO2
NaH
hydrosulfide
hydrosulfide
hydrosulfite
hydroxide
hydroxide
hypochlorite
iodide
iodide
lactate
nitrate (soda niter)
nitrite
NaSH⋅2H2O
NaSH⋅3H2O
Na2S2O4⋅2H2O
NaOH
NaOH⋅3½H2O
NaOCl
NaI∗
NaI⋅2H2O
NaC3H5O3
NaNO3
NaNO2
oxide
Na2O
perborate
perchlorate
perchlorate
peroxide
peroxide
phosphate, monobasic
phosphate, monobasic
phosphate, dibasic
phosphate, dibasic
phosphate, tribasic
phosphate, tribasic
phosphate, metaphosphate, pyrophosphate, pyrophosphate (pyrodisodium)
phosphate (pyrodisodium)
potassium tartrate
silicate, metaSodium silicate, metasilicate, orthosilicofluoride
stannate
sulfate (thenardite)
sulfate
NaBO3⋅H2O
NaClO4
NaClO4⋅H2O
Na2O2∗
Na2O2⋅8H2O
NaH2PO4⋅H2O∗
NaH2PO4⋅2H2O
Na2HPO4⋅7H2O
Na2HPO4⋅12H2O
Na3PO4
Na3PO4⋅12H2O∗
Na4P4O12
Na4P2O7∗
Na4P2O7⋅10H2O
Na2H2P2O7
Na2H2P2O7⋅6H2O
NaKC4H4O6⋅4H2O
Na2SiO3
Na2SiO3⋅9H2O
Na4SiO4
Na2SiF6
Na2SnO3⋅3H2O
Na2SO4
Na2SO4
226 .03
106 .44
41 .99
68 .01
24 .00
92 .09
110 .11
210 .14
40 .00
103 .05
74 .44
149 .89
185 .92
112 .06
84 .99
69 .00
61 .98
99 .81
122 .44
140 .46
77 .98
222 .10
137 .99
156 .01
268 .07
358 .14
163 .94
380 .12
407 .85
265 .90
446 .06
221 .94
330 .03
282 .22
122 .06
284 .20
184 .04
188 .06
266 .73
142 .04
142 .04
tet ., 1 .3258
wh ., mn .
silv . nd ., 1 .470
col ., delq ., nd .
rhb .
col . cr .
wh ., delq .
mn .
pa . yel ., in soln . only
col ., cb ., 1 .7745
col ., mn .
col ., amor .
col ., trig ., 1 .5874
pa . yel ., rhb .
wh ., delq .
wh . pd .
rhb ., 1 .4617
hex .
yel .-wh . pd .
wh ., hex .
col ., rhb ., 1 .4852
col ., rhb ., 1 .4629
col ., mn ., 1 .4424
col ., mn ., 1 .4361
wh .
wh ., trig ., 1 .4458
col .
wh .
mn ., 1 .4525
col ., mn ., 1 .510
col ., mn ., 1 .4645
rhb ., 1 .493
col ., rhb ., 1 .520
rhb .
col ., hex ., 1 .530
wh ., hex ., 1 .312
hex . tablets
col ., rhb ., 1 .477
col ., mn .
Specific
gravity
2.112
2.49015°
2.163
2.723
1.483
°
1 .857 23.5
4
2 .5218°
Melting
point, °C
d.
248
800.4
392
19.9
−11H2O, 150
563 .7
−2H2O, 84 .6;
356 (anh .)
Boiling
point, °C
d.
1413
d .
1496
d . 400
1 .458
2 .79
1 .919
0 .92
992
253
d . 800
2 .130
d .
22
d .
318 .4
15 .5
d .
651
3 .6670°
2 .448
2 .257
2 .1680°
d .
308
271
2 .27
subl .
2 .02
2 .805
2 .040
1 .91
1 .679
1 .52
2 .53717 .5°
1 .62
2 .476
2 .45
1 .82
1 .862
1 .848
1 .790
2 .679
2 .698
d . 40
482 d .
d . 130
d .
d . 30
−H2O, 100
60
d .
34 .6
1340
73 .4
616 d .
988
d .
d . 220
70 to 80
1088
47
1018
d .
d . 140
tr . 100 to mn .
tr . 500 to hex .
Solubility in 100 parts
Cold water
130°
790°
42100°
230100°
0°
1390
1300
d . 380
d . 320
d . 200
−12H2O, 180
−11H2O, 100
−4H2O, 215
−6H2O, 100
100°
35.7
320°
v. s.
9125°
4810°
2380°
39.8
126100°
∞
250100°
8235°
50880°
18 .90°
17 .920° (anh .)
67100°
6398 .5°
(anh .)
5100°
160100°
40°
440°
d .
d .
Hot water
s .
s .
2220°
420°
s .
260°
158 .70°
v . s .
v . s .
730°
72 .10°
s .
s .
d .
347100°
v . s .
15856°
302100°
v . s .
v . s .
180100°
163 .2100°
Forms
NaOH
sl . s .
1700°
20915°
s . d .
s . d .
710°
91 .10°
18540°
4 .30°
4 .50°
28 .315°
s .
2 .260°
5 .40°
4 .50°
6 .90°
260°
s .
v . s .
s .
0 .440°
500°
50°
48 .840°
d .
320100°
28450°
d .
d .
39083°
30840°
2000100°
76 .730°
77100°
∞
s .
4596°
93100°
2140°
3640°
6626°
s . d .
v . s .
s .
2 .45100°
6750°
42100°
42 .5100°
Other reagents
s. al.
sl. s. al.; i. conc. HCl
sl . s . al .
i . al .
s . NH3; sl . s . al .
i . al .
i . al .
v . sl . s . al .
sl . s . al .; i . et .
i . bz ., CS2, CCl4, NH3;
s . molten metal
s . al .; d . a .
s . al .; d . a .
i . al .
v . s . al ., et ., gly .; i . act .
v . s . al ., act .
v . s . NH3
s . al .; i . et .
s . NH3; sl . s . gly ., al .
0 .320° et .; 0 .3 abs . al .;
4 .420° m . al .; v . s . NH3
d . al .
s . gly ., alk .
s . al .; 51 m . al .; 52 act .; i . et .
s . al .
s . dil . a .
i . al .
i . al .
i . CS2
s . a ., alk .
d . a .
i . al ., NH3
sl . s . al .
i . Na or K salts, al .
2918°, aN NaOH
i . al .
i . al ., act .
i . al .
d . HI; s . H2SO4
sulfate
sulfate
sulfate (Glauber’s salt)
sulfide, monosulfide, tetrasulfide, pentasulfite
sulfite
tartrate
thiocyanate
thiosulfate
thiosulfate (hypo)
tungstate
tungstate
tungstate, parauranate
vanadate
vanadate, pyroStannic chloride
Na2SO4
Na2SO4⋅7H2O
Na2SO4⋅10H2O
Na2S
Na2S4
Na2S5
Na2SO3
Na2SO3⋅7H2O
Na2C4H4O6⋅2H2O
NaCNS
Na2S2O3
Na2S2O3⋅5H2O∗
Na2WO4
Na2WO4⋅2H2O∗
Na6W7O24⋅16H2O
Na2UO4
Na3VO4⋅16H2O
Na4V2O7
SnCl4
142 .04
268 .15
322 .19
78 .04
174 .24
206 .30
126 .04
252 .15
230 .08
81 .07
158 .11
248 .18
293 .82
329 .85
2097 .05
348 .01
472 .15
305 .84
260 .52
col., hex.
tet.
col., mn., 1.396
pink or wh., amor.
yel., cb.
yel.
hex. pr., 1.565
mn.
rhb.
delq., rhb., 1.625±
mn.
mn. pr., 1.5079
wh., rhb.
wh., rhb.
wh., tri.
yel.
col. nd.
hex.
col., fuming lq.
oxide (cassiterite)
SnO2
150 .71
wh ., tet ., 1 .9968
sulfate
Sn(SO4)2⋅2H2O
346 .87
col ., delq ., hex .
Stannous bromide
chloride
chloride (tin salt)
sulfate
Strontium
884
1.464
1.856
2.633 154°
1.561
1.818
2.226
866 (anh.)
654
−30.2
7 .0
1127
17°
yel ., rhb .
wh ., rhb .
wh ., tri .
wh . cr .
silv . met .
2 .6
acetate
carbonate (strontianite)
chloride
chloride
hydroxide
hydroxide
Sr(C2H3O2)2
SrCO3
SrCl2
SrCl2⋅6H2O∗
Sr(OH)2
Sr(OH)2⋅8H2O∗
205 .71
147 .63
158 .53
266 .62
121 .63
265 .76
wh . cr .
wh ., rhb ., 1 .664
wh ., cb ., 1 .6499
wh ., rhb ., 1 .5364
wh ., delq .
col ., tet ., 1 .499
2 .099
3 .70
3 .052
1 .93317°
3 .625
1 .90
nitrate
nitrate
oxide (strontia)
Sr(NO3)2∗
Sr(NO3)2⋅4H2O
SrO
211 .63
283 .69
103 .62
col ., cb ., 1 .5878
wh ., mn .
col ., cb ., 1 .870
2 .986
2 .2
4 .7
SrO2
SrO2⋅8H2O
SrSO4
Sr(HSO4)2
NH2SO3H
S
S8
S8
S2Br2
S2Cl2
SCl2
SCl4
SO2
119 .62
263 .74
183 .68
281 .76
97 .09
32 .07
256 .52
256 .52
223 .94
135 .04
102 .97
173 .88
64 .06
wh . pd .
wh . cr .
col ., rhb ., 1 .6237
col ., granular
wh ., rhb .
pa . yel . pd ., 2 .0–2 .9
pa . yel ., mn .
pa . yel ., rhb .
red, fuming lq .
red-yel . lq .
dark red fuming lq .
yel .-brn . lq .
col . gas
oxide, tri-(β)
Sulfuric acid
Sulfuric acid
∗Usual commercial form .
SO3
(SO3)2
H2SO4∗
H2SO4⋅H2O
80 .06
160 .13
98 .08
116 .09
col . pr .
col ., silky, nd .
col ., viscous lq .
pr . or lq .
d.
287
d. 48.0
692
−2H2O, 100
−16H2O, 300
278 .52
189 .62
225 .65
214 .77
87 .62
oxide, tri-(α)
−10H2O, 100
275
251.8
d.
−7H2O, 150
1.667
1.685
4.179
3.245
3.98714°
SnBr2
SnCl2
SnCl2⋅2H2O∗
SnSO4
Sr
peroxide
peroxide
sulfate (celestite)
sulfate, acid
Sulfamic acid
Sulfur, amorphous
Sulfur, monoclinic
Sulfur, rhombic
Sulfur bromide, monochloride, monochloride, dichloride, tetraoxide, di-
32.4
5 .12
2 .7115 .5°
3 .96
2 .03 124°
2 .046
1 .96
2 .07
2 .635
1 .687
1 .621 1515°
lq ., 1 .4340°;
2 .264 (A)
lq ., 1 .923;
2 .75 (A)
1 .9720°
1 .834 184°
1 .842 154°
215 .5
246 .8
37 .7
−SO2, 360
800
149760atm .
873
−4H2O, 61
375
−7H2O in
dry air
570
114.1
620
623
d .
1150
d .
−CO2, 1350
−6H2O, 100
19.420°
44.90°
3615°
15.410°
s.
s.
13.90°
34.72°
296°
11010°
500°
74.70°
57.580°
880°
8
i.
v. s.
s.
s.
45.360°
202.626°
41234°
57.390°
s.
s.
28.384°
67.818°
6643°
225100°
23180°
301.860°
97100°
123.5100°
d.
i.
d.
i .
i .
v . s .
d .
s .
83 .90°
118 .70°
1919°
d .
d .
269 .815°
∞
18100°
Forms
Sr(OH)2
36 .497°
0 .065100°
100 .8100°
19840°
21 .83100°
47 .7100°
36 .90°
0 .001118°
43 .50°
1040°
0 .410°
0 .900°
444 .6
444 .6
444 .6
540 .18mm
138
59
d . > −20
−10 .0
400°
62 .20°
Forms
Sr(OH)2
0 .00820°
0 .01820°
0 .01130°
d .
200°
i .
i .
i .
d .
d .
d .
d .
22 .80°
16 .83
44 .6
d .
50
10 .49
8 .62
d . 340
290
Forms H2SO4
∞
∞
2430
d .
−8H2O, 100
1580 d .
d .
205 d .
120
119 .0
112 .8
−46
−80
−78
−30
−75 .5
d .
d.
i. al.
sl. s. al.; i. et.
s. al.
s. al.
i. al., NH
i. al.
i. al.
v. s. al.
s. NH3; v. sl. s. al.
sl. s. NH3; i. a., al.
s. alk. carb., dil. a.
i. al.
i. al.
s. abs. al., act., NH3;
s. ∞ CS2
s . conc . H2SO4; i . alk .;
NH4OH, NH3
s . dil . H2SO4, HCl; d .
abs . al .
s . C6H5N
s . alk ., abs . al ., et .
s . tart . a ., alk ., al .
s . H2SO4
s . al ., a .
0 .2615° m . al .
s . a ., NH4 salts, aq . CO2
v . sl . s . act ., abs . al .; i . NH3
s . NH4Cl
s . NH4Cl; i . act .
10089°
12420°
s . NH3; 0 .012 abs . al .
i . HNO3
sl . s . al .; i . et .
d .
d .
0 .011432°
s . al ., NH4Cl; i . act .
s . al .; i . NH4OH
sl . s . a .; i . dil . H2SO4, al .
1470° H2SO4
sl . s . al ., act .; i . et .
sl . s . CS2
s . CS2, al .
240°, 18155° CS2
4070°
i .
i .
i .
s . CS2, et ., bz .
d . al .
4 .550°
s . H2SO4; al ., ac .
s . H2SO4
∞
∞
s . H2SO4
d . al .
d . al .
(Continued )
2-23
2-24
TABLE 2-1
Physical Properties of the Elements and Inorganic Compounds (Continued )
Name
Formula
Formula
weight
Color, crystalline form,
and refractive index
Specific
gravity
Melting
point, °C
Boiling
point, °C
Solubility in 100 parts
Cold water
Hot water
Sulfuric acid
Sulfuric acid, pyroSulfuric oxychloride
Sulfurous oxybromide
oxychloride
Tantalum
H2SO4⋅2H2O
H2S2O7
SO2Cl2
SOBr2
SOCl2
Ta
134 .11
178 .14
134 .97
207 .87
118 .97
180 .95
col. lq.
cr .
col . lq .
or .-yel . lq .
yel . fuming lq .
bk .-gray, cb .
1.650 04°
1 .920°
1 .667 204°
2 .6818°
1 .631
16 .6
−38.9
35
−54 .1
−50
−104 .5
2850
167
d .
69 .1760mm
6840mm
75 .6
>4100
∞
d .
d .
d .
d .
i .
∞
Tellurium
Te
127 .60
met ., hex .
(α) 6 .24;
(β) 6 .00
452
1390
i .
i .
Terbium
Thallium
acetate
chloride, monochloride, sesquichloride, trichloride, trisulfate (ic)
sulfate (ous)
sulfate, acid
Thio, cf. sulfo or sulfur
Thorium
Tb
Tl
TlC2H3O2
TlCl
Tl2Cl3
TlCl3
TlCl3⋅4H2O
Tl2(SO4)3⋅7H2O
Tl2SO4
TlHSO4
158 .93
204 .38
263 .43
239 .84
515 .13
310 .74
382 .80
823 .06
504 .83
301 .45
blue-wh ., tet .
silky nd .
wh ., cb .
yel ., hex .
hex . pl .
nd .
lf .
col ., rhb ., 1 .8671
trimorphous
11 .85
3 .68
7 .00
5 .9
303 .5
110
430
400–500
25
37
−6H2O, 200
632
115 d .
1650
806
d .
d .
−4H2O, 100
d .
d .
i .
v . s .
0 .210°
0 .2615°
v . s .
86 .217°
d .
2 .700°
d .
d .
18 .45100°
Th
232 .04
cb .
11 .2
1845
>3000
i .
i .
oxide, di- (thorianite)
sulfate
sulfate
Thulium
Tin
ThO2
Th(SO4)2
Th(SO4)2⋅9H2O
Tm
Sn
264 .04
424 .16
586 .30
168 .93
118 .71
wh ., cb .
>2800
4400
mn . pr .
9 .69
4 .22517°
2 .77
silv . met ., tet .
7 .31
231 .85
2260
i .
0 .740°
sl . s .
i .
i .
5 .2250°
sl . s .
i .
i .
Tin
Sn
118 .71
gray, cb .
5 .750
Stable −163
to +18
2260
i .
i .
Tin salts, cf. stannic and stannous
Titanic acid
H2TiO3
97 .88
wh . pd .
i .
i .
i .
d .
d .
s .
s .
i .
s .
d .
i .
i .
i .
6 .77
17 .5°
i .
i .
1 .8100°
1 .9100°
Other reagents
d . al .
d . al .
s . ac .; d . al .
s . bz ., CS2, CCl4; d . act .
s . bz ., chl .
s . fused alk ., HF; i . HCl,
HNO3, H2SO4
s . H2SO4, HNO3, KCN,
KOH, aq . reg .; i . CS2
s . HNO3, H2SO4; i . NH3
v . s . al .
sl . s . HCl; i . al ., NH4OH
s . al ., et .
s . al ., et .
s . dil . H2SO4
v . sl . s . dil . H2SO4
−9H2O, 400
>3000
s . HCl, H2SO; sl . s .
HNO3; i . HF, alk .
s . h . H2SO4; i . alk .
s . HCl, H2SO4, dil . HNO3
h . aq KOH
s . a ., h . alk . solns .
s . alk .; v . sl . s . dil . a .;
i . al .
s . a .
i . CS2, et ., chl .
Ti
TiCl2
47 .87
118 .77
dark gray, cb .
bk ., delq .
chloride, trichloride, tetraoxide, di- (anatase)
TiCl3
TiCl4∗
TiO2
154 .23
189 .68
79 .87
oxide, di- (brookite)
TiO2
4 .26
1640 d .
<3000
i .
i .
s . H2SO4, alk .
19 .3
3370
5900
i .
i .
6000
6000
i .
i .
i .
i .
i .
i .
i .
sl . s .
s . h . conc . KOH; sl . s .
NH3, HNO3, aq . reg .
s . F2; i . a .
s . h . HNO3; sl . s . HCl,
H2SO4
s . alk .; i . a .
s . HF, alk ., NH3
i .
i .
s . a ., alk . carb .; i . alk .
i .
d .
i .
i .
s . a .; i . alk .
d . a .
s . HNO3, conc . H2SO4
Titanium
chloride, di-
4 .50
1800
Unstable in
air
d . 440
−30
W
183 .84
vl ., delq .
col . lq .
brn . or bk ., tet .,
2 .534–2 .564
brn . or bk ., rhb .,
2 .586
col . if pure, tet .,
2 .615
gray-bk ., cb .
WC
W 2C
195 .85
379 .69
gray pd ., cb .
iron gray
15 .718°
16 .0618°
2777
2877
oxide, triTungstic acid (tungstite)
WO3
H2WO4
231 .84
249 .85
yel ., rhb .
yel ., rhb . 2 .24
7 .16
5 .5
Uranic acid
H2UO4
304 .04
yel . pd .
5 .92615°
Uranium
carbide
oxide, di- (uraninite)
U
U2C3
UO2
238 .03
512 .09
270 .03
wh . cr .
cr .
bk ., rhb .
18 .485 134°
11 .28
10 .9
>2130
−½H2O,
100; 1473
−H2O, 250
to 300
1133
2400
2176
oxide, di- (rutile)
Tungsten
carbide
carbide
TiO2
79 .87
79 .87
lq ., 1 .726
3 .84
136 .4
4 .17
3500
i .
s . dil . HCl
sl . s . alk .
oxide (pitchblende)
sulfate (ous)
Uranyl acetate
carbonate (rutherfordine)
nitrate
sulfate
Vanadic acid, metaVanadic acid, pyroVanadium
chloride, dichloride, trichloride, tetraoxide, dioxide, trioxide, tetraoxide, pentaoxychloride, monoVanadyl chloride
chloride, dichloride, triWater†
U3O8
U(SO4)2⋅4H2O
UO2(C2H3O2)2⋅2H2O
UO2CO3
UO2(NO3)2⋅6H2O
UO2SO4⋅3H2O
HVO3
H4V2O7
V
VCl2
VCl3
VCl4
V2O2
V2O3
V2O4
V2O5
VOCl
(VO)2Cl
VOCl2
VOCl3
H2O
842 .08
502 .22
424 .15
330 .04
502 .13
420 .14
99 .95
217 .91
50 .94
121 .85
157 .30
192 .75
133 .88
149 .88
165 .88
181 .88
86 .39
169 .33
137 .85
173 .30
18 .02
Water, heavy
Xenon
D 2O
Xe
20 .029
131 .29
olive gn.
gn., rhb.
yel., rhb.
tet.
yel., rhb., 1.4967
yel . cr .
yel . scales
pa . yel ., amor .
lt . gray, cb .
gn ., hex ., delq .
pink, tabular, delq .
red lq .
lt . gray cr .
bk . cr .
blue cr .
red-yel ., rhb .
brn . pd .
yel . cr .
gn ., delq .
yel . lq .
col . lq ., 1 .3330020°;
hex . solid, 1 .309
col . lq ., 1 .3284420°
col . gas
Ytterbium
Yttrium
Zinc
acetate
acetate
bromide
carbonate
Yb
Y
Zn
Zn(C2H3O2)2
Zn(C2H3O2)2⋅2H2O∗
ZnBr2
ZnCO3
173 .04
88 .91
65 .41
183 .50
219 .53
225 .22
125 .42
dark gray, hex .
silv . met ., hex .
mn .
wh ., mn ., 1 .494
rhb .
wh ., trig ., 1 .818
chloride
ZnCl2
136 .32
cyanide
hydroxide
iodide
Zn(CN)2
Zn(OH)2
ZnI2
117 .44
99 .42
319 .22
wh ., delq ., 1 .687,
uniaxial
col ., rhb .
col ., rhb .
cb .
nitrate
oxide (zincite)
oxide
peroxide
phosphide
silicate
Zn(NO3)2⋅6H2O
ZnO
ZnO
ZnO2
Zn3P2
ZnSiO3
297 .51
81 .41
81 .41
97 .41
258 .17
141 .49
sulfate (zincosite)
sulfate
sulfate
sulfate (goslarite)
sulfide (α) (wurzite)
sulfide (β) (sphalerite)
ZnSO4
ZnSO4⋅H2O
ZnSO4⋅6H2O
ZnSO4⋅7H2O∗
ZnS
ZnS
161 .47
179 .49
269 .56
287 .58
97 .47
97 .47
2-25
sulfide (blende)
ZnS
97 .47
sulfite
ZnSO3⋅2½H2O
190 .51
Zirconium
Zr
91 .22
oxide, di- (baddeleyite)
ZrO2
123 .22
123 .22
oxide, di- ( free from Hf)
ZrO2
∗Usual commercial form .
†
Cf. special tables on water and steam, Tables 2-3, 2-4, and 2-5 .
note: °F = 9⁄ 5°C + 32 .
col ., tet .
wh ., hex ., 2 .004
wh ., amor .
yel .
steel gray, cb .
hex . or rhb .; glass,
1 .650
wh ., rhb ., 1 .669
col .
mn .
rhb ., 1 .4801
wh ., hex ., 2 .356
wh ., cb .; glass (?)
2 .18–2 .25
wh ., granular
mn .
cb ., pd . ign . easily
yel . or brn ., mn ., 2 .19
wh ., mn .
7.31
2.8915°
5.6
2.807
3 .2816 .5°
5 .96
3 .2318°
3 .0018°
1 .81630°
3 .64
4 .87 184°
4 .399
3 .357 184°
2 .824
3 .64
2 .8813°
1 .829
1 .004° (lq .);
0 .9150° (ice)
1 .10720°
lq ., 3 .06−109 .1
2 .7−140°
4 .53 (A)
d.
−4H2O, 300
−2H2O, 110
60.2
d . 100
118
1710
3000
d .
−109
ign .
1970
1967
800
148 .5755mm
d . 1750
d . in air
i.
2311°
9.217°
i.
963°
d.
s. HNO3, H2SO4
s. dil. a.
s. al., act.
170.30°
18 .913 .2°
i .
i .
i .
s .
s .
s . d .
i .
sl . s .
i .
0 .820°
i .
i .
d .
s . d .
∞60°
23025°
v . s . ac ., al ., et .; i . dil ., alk .
4 al .; s . a .
s . a ., alk .; i . NH3
s . a ., alk ., NH4OH
s . HNO3, H2SO4; i . aq ., alk .
s . al ., et .
s . abs . al ., et .
s . abs . al ., et ., chl ., ac .
s . a .
s . HNO3, HF, alk .
s . a ., alk .
s . a ., alk .; i . abs . al .
v . s . HNO3
s . HNO3
s . abs . al ., dil . HNO3
s . al ., et ., ∞Br2
∞ al .; sl . s . et .
i .
d .
d .
i .
s .
i .
<−15
0
127 .19
100
3 .82
−140
101 .42
−109 .1
∞
24 .20° cc
∞
7 .350° cc
∞ al .; sl . s . et .
5 .51
7 .140
1 .840
1 .735
4 .2194°
4 .42
1490
419 .4
242
237
394
−CO2, 300
2500
907
subl . in vac .
−2H2O, 100
650
sl . d .
i .
3025°
4025°
3900°
0 .00115°
d .
i .
44 .6100°
66 .6100°
670100°
2 .91 254°
283
732
43225°
615100°
d . 80
d . 125
446
624
0 .000518°
0 .0005218°
4300°
sl . s .
3 .053
°
4 .666 14.2
4
2 .065 144°
5 .606
5 .47
1 .571
4 .55 134°
3 .52
36 .4
>1800
>1800
expl . 212
>420
1437
v . s . dil . a ., h . KOH
s . a ., ac ., alk .
2 .825°, 16679° al .
v . s . al .
v . s . NH4OH, al ., et .
s . a ., alk ., NH4 salts;
i . act ., NH3
10012 .5° al .; v . s . et .; i .
NH3
s . KCN, NH3, alk .; i . al .
s . a ., alk ., NH4OH
s . a ., al ., NH3, aq .
(NH4)2CO3
v . s . al .
s . a ., alk ., NH4Cl; i . NH3
3 .74 154°
3 .28 154°
2 .072 154°
1 .96616 .5°
4 .087
4 .102 254°
d . 740
d . 238
−5H2O, 70
tr . 39
1850150atm .
tr . 1020
−6H2O, 105
1100
−7H2O, 280
subl . 1185
4 .04
6 .4
5 .49
5 .73
−2½H2O, 100
1700
2700
d . 200
>2900
4300
510100°
324 .5
0 .0004218°
0 .0004218°
0 .0022
i .
i .
∞36 .4°
420°
s .
s .
115 .20°
0 .0006918°
i .
61100°
89 .5100°
s .
653 .6100°
i .
i .
sl . s . al .; i . act .; NH3
sl . s . al .; i . act .; NH3
v . s . a .; i . ac .
s . a .
i .
0 .16
i .
i .
i .
i .
d .
i .
i .
i .
v . s . a .; i . ac .
s . H2SO3, NH4OH; i . al .
s . HF, aq . reg .; sl . s . a .
s . H2SO4, HF
s . H2SO4, HF
i . NH4OH; d . a .
s . dil . a .
sl . s . al .; s . gly .
2-26
TABLE 2-2 Physical Properties of Organic Compounds*
Abbreviations Used in the Table
(A), density referred to air
cr., crystalline
i-, iso-, containing the group
al., ethyl alcohol
d., decomposes
(CH3)2CHamor., amorphous
d-, dextrorotatory
i., insoluble
aq., aqua, water
dl-, dextro-laevorotatory
ign., ignites
brn., brown
et., ethyl ether
l-, laevorotatory
bz., benzene
expl., explodes
lf., leaflets
c., cubic
gn., green
lq., liquid
cc., cubic centimeter
h., hot
m-, meta
chl., chloroform
hex., hexagonal
mn., monoclinic
col., colorless
n-, normal
This table of the physical properties includes the organic compounds of most general interest . For the
properties of other organic compounds, reference must be made to larger tables in Lange’s Handbook of
Chemistry (Handbook Publishers), Handbook of Chemistry and Physics (Chemical Rubber Publishing Co .),
Van Nostrand’s Chemical Annual, International Critical Tables (McGraw-Hill), and similar works .
The molecular weights are based on the atomic weight values in “Atomic weights of the Elements 2001,”
PURE Appl. Chem., 75, 1107, 2003 . The densities are given for the temperature indicated and are usually
nd., needles
s-, sec-, secondary
v. s., very soluble
v. sl. s., very slightly soluble
o-, ortho
silv., silvery
wh., white
or., orange
sl., slightly
yel., yellow
p-, para
subl., sublimes
(+), right rotation
pd., powder
sym., symmetrical
>, greater than
pet., petroleum ether
t-, tertiary
<, less than
pl., plates
tet., tetragonal
∞, infinitely
pr., prisms
tri., triclinic
rhb., rhombic
uns., unsymmetrical
s., soluble
v., very
referred to water at 4°C, e.g., 1 .02895/4 a density of 1 .028 at 95°C referred to water at 4°C, the 4 being omitted
when it is not clear whether the reference is to water at 4°C or at the temperature indicated by the upper
figure . The melting and boiling points given have been selected from available data as probably the most
accurate . The solubility is given in grams of the substance in 100 of the solvent . In the case of gases, the
solubility is often expressed in some manner as “510 cc .” which indicates that, at 10°C, 5 cc . of the gas are
soluble in 100 of the solvent .
Name
Synonym
Formula
Formula
weight
Form and
color
Abietic acid
Acenaphthene
Acetal
Acet-aldehyde
-aldehyde, par-aldehyde ammonia
-amide
-anilide
-phenetidide (o-)
(m-)
-toluidide (o-)
(p-)
Acetic acid
anhydride
nitrile
Acetone
Acetonyl urea
Acetophenone benzoyl hydride
Acetyl-chloride
-phenylenediamine (-p)
Acetylene
dichloride (cis)
(trans)
Aconitic acid
Acridine
Acrolein ethylene aldehyde
Acrylic acid
nitrile
Adipic acid
amide
nitrile
Adrenaline (1-) (3,4,1)
Alanine (α) (dl-)
Aldol acetaldol
Alizarin
Allyl alcohol
bromide
chloride
thiocyanate (i)
thiourea
Aluminum ethoxide
Amino-anthraquinone (α)
(β)
-azobenzene
-benzoic acid (m-)
(p-)
sylvic acid, abietinic acid
naphthylene ethylene
acetaldehyde diethylacetal
ethanal
paraldehyde
C20H30O2
C10H6(CH2)2
CH3CH(OC2H5)2
CH3CHO
(C2H4O)3
CH3CHOHNH2
CH3CONH2
C6H5NHCOCH3
CH3CONHC6H4OC2H5
CH3CONHC6H4OC2H5
CH3C6H4NHCOCH3
CH3C6H4NHCOCH3
CH3CO2H
(CH3CO)2O
CH3CN
CH3COCH3
<NHCONHCOC>(CH3)2
CH3COC6H5
CH3COCl
C2H3ONHC6H4NH2
HC⋮CH
CHCl:CHCl
CHCl:CHCl
C3H3(CO2H)3
C6H4 < (CH)(N) > C6H4
CH2:CH⋅CHO
CH2:CH⋅CO2H
CH2:CH⋅CN
(CH2CH2CO2H)2
(CH2CH2CONH2)2
(CH2CH2CN)2
C6H3(OH)2(CHOHCH2NHCH3)
CH3CH(NH2)CO2H
CH3CH(OH)CH2COH
C6H4(CO)2C6H2(OH)2
CH2:CH⋅CH2OH
CH2:CH⋅CH2Br
CH2:CH⋅CH2Cl
CH2:CH⋅CH2NCS
CH2:CH⋅CH2NHCSNH2
Al(OCH2CH3)3
C6H4(CO)2C6H3NH2
C6H4(CO)2C6H3NH2
C6H5⋅N:N⋅C6H4NH2
H2N⋅C6H4CO2H
H2N⋅C6H4CO2H
302 .45
154 .21
118 .17
44 .05
132 .16
61 .08
59 .07
135 .16
179 .22
179 .22
149 .19
149 .19
60 .05
102 .09
41 .05
58 .08
128 .13
120 .15
78 .50
150 .18
26 .04
96 .94
96 .94
174 .11
179 .22
56 .06
72 .06
53 .06
146 .14
144 .17
108 .14
183 .20
89 .09
88 .11
240 .21
58 .08
120 .98
76 .52
99 .15
116 .18
162 .16
223 .23
223 .23
197 .24
137 .14
137 .14
lf .
rhb ./al .
lq .
col . lq .
col . cr .
col . cr .
col . cr .
rhb ./al .
lf ./al .
lf ./al .
rhb .
rhb . or mn .
col . lq .
col . lq .
col . lq .
col . lq .
tri ./al .
lf .
col . lq .
nd ./aq .
col . gas
col . lq .
col . lq .
cr ./aq .
rhb ./aq . al .
col . lq .
col . lq .
col . lq .
mn . pr .
cr . pd .
col . oil
col . pd .
nd ./aq .
col . lq .
red rhb .
col . lq .
lq .
col . lq .
col . oil
col . pr .
pd .
red nd .
red nd .
yel . mn .
nd ./aq .
mn . pr .
ethanamide
antifebrin
o-ethoxyacetanilide
acetyl-m-phenetidine
N-tolylacetamide
N-tolylacetamide
ethanoic acid, vinegar acid
acetyl oxide, acetic oxide
methyl cyanide
propanone, dimethyl ketone
dimethyl hydantoin
methyl-phenyl ketone
ethanoyl chloride
amino-acetanilide (p)
ethyne; ethine
1,2-dichloroethene
dioform
equisetic acid; citridic acid
acrylic aldehyde, propenal
propenoic acid
vinyl cyanide
hexandioc acid, adipinic acid
tetramethylene
1-suprarenine
2-hydroxybutyraldehyde
Anthraquinoic acid
propen-1-ol-3,propenyl alcohol
3-bromo-propene-1
3-chloro-propene-1
mustard oil
thiosinamide
aminodracylic acid
Specific
gravity
1 .06995/95
0 .82122/4
0 .78318/4
0 .99420/4
1 .159
1 .214
1 .16815
1 .21215
1 .04920/4
1 .08220/4
0 .78320/4
0 .79220/4
1 .03315/15
1 .10520/4
(A) 0 .906
1 .29115/4
1 .26515/4
0 .84120/4
1 .06216/4
0 .81120
1 .36025/4
0 .95119/19
1 .10320/4
0 .85420/4
1 .39820/4
0 .93820/4
1 .01320/4
1 .21920/20
1 .14220/0
1 .5114°
Melting
point, °C
182
95
−123 .5
10 .5–12
97
81(69 .4)
113–4
79
96–7
110
153
16 .7
−73
−41
−94 .6
175
20 .5
−112 .0
162
−81 .5891
−80 .5
−50
192 d .
110–1
−87 .7
12–13
−82
151–3
226–7
1
d . 207–11
295 d .
289–90
−129
−119 .4
−136 .4
−80
77–8
150–60
256
302
126–7
173–4
187–8
Boiling
point, °C
278–9
102 .2
20 .2
124 .4752
100–10 d .
222
305
>250
296
306–7
118 .1
139 .6
81 .6–2 .0
56 .5
subl .
202 .3749
51–2
−84760
60 .3
48 .4
346
52 .5
141–2
78–9
26510
295
subl . >200
8320
430
96 .6
70–1753
44 .6
152
200–510
subl .
subl .
225120
Solubility in 100 parts
Water
Alcohol
Ether
i .
i .
625
∞
1213
v . s .
s .
0 .56
i .
sl . s .
0 .8619
0 .0922
∞
12 c .
∞
∞
s .
i .
d .
s . h .
100 cc .18
0 .3520
0 .6320
3315
sl . s . h .
40
∞
s .
1 .415
0 .412
v . sl . s .
0 .0320
2217
∞
0 .03100
∞
i .
<0 .1
0 .2
30
d .
i .
i .
sl . s . h .
v . sl . s .
0 .313
v . s .
s . h .
∞
∞
∞
v . s .
s .
2120
s .
s .
s .
1025
∞
∞
∞
∞
s .
s .
d .
v . s .
600 cc .18
∞
∞
sl . s .
s .
s .
∞
v . s .
s . chl .
∞
∞
∞
sl . s .
v . sl . s .
7 25
v . s .
0 .615
s .
v . sl . s .
v . sl . s .
∞
v . s .
∞
∞
∞
∞
s .
i .
s .
s .
s . h .
210
1110
v . sl . s .
i .
i .
s .
v . s .
∞
∞
∞
∞
v . sl . s .
v . sl . s .
s .
i .
s .
1 .86
8 .26
s .
s .
∞
∞
∞
∞
s .
s .
∞
v . s .
∞
∞
v . sl . s .
s .
s .
Amino-diphenylamine (p-)
-G-acid (2-)(6-,8-), Na2 salt
-mono-potassium salt
-sodium salt
-J-acid (2-)(5-,7-)
-mono-potassium salt
-naphthol sulfonic (1-,2-,4-)(α-)
(1-,8-,4-)
-phenol (o-)
(m-)
(p-)
-toluene sulfonic acid (1-,2-,3-)
(1-,4-,2-)
(1-,4-,3-)
(1-,2-,5-)
Amyl acetate (n-)
(i-)
(s-)
(s-)
(t-)
alcohol (n-) fusel oil,
(s-,n-) methyl-propyl carbinol,
(prim .-,i-) isobutyl carbinol,
(s-,i-)
(t-)
(d-)
-amine (n-)
(s-,n-)
(i-)
(t-)
2-aminophenol
3-aminophenol
p-hydroxyaniline
common amyl acetate
α-Me-Bu-acetate
di Et-carbinol acetate
pentanol-1
pentanol-2
2-methyl-butanol-4
2-methyl-butanol-3
2-methyl-butanol-2
active amyl alcohol
1-NH2-2-Me-butane
3-amino pentane
3-NH2-2-Me-butane
aniline (i-)
benzoate (i-)
bromide (n-)
(i-)
(t-)
n-butyrate (n-)
(i-)
(t-)
i-butyrate (i-)
chloride (n-)
(s-)
(s-)
(i-)
(s-,i-)
(t-)
i-cyanide (i-)
formate (n-)
(i-)
iodide (n-)
(i-)
(s-,n-)
(t-)
1-bromopentane
4-Br-2-Me-butane
2-Br-2-Me-butane
1-chloropentane
2-chloropentane
3-chloropentane
4-Cl-2-Me-butane
3-Cl-2-Me-butane
2-Cl-2-Me-butane
1-Cl-2-Me-butane
iso-caproic iso-nitrile
1-iodopentane
4-I-2-Me-butane
2-iodopentane
2-I-2-Me-butane
2-27
H2N⋅C6H4NH⋅C6H5
C10H5(NH2)(SO3Na)2
C10H5(NH2)S2O6HK
C10H5(NH2)S2O6HNa
C10H5(NH2)(SO3H)2
C10H5(NH2)S2O6HK
C10H5OHNH2SO3H½H2O
NH2(OH)C10H5SO3H
H2N⋅C6H4⋅OH
H2N⋅C6H4⋅OH
H2N⋅C6H4⋅OH
C6H3(CH3)(NH2)SO3H
C6H3(CH3)(NH2)SO3H⋅H2O
C6H3(CH3)(NH2)SO3H⋅½H2O
C6H3(CH3)(NH2)SO3H⋅H2O
CH3CO2CH2(CH2)3CH3
CH3CO2CH2CH2CH(CH3)2
CH3CO2CH2CH(CH3)C2H5
CH3CO2CH(CH3)CH2C2H5
CH3CO2CH(C2H5)2
CH3CO2C(CH3)2C2H5
CH3(CH2)3CH2OH
C2H5CH2CH(OH)CH3
(CH3)2CHCH2CH2OH
(C2H5)2CHOH
(CH3)2CHCH(OH)CH3
(CH3)2C(OH)C2H5
(CH3)3CCH2OH
C2H5CH(CH3)CH2OH
CH3(CH2)4NH2
(C3H7)(CH3)CHNH2
(CH3)2CH(CH2)2NH2
(C2H5)(CH3)2CNH2
C2H5CH(CH3)CH2NH2
(C2H5)2CHNH2
(CH3)2CHCH(CH3)NH2
C6H5NHC5H11
C6H5CO2C5H11
CH3(CH2)3CH2Br
(CH3)2CH(CH2)2Br
(CH3)2C(Br)C2H5
C2H5CH2CO2(CH2)4CH3
C2H5CH2CO2⋅C5H11
C3H7CO2C(CH3)2C2H5
(CH3)2CHCO2C5H11
CH3(CH2)3CH2Cl
C2H5CH2CHClCH3
(C2H5)2CHCl
(CH3)2CH(CH2)2Cl
(CH3)CHCHClCH3
(CH3)2CClC2H5
(CH3)(C2H5)CHCH2Cl
(CH3)2CH(CH2)2NC
HCO2CH2(CH2)3CH3
HCO2CH2CH2CH(CH3)2
CH3(CH2)3CH2I
(CH3)2CHCH2CH2I
C2H5CH2CHICH3
(CH3)2CIC2H5
C2H5CH(CH3)CH2I
CH3(CH2)3CH2SH
(C2H5)2CHSH
(CH3)2CH(CH2)2SH
C5H11⋅C6H4OH
C2H5CO2(CH2)4CH3
C2H5CO2(CH2)2CH(CH3)2
C2H5CO2C5H11
HOC6H4CO2C5H11
C4H9CO2C5H11
C4H9CO2C5H11
184 .24
347 .28
341 .40
325 .29
303 .31
341 .40
248 .26
239 .25
109 .13
109 .13
109 .13
187 .22
205 .23
196 .22
205 .23
130 .18
130 .18
130 .18
130 .18
130 .18
130 .18
88 .15
88 .15
88 .15
88 .15
88 .15
88 .15
88 .15
88 .15
87 .16
87 .16
87 .16
87 .16
87 .16
87 .16
87 .16
163 .26
192 .25
151 .04
151 .04
151 .04
158 .24
158 .24
158 .24
158 .24
106 .59
106 .59
106 .59
106 .59
106 .59
106 .59
106 .59
97 .16
116 .16
116 .16
198 .05
198 .05
198 .05
198 .05
198 .05
104 .21
104 .21
104 .21
164 .24
144 .21
144 .21
144 .21
208 .25
172 .26
172 .26
nd./aq. al.
67
354
col. nd.
pr.
lf.
nd.
mn.
nd.
tri./aq.
col. lq.
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
cr .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
lq .
col . lq .
col . lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
lq .
col . lq .
lq .
cr .
lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
173
122–3
184–6 d.
subl.
subl.
d.
0.87920/20
0 .87615/4
0 .88013
0 .9220
0 .87120/4
0 .87419
0 .817 20/20
0 .81020/20
0 .81315/4
0 .815 25/4
0 .81919
0 .809 20/4
20/4
0 .816
0 .76619
0 .749 20/4
0 .75118/4
0 .73125/4
0 .75518
0 .749 20/4
0 .75718
0 .92815/4
0 .99214/14
1 .21820/4
1 .22017/15
1 .21619/0
0 .87115/4
0 .86619/15
0 .86515/0
0 .8760/4
0 .878 20/4
0 .870 20/4
0 .895 21
0 .89320/4
0 .8830
0 .87120/4
0 .88117 .5
0 .9020
0 .882 20/4
1 .51020/4
1 .515 18/4
1 .507 17/4
1 .47119/15
1 .524 20/4
0 .857 20
−H2O, 120
−70.8
−78 .5
−117 .2
−11 .9
52–3
−55
−105
−95
−73 .2
−99
−72 .9
−73 .5
−93 .5
−86
148.4737
142757
141–2
133 .5
133
124 .5 749
137 .9
119 .5
132 .0
115 .6
113–4
102
113–4
128
103–4
91–2
95
77–8
95–6
90–1
83–4
254 .5
261746
129 .7
120745
108765
186 .4
178 .6
164
168 .8
108 .4
96 .7
97 .3
99 .7 758
91753
85 .7
98–9
137–9
132
123 .5
157 .0
147 765
144–5
127 765
148
126767
105
120
265–7
168 .7
160 .2
5816
265
194
173–4
mercaptan (n-)
pentanthiol-1
(n-)
pentanthiol-3
(i-)
2-Me-butanthiol-4
0 .83520/4
phenol (t-)(p-)
pentaphen
93
propionate (n-)
0 .87615/4
−73 .1
(i-)
0 .870 20/4
(act .)
0 .866 20/4
salicylate (n-)
1 .06515
Amyl i-valerate (i)
0 .85820/15
(t-)
0 .86114/0
∗By N . A . Lange, Ph .D ., Handbook Publishers, Inc ., Sandusky, Ohio . Abridged from table of Physical Constants of Organic Compounds in Lange’s Handbook of Chemistry.
sl. s.
v. sl. s.
12.820
2.718
10.0 20
3.418
v. s.
v. sl. s.
1.7 0
2.6 0
1.10
0.97 11
0.5 20
0.47
311
v. sl. s.
0 .315
v . sl . s .
sl . s .
sl . s .
v . sl . s .
2 .7 22
420
214
5 .5 30
2 .830
sl . s .
sl . s .
3 .630
s .
∞
∞
∞
∞
∞
∞
i .
i .
i .
0 .0216
i .
0 .05 50
i .
sl . s .
i .
i .
i .
i .
i .
i .
i .
i .
i .
v . sl . s .
0 .322
i .
i .
i .
i .
i .
i .
i .
i .
sl . s .
i .
0 .125
v . sl . s .
i .
v . sl . s .
sl . s .
s.
s.
4.30
s.
40
v. s.
sl. s.
i. bz.
i.
i.
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
s .
s .
s .
∞
∞
∞
s .
s .
s .
∞
s .
s .
s .
s .
s .
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
s .
∞
∞
∞
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
s .
s .
∞
∞
∞
s .
s .
s .
∞
∞
s .
s .
s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
∞
∞
∞
∞
∞
s .
(Continued )
2-28
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Amylene (n-)(α-)
(i-)
(α-)
(-n)(β-)
(i-)(β-)
Anethole (p-)
Anhydroformald-aniline
Aniline
hydrochloride
nitrate
sulfate
Anisal-acetone (p-)
Anisic acid (p-)
aldehyde (p-)
Anisidine (o-)
(m-)
(p-)
Anisole
Anthracene
Anthramine (α)
(β)
Anthranil
Anthranilic acid (o-)
Anthrapurpurin (1-,2-,7-)
Anthraquinone
disulfonate Na2 (1-,5-)
(1-,8-)
(2-,6-)
(2-,7-)
sulfonate Na (1-)
(2-)
Anthrarufin (1-,5-)
Antipyrene
Apiole
Arabinose (α)(d- or l-)
(dl-)
Arachidic acid
Arsanilic acid (p-)
Asparagine (l-)
Aspirin (o-)
Atropic acid
Auramine
Aurine, coralline (4-,4′-)
Azo-anisole (2-,2′-)
benzene
Azoxybenzene
Barbituric acid
Benzal acetone
Benzaldehyde
Benzamide
Benzanilide
Benzene
sulfinic acid
sulfonic acid
sulfonic amide
sulfonic chloride
Benzidine (4-,4′-)
disulfonic acid (2-,2′-)
(3-,3′-)
Benzil
Benzoic acid
anhydride
nitrile
Synonym
pentene-1
2-methyl-butene-3
2-methyl-butene-1
pentene-2
2-methyl-butene-2
p-propenyl anisole
methylene aniline
amino benzene, phenyl amine,
cyanol
aniline salt, aniline chloride
MeO-benzalacetone
2-amino-anisole
MeO-aniline(m)
4-amino anisole
methyl phenyl ether
paranaphthalene, anthracin
green oil
α-amino-anthracene
β-amino-anthracene
diphenyleneketone,
dihydrodiketoanthracene
ρ-anthraquinone disulfonate
x-anthraquinone disulfonate
1-ph-2,3-diMepyrazolone-5
1-allyl-2, 5-diMeO-3,4 methylenedioxybenzene
eicosanoic acid
α-phenyl acrylic acid
4,4′-dimethylaminobenzophenomide
diMeO-azobenzene
diphenyldiimide
malonyl urea
Me-cinnamyl ketone
artificial almond oil
benzol, phenyl hydride,
cyclohexatriene
benzene sulfonamide
benzene sulfonyl chloride
dibenzoyl
phenyl cyanide
Formula
Formula
weight
Form and
color
Specific
gravity
Melting
point, °C
20
C2H5CH2CH:CH2
(CH3)2CHCH:CH2
(C2H5)(CH3)C:CH2
C2H5CH:CHCH3
(CH3)2C:CHCH3
CH3CH:CH⋅C6H4OCH3
(CH2NC6H5)3
C6H5NH2
70 .13
70 .13
70 .13
70 .13
70 .13
148 .20
315 .41
93 .13
lq.
col . lq .
col . lq .
col . lq .
col . lq .
lf ./al .
pr ./al .
col . oil
0.644
0 .63215
0 .667 0/0
0 .650 20/4
0 .66319/4
0 .99120/20
C6H5NH2⋅HCl
C6H5NH2⋅HNO3
(C6H5NH2)2⋅H2SO4
CH3OC6H4CH:CHCOCH3
CH3OC6H4CO2H
CH3OC6H4CHO
CH3OC6H4NH2
CH3OC6H4NH2
CH3OC6H4NH2
CH3OC6H5
C6H4:(CH)2:C6H4
129 .59
156 .14
284 .33
176 .21
152 .15
136 .15
123 .15
123 .15
123 .15
108 .14
178 .23
cr .
rhb .
lf ./al .
lf ./et .
mn ./aq .
col . oil
col . lq .
oil
pl ./aq .
col . lq .
col . mn .
1 .222 4
1 .356 4
1 .377 4
C6H4:(CH)2:C6H3NH2
C6H4:(CH)2:C6H3NH2
C6H4:(NH)CO
H2NC6H4CO2H
C14H5O2(OH)3
C6H4:(CO)2:C6H4
193 .24
193 .24
119 .12
137 .14
256 .21
208 .21
yel ./al .
yel ./al .
col . oil
col . rhb .
or . nd ./al .
yel . rhb .
C14H6O2(SO3Na)2⋅5H2O
C14H6O2(SO3Na)2⋅4H2O
C14H6O2(SO3Na)2⋅7H2O
C14H6O2(SO3Na)2⋅4H2O
C14H7O2SO3Na
C14H7O2SO3Na
C14H6O2(OH)2
C11H12ON2
C12H14O4
502 .38
484 .36
538 .41
484 .36
310 .26
310 .26
240 .21
188 .23
222 .24
yel . lf .
yel . pr .
col . cr .
cr .
yel . lf .
silv . lf .
yel . lf .
mn ./aq .
col . nd .
1 .088113/4
1 .0220/4
CH2OH(CHOH)3CHO
CH2OH(CHOH)3CHO
CH3(CH2)18CO2H
H2N⋅C6H4 .AsO3H2
HO2C⋅C2H3(NH2)⋅CONH2
CH3CO2⋅C6H4⋅CO2H
C6H5C(:CH2)⋅CO2H
[(CH3)2NC6H4]2C:NH
150 .13
150 .13
312 .53
217 .05
132 .12
180 .16
148 .16
267 .37
rhb . pr .
1 .585 20/4
col . lf .
nd ./aq .
rhb .
nd ./aq .
nd ./aq .
col ./al .
(HOC6H4)2C:C6H4:O
(CH3O⋅C6H4N:)2
C6H5N:N⋅C6H5
(C6H5)2N2O
CO:(NHCO)2:CH2⋅2H2O
C6H5CH:CHCOCH3
C6H5CHO
C6H5CONH2
C6H5CONHC6H5
C6H6
290 .31
242 .27
182 .22
198 .22
164 .12
146 .19
106 .12
121 .14
197 .23
78 .11
red
or . pr .
or . mn .
yel . rhb .
col ./aq .
pl .
col . lq .
col . pr .
lf ./al .
col . lq .
C6H5SO2H
C6H5SO3H
C6H5SO2NH2
C6H5SO2Cl
NH2⋅C6H4⋅C6H4⋅NH2
(⋅C6H3(NH2)SO3H)2⋅3H2O
(⋅C6H3(NH2)SO3H)2
C6H5CO⋅COC6H5
C6H5CO2H
(C6H5CO)2O
C6H5CN
142 .18
158 .18
157 .19
176 .62
184 .24
398 .41
344 .36
210 .23
122 .12
226 .23
103 .12
pr ./aq .
col . nd .
mn ./aq .
cr .
cr ./aq .
pr ./aq .
1 .38415/15
83–4
65–6
156
14 .5
128–9
d . >175
pr .
mn . pr .
rhb ./et .
col . lq .
1 .2315
1 .26615/4
1 .19915/4
1 .00125/6
95
121 .7
42
−12 .9
1 .02220/4
1 .385 4
1 .123 20/4
1 .09815/15
1 .096 20/4
1 .089 55/55
0 .990 22/4
1 .25 27/4
1 .18715/4
1 .438 20/4
1 .54315/4
1 .20320/4
1 .248 20/20
1 .035 20/20
1 .046 20/4
1 .341
1 .314
0 .879 20/4
−135
−139
−124
22 .5
143
−6 .2
Boiling
point, °C
Solubility in 100 parts
Water
Alcohol
Ether
30–1
20 .5 771
31–2758
36 .4
37–8
235 .3
185
184 .4
i.
i .
i .
v . sl . s .
i .
v . sl . s .
i .
3 .618
∞
∞
∞
∞
s .
s .
sl . s .
∞
∞
∞
∞
∞
∞
∞
s .
∞
245
s .
s .
sl . s .
v . s .
v . s .
∞
∞
s .
s .
s .
1 .520
i .
sl . s .
i .
v . s .
v . s .
∞
∞
s .
s .
s .
198
d . 190
d .
73–4
184 .2
2 .5
5 .2
<−12
57 .2
−37 .3
217–8
275–80
247–8
225
251
243
154–5
340–2
1815
s .
514
i .
0 .0319
v . sl . s .
v . sl . s .
v . sl . s .
s . h .
i .
i .
130±
238
<−18
144–5
369
286
subl .
d . >215
subl .
462
379–81
i .
i .
sl . s . h .
0 .35 14
sl . s . h .
i .
s .
sl . s .
s .
1110
v . s . h .
0 .0518
sl . s .
s .
167
sl . s .
v . sl . s .
i .
i .
subl .
319174
294
v . s .
sl . s .
3 .920
30 .5 20
0 .5320
0 .8425
i .
100 25
i
v . sl . s .
i .
i .
sl . s .
100
s .
i .
i .
i .
s .
sl . s .
s .
280
113(109)
30
159 .5
164 .5
77
232
227–35
135–6
106–7
136
310 d .
153
68
36
d . 245
41–2
−26
130
163
5 .5
328
d . 235
267 d .
297
d .
260–2
179
290
117–910
80 .1
d . > 100
d .
251 .5
400740
348 d .
249 .2
360
190 .7
460
16 .910
i .
v . s . h .
3 .128
137
0 .1 c .
i .
0 .59°
i .
s . h .
v . s . h .
i . c .
s .
s .
720
v . s .
i .
i .
i .
i .
i .
s . h .
i .
0 .3
1 .35 25
i .
0 .07 22
s .
s .
4 .220
11 .415
sl . s .
s .
∞
1725
430
s .
s .
s .
∞
sl . s .
sl . s .
∞
v . s . h .
v . s .
0 .4316
i .
1 h .
0 .09 25
v . sl . s .
i .
0 .217
i .
1100
v . s .
v . s .
v . s .
v . s .
1 h .
i .
v . s .
i .
v . s .
s .
2
i .
v . s .
4615
s .
∞
v . s .
6615
s .
∞
520
s .
2 .320
s .
s .
2-29
Benzoin (dl-)
Benzophenone
Benzotrichloride
Benzoyl-benzoic acid (o-)
-chloride
-peroxide
Benzyl acetate
alcohol
amine
aniline
benzoate
butyrate
chloride
ether
formate
propionate
Berberonic acid (2-,4-,5-)
Biuret
Borneol (dl-)
(d- or l-)
(iso-)
Bornyl acetate (d-)
Bromo-aniline (p-)
-benzene
-camphor (3-)(d-)
-diphenyl (p-)
-naphthalene (α-)
(β-)
-phenol (o-)
(m-)
(p-)
-styrene (ω)(1)
(2)
-toluene (o-)
(m-)
(p-)
Bromoform
Butadiene (1-,2-)
(1-,3-)
Butadienyl acetylene
Butane
(i-)
Butyl acetate (n-)
(s-)
(i-)
(tert-)
alcohol (n-)
(s-)
(i-)
(tert-)
amine (n-)
(s-)
(i-)
(t-)
p-aminophenol (N)(n)
(N)(i-)
aniline (n-)
(i-)
arsonic acid (n-)
benzoate (n-)
(i-)
bromide (n-)
(s-)
(i-)
(t-)
butyrate (n-)(n-)
(n-)(i-)
(i-)(i-)
caproate
carbamate (i-)
cellosolve (n-)
diphenyl ketone
phenyl chloroform
phenyl carbinol
ω-amino toluene
phenyl-benzylamine
ω-chlorotoluene
dibenzyl ether
allophanamide
phenyl bromide
α-bromocamphor
α-naphthyl bromide
β-naphthyl bromide
o-tolyl bromide
tribromo-methane
methyl-allene
erythrene
diethyl
trimethyl-methane
butanol-1
butanol-2
2-methyl-propanol-1
2-methyl-propanol-2
1-bromo-butane
2-bromo-butane
1-Br-2-Me-propane
2-Br-2-Me-propane
2-BuO-ethanol-1
C6H5CO⋅CHOHC6H5
C6H5COC6H5
C6H5CCl3
C6H5COC6H4CO2H⋅H2O
C6H5COCl
(C6H5CO)2O2
CH3CO2CH2C6H5
C6H5CH2OH
C6H5CH2NH2
C6H5CH2NHC6H5
C6H5CO2CH2C6H5
C2H5CH2CO2CH2C6H5
C6H5CH2Cl
(C6H5CH2)2O
HCO2CH2C6H5
C2H5CO2CH2C6H5
C5H2N(CO2H)3⋅2H2O
NH(CONH2)2
C10H17OH
C10H17OH
C10H17OH
CH3CO2C10H17
BrC6H4NH2
C6H5Br
BrC10H15O
BrC6H4⋅C6H5
C10H7Br
C10H7Br
BrC6H4OH
BrC6H4OH
BrC6H4OH
C6H5CH:CHBr
C6H5CH:CHBr
CH3⋅C6H4Br
CH3⋅C6H4Br
CH3⋅C6H4Br
CHBr3
CH3CH:C:CH2
CH2:CHCH:CH2
CH2:(CH)2:CH⋅C⋮CH
CH3CH2CH2CH3
(CH3)2CHCH3
CH3CO2(CH2)2C2H5
CH3CO2CH(CH3)C2H5
CH3CO2CH2CH(CH3)2
CH3CO2C(CH3)3
C2H5CH2CH2OH
C2H5CH(OH)CH3
(CH3)2CHCH2OH
(CH3)3COH
C2H5CH2CH2NH2
C2H5CH(NH2)CH3
(CH3)2CHCH2NH2
(CH3)3CNH2
C4H9NH⋅C6H4⋅OH
C4H9NH⋅C6H4⋅OH
C4H9NHC6H5
C4H9NHC6H5
C4H9AsO(OH)2
C6H5CO2C4H9
C6H5CO2C4H9
C2H5CH2CH2Br
C2H5CH(Br)CH3
(CH3)2CHCH2Br
(CH3)3CBr
C2H5CH2CO2CH2CH2C2H5
C2H5CH2CO2CH2CH(CH3)2
(CH3)2CHCO2CH2CH(CH3)2
CH3(CH2)4CO2C4H9
NH2CO2CH2CH(CH3)2
C4H9OCH2CH2OH
212 .24
182 .22
195 .47
244 .24
140 .57
242 .23
150 .17
108 .14
107 .15
183 .25
212 .24
178 .23
126 .58
198 .26
136 .15
164 .20
247 .16
103 .08
154 .25
154 .25
154 .25
196 .29
172 .02
157 .01
231 .13
233 .10
207 .07
207 .07
173 .01
173 .01
173 .01
183 .05
183 .05
171 .03
171 .03
171 .03
252 .73
54 .09
54 .09
78 .11
58 .12
58 .12
116 .16
116 .16
116 .16
116 .16
74 .12
74 .12
74 .12
74 .12
73 .14
73 .14
73 .14
73 .14
165 .23
165 .23
149 .23
149 .23
182 .05
178 .23
178 .23
137 .02
137 .02
137 .02
137 .02
144 .21
144 .21
144 .21
172 .26
117 .15
118 .17
mn.
col. rhb.
col. lq.
tri./aq.
col. lq.
rhb ./et .
col . lq .
col . lq .
lq .
mn . pr .
nd .
col . lq .
col . lq .
lq .
col . lq .
lq .
tri .
nd ./al .
col . cr .
col . cr .
col . cr .
rhb ./pet .
rhb .
col . lq .
cr .
cr ./al .
col . oil
lf ./al .
col . lq .
cr .
tet . cr .
lq .
lq .
col . lq .
col . lq .
cr ./al .
col . lq .
lq .
col . gas
col . lq .
col . gas
col . gas
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
oil
col . lf .
col . oil
col . oil
lq .
lq .
lq .
lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lf .
col . lq .
1.08354
1.38014
1.21220/4
1 .05717
1 .04320/4
0 .98220/4
1 .065 25/25
1 .1220/4
1 .01616/18
1 .100 20/20
1 .03616
1 .08123
1 .03616/17
20/4
1 .011
1 .01120/4
0 .99115
1 .820
1 .495 20/4
1 .449 20/4
1 .48220/4
1 .605 0
1 .55380
1 .588 80
1 .42220/4
1 .427 20/4
1 .42220/4
1 .410 20/4
1 .390 20/4
2 .890 20/4
0 .62120/4
0 .773 20/4
0 .600
0 .600
0 .882 20
0 .865 25/4
0 .87120/4
0 .866 20/4
0 .810 20/4
0 .808 20/4
0 .80517 .5
0 .779 26
0 .739 25/4
0 .724 20/4
0 .73220/20
0 .69818/4
133–7
48.5
−4.75
93(128)
−0.5
108 d .
−51 .5
−15 .3
37–8
21
238–40
−39
3 .6
243
192–3 d .
210 .5
208–9
212
29
63–4
−30 .6
77–8
90–1
5–6
59
5 .6
32–3
63 .5
7
−7 .5
−28
−39 .8
28 .5
8–9
−108 .9
−135
−145
−76 .3
−98 .9
−79 .9
−114 .7
−108
25 .5
−50
−104
−85
−67 .5
71
79
0 .940 20/4
1 .005 25/25
0 .997 25/25
1 .277 20/4
1 .25125/4
1 .258 25/4
1 .21120/4
0 .87220/20
0 .86318/4
0 .875 0/4
0 .8820/0
0 .95676/4
0 .90320/4
158–9
−22
−112 .4
−112
−118 .5
−16 .2
−80 .7
65
344768
305.4
220.7
197.2
expl .
213 .5
204 .7
184 .5
306750
323–4
i .
179 .4
295–8
202–3747
220–2
subl .
212–3
226–7
156 .2
274
310
281 .1
281–2
194–5
236–7
238
221
10826
181 .8
183 .7
184–5
150 .5
18–9
−4 .41
83–6
−0 .6
−10
125 740
112744
118
95–6760
117
99 .5
107–8
82 .9
77 .8
66772
68–9
45 .2
235720
231–2
249–50
241 .5
101 .6
91 .3
91 .5
73 .3
165 .7736
156 .9
148–9
204 .3
206–7
171 .2
v. sl. s.
i.
i.
sl. s.
d.
i .
i .
417
∞
i .
i .
v . s .
i .
i .
i .
i .
v . sl . s .
1 .30
v . sl . s .
v . sl . s .
i .
i .
i . c .
i .
i .
i .
i .
i .
s .
1 .415
i .
i .
i .
i .
i .
0 .1 c .
i .
i .
i .
i .
i .
0 .7
i .
0 .625
i .
915
12 .520
1015
∞
∞
∞
∞
i .
i .
i .
0 .0115
s .
i .
i .
0 .0616
i .
0 .0618
i .
i .
i .
i .
i .
i .
∞
s. h.
6.515
s.
sl. s.
1513
s.
d. h.
s . h .
∞
∞
∞
∞
s .
∞
∞
∞
s .
∞
∞
v . s .
∞
s . h .
s .
sl . s . h .
s .
∞
s .
∞
i .
v . s .
v . s .
s .
v . s .
s .
2026
s .
s .
620
s .
s .
v . s .
∞
∞
s .
s .
s .
∞
∞
∞
s .
v . s .
∞
v . s .
34 25
∞
v . s .
∞
s .
v . s .
∞
∞
∞25
s .
∞25
∞
∞
∞
s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
v . s .
v . s .
s .
s .
∞
∞
v . s .
v . s .
i .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
∞
s .
∞
(Continued )
2-30
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
chloride (n-)
(s-)
(i-)
(t-)
dimethylbenzene (t-)(1-,3-,5-)
formate (n-)
(s-)
(i-)
furoate (n-)
iodide (n-)
(s-)
(i-)
(t-)
lactate (n-)
mercaptan (n-)
(i-)
(t-)
methacrylate (n-)
(i-)
phenol (p-)(t-)
propionate (n-)
(s-)
(i-)
stearate (n-)
(i-)
iso-thiocyanate (n-)
(i-)
(s-)(d-)
(t-)
valerate (n-)(n-)
(i-)(n-)
(i-)(s-)
(i-)(i-)
Butylene (α-)
(β-)
Butyraldehyde (n-)
(i-)
Butyric acid (n-)
(i-)
amide (n-)
(i-)
anhydride (n-)
(i-)
anilide (n-)
Caffeic acid (3-,4-)
Caffeine
Camphene (dl-)
(d- or l-)
Camphor (d-)
Camphoric acid (d-)
Cantharidine
Capric acid
Caproic acid (n-)
(i-)
Caprylic acid (n-)
Carbazole
Carbitol
Carbon disulfide
monoxide
suboxide
tetrabromide
tetrachloride
tetrafluoride
Carbonyl sulfide
Carminic acid
Carvacrol (1-,2-,4-)
Synonym
1-chloro-butane
2-chloro-butane
1-Cl2-2-Me-propane
2-Cl2-2-Me-propane
1-iodo-butane
2-iodo-butane
1-iodo-2-Me-propane
2-iodo-2-Me-propane
butanthiol-1
2-Me-propanthiol-1
butyl mustard oil
iso-Bu mustard oil
butene-1
butene-2
2-Me-propanol
butanoic acid
2-Me-propanoic acid
n-butyramide
iso-butyramide
n-butyranilide
decanoic acid
hexanoic acid
2-Me-pentanoic-5 acid
octanoic acid
diphenylenelimine, dibenzopyrrole
diethylene glycol mono-Et ether
tetrabromomethane
tetrachloromethane
tetrafluoromethane
Formula
C2H5CH2CH2Cl
C2H5⋅CHCl⋅CH3
(CH3)2CHCH2Cl
(CH3)3CCl
(CH3)3C⋅C6H3:(CH3)2
HCO2CH2CH2C2H5
HCO2CH(CH3)C2H5
HCO2CH2CH(CH3)2
OC4H3CO2C4H9
C2H5CH2CH2I
C2H5CHICH3
(CH3)2CHCH2I
(CH3)3CI
CH3CH(OH)CO2C4H9
C2H5CH2CH2SH
(CH3)2CHCH2SH
(CH3)3CSH
CH2:C(CH3)CO2C4H9
CH2:C(CH3)CO2C4H9
(CH3)3C⋅C6H4⋅OH
C2H5CO2C4H9
C2H5CO2C4H9
C2H5CO2C4H9
CH3(CH2)16CO2C4H9
CH3(CH2)16CO2C4H9
C2H5CH2CH2⋅N:CS
(CH3)2CHCH2⋅N:CS
C4H9⋅N:CS
(CH3)3C⋅N:CS
CH3(CH2)3CO2(CH2)3CH3
(CH3)2CHCH2CO2(CH2)3CH3
(CH3)2CHCH2CO2C4H9
C4H9CO2C4H9
C2H5CH:CH2
CH3CH:CHCH3
CH3CH2CH2CHO
(CH3)2CHCHO
C2H5CH2CO2H
(CH3)2CHCO2H
C2H5CH2CONH2
(CH3)2CHCONH2
(C2H5CH2CO)2O
[(CH3)2CHCO]2O
C3H7CONHC6H5
(HO)2C6H3C2H2CO2H
C8H10O2N4⋅H2O
C10H16
C10H16
C10H16O
C8H14(CO2H)2
C10H12O4
CH3(CH2)8CO2H
CH3(CH2)4CO2H
(CH3)2CH(CH2)2⋅CO2H
CH3(CH2)6CO2H
(C6H4)2NH
C2H5O(CH2)2O(CH2)2OH
CS2
CO
OC:C:CO
CBr4
CCl4
CF4
COS
C22H20O13
CH3C6H3(OH)CH(CH3)2
Formula
weight
92 .57
92 .57
92 .57
92 .57
162 .27
102 .13
102 .13
102 .13
168 .19
184 .02
184 .02
184 .02
184 .02
146 .18
90 .19
90 .19
90 .19
142 .20
142 .20
150 .22
130 .18
130 .18
130 .18
340 .58
340 .58
115 .20
115 .20
115 .20
115 .20
158 .24
158 .24
158 .24
158 .24
56 .11
56 .11
72 .11
72 .11
88 .11
88 .11
87 .12
87 .12
158 .19
158 .19
163 .22
180 .16
212 .21
136 .23
136 .23
152 .23
200 .23
196 .20
172 .26
116 .16
116 .16
144 .21
167 .21
134 .17
76 .14
28 .01
68 .03
331 .63
153 .82
88 .00
60 .08
492 .39
150 .22
Form and
color
Specific
gravity
Melting
point, °C
Boiling
point, °C
col. lq.
col . lq .
col . lq .
col . lq .
col . lq .
lq .
lq .
lq .
col . lq .
lq .
lq .
lq .
lq .
col . lq .
col . lq .
lq .
lq .
lq .
lq .
nd ./aq .
col . lq .
col . lq .
col . lq .
col . lq .
wax
lq .
lq .
lq .
lq .
lq .
lq .
col . lq .
col . lq .
col . gas
col . gas
col . lq .
col . lq .
col . lq .
col . lq .
rhb .
mn . pl .
col . lq .
col . lq .
mn . pr .
yel ./aq .
nd ./al .
cr .
cr .
trig .
mn .
cr .
col . nd .
oily lq .
col . oil
col . lf .
lf .
col . lq .
col . lq .
col . gas
gas
col . mn .
col . lq .
gas
col . gas
red pd .
col . lq .
0.887 20
0 .87120/4
0 .88415
0 .84715
−123.1
−131
−131 .2
−26 .5
77.9763
67 .8767
68 .9
51–2
200–2147
106 .9
97
98 .2
118–2025
129 .9
118–9
120
99
75–66
97–8
88
65–7
155
155
236–8
146
132 .5
136 .8
220–525
0 .9110
0 .88220/4
0 .885 20/4
1 .056 20/4
1 .617 20/4
1 .595 20
1 .606 20/4
1 .370 19/15
0 .968
0 .837 25/4
0 .836 20/4
0 .889 15 .6
0 .889 15 .6
0 .908 112/4
0 .88315
0 .866 20/4
0 .888 0/4
0 .855 25/25
0 .95611
0 .96414/4
0 .943 20/4
0 .91910
0 .87015/4
0 .862 25/4
0 .848 20/4
0 .8740/4
0 .69
20/4
0 .817
0 .79420/4
0 .96420/4
0 .949 20/4
1 .032
1 .013
0 .968 20/20
0 .950 25/4
1 .134
1 .2319
0 .82278
0 .845 50/4
0 .999 9/9
1 .186
0 .889 87
0 .922 20/4
0 .925 20/4
0 .910 20/4
0 .990 20/20
1 .263 20/4
0 .81−195/4
1 .1140
3 .42
1 .595 20/4
1 .24−87
0 .977
20/4
−95 .3
−103 .5
−104
−90 .7
−34
−116
<−79
99
−89 .55
−71 .4
27 .5
25
10 .5
−93
−130
−127
−99
−65 .9
−4 .7
−47
115–6
129–30
−75
−53 .5
92
195–213
237
50
42 .7
178–9
187
212
31 .5
−1 .5
−35
16
244 .8
−108 .6
−207
−107
90 .1(48)
−22 .6
−138 .2
d . 136
0 .5
165724
162
159–63
140770
186
168 .8
163–4752
168 .7
−5758
3746
75 .7
64757
163 .5757
154 .5
216
216–20
199 .5
181 .5734
18915
d .
subl .
160
159 .6
209 .1759
268–70
202761
207 .7
237 .5
354 .8
201 .9
46 .3
−192
7761
189 .5
76 .8
−128
−50 .2760
238
Solubility in 100 parts
Water
0.0718
i .
i .
i .
i .
v . sl . s .
sl . s .
1 .122
i .
i .
i .
i .
i .
sl . s .
sl . s .
v . sl . s .
i .
i .
sl . s .
i .
i .
i .
0 .3 25
i .
i .
i .
i .
i .
v . sl . s .
i .
i .
i .
i .
4
1120
∞
20 20
16 .315
v . s .
d .
d .
i .
s . h .
2
i .
i .
0 .1
0 .612
0 .003
0 .003
1 .120
v . sl . s .
0 .0715
i .
∞
0 .20
3 .50 cc .
d .
0 .0230
0 .0820
sl . s .
8014 cc .
s .
v . sl . s .
Alcohol
Ether
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
v . s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
v . s .
s .
s .
∞
∞
∞
s .
s .
∞
∞
∞
s .
s .
s .
s .
s .
∞
∞
∞
∞
v . s .
s .
s .
s .
s .
∞
∞
∞
∞
v . s .
∞
∞
∞
∞
s .
s .
d
d
s .
s .
2
s .
s .
12012
s .
∞
∞
∞
∞
sl . s .
sl . s .
∞
∞
s .
sl . s .
0 .3
s .
s .
v . s .
s .
s .
s .
s .
0 .9214
v . s .
∞
s .
s .
s .
s .
s .
sl . s .
s .
∞
s .
∞
s .
s .
∞
s .
s .
∞
s .
v . sl . s .
∞
2-31
Carvacrylamine (2-,1-,4-)
Carvone (d-)
Cellosolve
acetate
Cellulose
Cetyl acetate
alcohol
Chloral
hydrate
Chloranil
Chloretone
Chloro-acetanilide (p-)
-acetic acid
-acetone
-acetophenone (ω-)
-acetyl chloride
-aniline (o-)
(m-)
(p-)
-anthraquinone (1-)
(2-)
-benzaldehyde (o-)
(m-)
(p-)
-benzene
-benzoic acid (o-)
(m-)
(p-)
-buta-1,3-diene (2-)
(1-)
-buta-1,2-diene (4-)
-dimethylhydantoin
-dinitrobenzene (α)(1-,2-)(4-)
(α)(1-,3-)(4-)
-diphenyl (o-)
(m-)
(p-)
-hydroquinone
-naphthalene (α-)
(β-)
-nitrobenzene (o-)
(m-)
(p-)
-nitrotoluene (2-,4-)
(2-,6-)
-phenol (o-)
(m-)
(p-)
-propionic acid (α)(dl-)
-toluene (o-)
(m-)
(p-)
Chloroform
Chlorophyll (α-)
Chloropicrin
Cholesterol
Chrysene
Chrysoidine (2-,4-)
Chrysophanic acid
Cinchomeronic acid (3-,4-)
Cineole, eucalyptole
Cinnamic acid (cis-)
(trans-)
aldehyde
Cinnamyl alcohol
cinnamate
Citraconic acid (cis-)
Citral (α)
Citric acid
Citronellal (d-)
Citronellol (d-)
Coniine (d-)(2-)
H2NC6H3(CH3)C3H7
C10H14O
C2H5O(CH2)2OH
CH3CO2CH2CH2OC2H5
(C6H10O5)x
CH3CO2(CH2)15CH3
CH3(CH2)14CH2OH
CCl3⋅CHO
CCl3⋅CH(OH)2
OC:(CCl⋅CCl)2:CO
Cl3C⋅C(OH)(CH3)2
CH3CONHC6H4CI
ClCH2CO2H
CH3COCH2Cl
C6H5COCH2Cl
ClCH2COCl
ClC6H4NH2
ClC6H4NH2
ClC6H4NH2
C6H4(CO)2C6H3Cl
C6H4(CO)2C6H3Cl
ClC6H4CHO
ClC6H4CHO
ClC6H4CHO
C6H5Cl
ClC6H4CO2H
ClC6H4CO2H
ClC6H4CO2H
CH2:CCl⋅CH:CH2
CH2:CH⋅CH:CHCl
CH2:C:CH⋅CH2Cl
—C(CH3)2N(Cl)CON(Cl)CO—
ClC6H3(NO2)2
ClC6H3(NO2)2
C6H5⋅C6H4Cl
C6H5⋅C6H4Cl
C6H5⋅C6H4Cl
ClC6H3(OH)2
C10H7Cl
C10H7Cl
ClC6H4NO2
ClC6H4NO2
ClC6H4NO2
CH3C6H3(NO2)(Cl)
CH3C6H3(NO2)(Cl)
ClC6H4OH
ClC6H4OH
ClC6H4OH
CH3⋅CHCl⋅CO2H
CH3⋅C6H4Cl
CH3⋅C6H4Cl
CH3⋅C6H4Cl
CHCl3
C55H72O5N4Mg
Cl3CNO2
C27H45OH⋅H2O
C18H12
C6H5⋅N:N⋅C6H3(NH2)2
C14H5(OH)2(CH3)O2
C5H3N(CO2H)2
C10H18O
C6H5CH:CHCO2H
C6H5CH:CHCO2H
C6H5CH:CHCHO
C6H5CH:CHCH2OH
C8H7CO2C9H9
CH3C(CO2H):CHCO2H
C9H15CHO
C3H4(OH)(CO2H)3
C9H17⋅CHO
C10H20O
C3H7⋅C5H10N
149 .23
150 .22
90 .12
132 .16
162 .14
284 .48
242 .44
147 .39
165 .40
245 .88
177 .46
169 .61
94 .50
92 .52
154 .59
112 .94
127 .57
127 .57
127 .57
242 .66
242 .66
140 .57
140 .57
140 .57
112 .56
156 .57
156 .57
156 .57
88 .54
88 .54
88 .54
197 .02
202 .55
202 .55
188 .65
188 .65
188 .65
144 .56
162 .62
162 .62
157 .55
157 .55
157 .55
171 .58
171 .58
128 .56
128 .56
128 .56
108 .52
126 .58
126 .58
126 .58
119 .38
893 .49
164 .38
404 .67
228 .29
212 .25
254 .24
167 .12
154 .25
148 .16
148 .16
132 .16
134 .18
264 .32
130 .10
152 .23
192 .12
154 .25
156 .27
127 .23
oil
col. lq.
col . lq .
col . lq .
amor .
nd .
lf .
col . lq .
mn . pr .
yel ./bz .
col . cr .
rhb .
col . cr .
col . lq .
rhb .
col . lq .
lq .
lq .
rhb .
yel . nd .
nd ./al .
nd .
pr .
pr .
col . lq .
mn ./aq .
pr .
tri .
col . lq .
col . lq .
col . lq .
cr ./et .
rhb ./et .
cr .
cr .
lf .
mn .
col . lq .
lf ./al .
mn . nd .
yel ./al .
mn . pr .
cr .
cr .
col . lq .
nd .
nd .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
rhb ./al .
col . rhb .
yel . cr .
yel ./al .
cr ./HCl
col . oil
mn . pr .
mn . pr .
lq .
nd .
nd . or pr .
nd .
col . oil
cr .
col . oil
col . oil
col . lq .
0.99420
0.96120/4
0 .93120/4
0 .975 20/4
1 .3–1 .4
0 .858 20
0 .818 50/4
1 .505 25/4
1 .619 50/4
1 .385 22
1 .58 20/20
1 .16216
1 .32415
1 .498 20/20
1 .21320/4
1 .216 20/4
1 .42719
1 .298
1 .25015
1 .196 61
1 .107 20/4
1 .544 25/4
1 .496 25/4
1 .54124
0 .958 20/20
0 .965 20/20
0 .99120/20
1 .5 20/20
1 .697
22
1 .194 20/4
1 .26616
1 .305 80/4
1 .34350/4
1 .298 91
1 .256 80
1 .24118/15
1 .268 25
1 .306 20/4
1 .306 9
1 .082 20/4
1 .07220/4
1 .070 20/4
1 .489 20
1 .65123/4
1 .067
20
0 .927
1 .2844
1 .245
1 .110 20/20
1 .040 35/35
1 .08516 .5
1 .617
0 .89017/4
1 .54220/4
0 .85517 .5
0 .84820/4
0 .84717
−16
−70
22–3
49–50
−57
51 .7
290
97
175–6
61 .2
−44 .5
58–9
0
−10 .4
70–1
162
208–9
11
17–8
47 .8
−45 .2
141–2
158
242–3
130
39(36)
53(43)
34
89
77 .5
106
−20
56–7
32 .5
44 .4(24)
83–4
38 .2
37 .5
7(0)
32–3
41–3
<−20
−34
−47 .8
7 .5
−63 .5
d .
−64
149–51
253–4
117 .5
195
258–9 d .
1 .5
68
133
−7 .5
33
44
92–3
153
−2
241
230766
135 .1
156 .3
i .
20015
189 .515
97 .6768
d . 98
subl .
167
189 .5
121
245–7
105
210 .5
230767
230–1
subl .
208748
213–4
213748
132 .1
subl .
59 .4
69
88
315 d .
315 d .
267–8
284–5
282
263 sl . d .
259 .3
264751
245 .5753
235 .6
242761
240718
238
175–6
214
217
186
159 .5
161 .6
162 .2
61 .2
i .
112 .3766
subl .
448
subl .
subl . d .
176–7
12519
300
252 sl . d .
257 .5
229
d .
204–8
224–5
166–7
v. sl. s.
i.
∞
22
i .
i .
i .
v . s .
47417
i .
0 .8 c .
sl . s .
v . s .
∞
0 .11
d .
i .
i .
s . h .
i .
i .
v . sl . s .
v . sl . s .
s . h .
0 .049 20
0 .20825
0 .04125
0 .00825
v . sl . s .
v . sl . s .
d .
0 .2125
i .
i .
i .
i .
i .
v . s .
i .
i .
i .
i .
i .
i .
i .
2 .8520
2 .6020
2 .7120
∞
i .
i .
i .
0 .8220
s .
0 .1718
0 .2620
i .
sl . s . h .
i . c .
v . sl . s .
1 .915
0 .0418
v . sl . s .
sl . s .
i .
36025
i .
207 .725
v . sl . s .
v . sl . s .
1 .1
s.
∞
∞
∞
i .
v . sl . s . c .
s .
∞
v . s .
i . c .
111
s .
s .
∞
v . s .
d .
s .
sl . s . h .
s.
∞
∞
∞
s .
∞
s .
i . c .
s .
v . s .
s .
∞
v . s .
s .
s .
s .
v . s .
v . s .
v . s .
∞
s .
s .
s .
∞
∞
v . s .
v . s .
v . s .
∞
s .
s .
s .
∞
∞
v . s . h .
s . h .
v . s .
s .
v . s .
s .
v . s .
s . h .
v . s . h .
v . s . h .
v . s .
∞
v . s .
s .
v . s .
v . s .
s .
s .
v . s .
∞
s .
s .
s .
∞
s .
s .
v . s .
∞
∞
∞
∞
∞
s .
1 .117
0 .116
s .
s . h .
sl . s .
∞
s .
18
v . sl . s .
s .
sl . s .
i .
∞
2420
s .
v . s .
4 c .
s .
∞
7615
∞
∞
v . s .
v . s .
∞
v . s .
33
s .
∞
215
∞
∞
v . s .
(Continued )
2-32
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Coumaric acid (o-)
(p-)
Coumarin
Coumarone
Creatine
Creatinine
Creosol (3-,1-,4-)
Cresidine (1-,2-,4-)
Cresol (o-)
(m-)
(p-)
Cresyl benzoate (o-)
(m-)
(p-)
Crotonic acid (α-)
acid (β-)(cis-)
aldehyde (α)
Cumene
Cumic acid (p-)
Cumidine (p-)
Cyanamide
Cyanic acid
Cyanoacetic acid
Cyanogen
bromide
chloride
Cyanuric acid
Cyclo-butane
-heptane
-hexane
-hexanol
-hexanone
-hexene
-hexyl acetate
amine
bromide
chloride
-pentadiene (1-,3-)
-pentane
-pentanone
-propane
Cymene (o-)
(m-)
(p-)
Cystine (l-)
Dambose
Decahydronaphthalene (cis-)
(trans-)
Decane (n-)
Decyl alcohol
Dextrin
Diacetone alcohol
Diamino-benzophenone (4-,4′-)
-diphenylamine (4-,4′-)
-diphenylmethane (4-,4′-)
-diphenylurea (4-,4′-)
Diamyl-amine (i-)
ether (n-)
(i-)
Diamyl ketone (i-)
phthalate (n-)
(i-)
tartrate (i-)
Dianisidine (o-)(4-,3-)2
Diazo-aminobenzene
-aminotoluene (2-,2′-)
-methane
Formula
HOC6H4CH:CHCO2H
HOC6H4CH:CHCO2H
C9H6O2
C8H6O
C4H9N3O2⋅H2O
C4H7N3O
CH3O⋅C6H3(CH3)OH
CH3(NH2)C6H3⋅OCH3
CH3C6H4OH
CH3C6H4OH
CH3C6H4OH
C6H5CO2C6H4CH3
C6H5CO2C6H4CH3
C6H5CO2C6H4CH3
CH3CH:CHCO2H
CH3CH:CHCO2H
CH3CH:CHCHO
C6H5CH(CH3)2
(CH3)2CH⋅C6H4CO2H
(CH3)2CH⋅C6H4NH2
H2N⋅CN
HOCN or HNCO
CH2(CN)CO2H
(CN)2
BrCN
ClCN
C3H3O3N3⋅2H2O
CH2 < (CH2)2 > CH2
CH2 < (CH2CH2CH2)2 >
CH2 < (CH2CH2)2 > CH2
CH2 < (CH2CH2)2 > CHOH
CH2 < (CH2CH2)2 > CO
(⋅CH2⋅CH2CH:)2
CH3CO2C6H11
CH2 < (CH2CH2)2 > CHNH2
CH2 < (CH2CH2)2 > CHBr
CH2 < (CH2CH2)2 > CHCl
CH2 < (CH:CH)2 >
CH2 < (CH2CH2)2 >
< (CH2CH2)2 > CO
< CH2CH2CH2 >
CH3⋅C6H4CH(CH3)2
CH3⋅C6H4CH(CH3)2
CH3⋅C6H4CH(CH3)2
[⋅SCH2CH(NH2)CO2H]2
C6H6(OH)6
C10H18
C10H18
CH3(CH2)8CH3
CH3(CH2)8CH2OH
(C6H10O5)x
(CH3)2C(OH)⋅CH2COCH3
H2NC6H4COC6H4NH2
H2NC6H4NHC6H4NH2
H2NC6H4CH2C6H4NH2
(H2NC6H4NH)2CO
[(CH3)2CHCH2CH2]2NH
(C2H5CH2CH2CH2)2O
[(CH3)2CH(CH2)2]2O
[(CH3)2CHCH2CH2]2CO
C6H4(CO2C5H11)2
C6H4(CO2C5H11)2
(HOCH⋅CO2C5H11)2
[NH2(OCH3)C6H3⋅]2
C6H5N:N⋅NHC6H5
C7H7N:N⋅NHC7H7
CH2:N2
Formula
weight
164 .16
164 .16
146 .14
118 .13
149 .15
113 .12
138 .16
137 .18
108 .14
108 .14
108 .14
212 .24
212 .24
212 .24
86 .09
86 .09
70 .09
120 .19
164 .20
135 .21
42 .04
43 .02
85 .06
52 .03
105 .92
61 .47
165 .10
56 .11
98 .19
84 .16
100 .16
98 .14
82 .14
142 .20
99 .17
163 .06
118 .60
66 .10
70 .13
84 .12
42 .08
134 .22
134 .22
134 .22
240 .30
180 .16
138 .25
138 .25
142 .28
158 .28
162 .14
116 .16
212 .25
199 .25
198 .26
242 .28
157 .30
158 .28
158 .28
170 .29
306 .40
306 .40
290 .35
244 .29
197 .24
225 .29
42 .04
Form and
color
nd./aq.
cr./aq.
rhb./et.
oil
mn./aq.
mn.
pr.
nd ./pet .
cr .
lq .
pr .
lq .
cr .
cr .
col . mn .
nd .
col . lq .
col . lq .
tri .
lq .
col . nd .
gas
col . lq .
col . gas
nd .
gas
mn ./aq .
col . gas
oil
col . lq .
col . nd .
col . oil
lq .
oil
col . lq .
col . lq .
col . lq .
col . lq .
col . oil
col . oil
col . gas
col . lq .
col . lq .
col . lq .
pl .
mn ./aq .
lq .
lq .
col . lq .
col . oil
amor .
lq .
yel . nd .
lf ./aq .
nd ./aq .
cr .
col . lq .
col . lq .
col . lq .
yel . oil
col . lq .
col . lq .
lq .
col . lf .
yel . lf .
or . cr .
gas
Specific
gravity
0.93520/4
1.07815/15
1.09220/20
20/4
1 .048
1 .03420/4
1 .03520/4
79 .7
0 .964
1 .03115/4
0 .85320/20
0 .86220/4
1 .1624
0 .953
1 .07348/4
1 .1400
0 .86617
2 .01520/4
1 .2220
1 .7680/4
0 .7030/4
0 .81020/4
0 .77920/4
0 .96220/4
0 .94719/4
0 .81020/4
0 .9850/4
0 .86520/0
1 .32420/20
0 .97718/4
0 .80519/4
0 .74520/4
0 .94820
0 .720−79
0 .87520/4
0 .86220
0 .85720/4
1 .752
0 .89518/4
0 .87220/4
0 .7302
0 .83020/4
1 .038
0 .93125
0 .76721/4
0 .77420/4
0 .77720/4
0 .82125/4
Melting
point, °C
Boiling
point, °C
207–8
206–7 d.
70
<−18
295
260 d.
5.5
93–4
30 .8
10 .9
35–6
subl.
55
71 .5
72
15 .5
−69
−96 .9
116–7
<−20
44–5
−80
65–6
−34 .4
52
−6 .5
>360
−50
−12
6 .5
23 .9
−45
−103 .7
−43 .9
−85
−93 .3
−58 .2
−126 .6
<−25
−73 .5
d . 258–61
253
−51
−32
−29 .7
7
−47
237–9
158
93–4
subl . 310
−44
−69
14 .6
1 .03
1 .06315/4
131 .5
96–8
51
−145
290–1
173–4
221–2765
235
190 .8
202 .8
202
308
314
316
189
170–1 d .
102 .2
152 .5
subl .
225761
14019
−640
1080 .2
−21
61 .3750
12 .5–13
d .
11–12726
118–20
80–1
160–1
155–6
83 .3
174750
134
165714
142
41–2
49–50
129–30
−34749
177
175–6
176–7
31915
193 .3
185 .3
174 .0
232 .9
167 .9
d .
249–5315
188–90
190
173 .4
228
204–611
22540
19516
expl .
−23
Solubility in 100 parts
Water
sl. s. c.
s. h.
0.3 c.
i.
1.418
8.716
v. sl. s.
v . sl . s .
2 .5
0 .5
1 .8
i .
i .
i .
8 .315
∞25
18
i .
0 .0225
i .
v . s .
sl . s .
s .
45020 cc .
s .
250020 cc .
0 .2717
i .
i .
i .
3 .620
s .
v . sl . s .
i .
i .
i .
i .
i .
i .
v . sl . s .
i .
i .
i .
i .
0 .0119
212
i .
i .
i .
i .
s .
∞
sl . s . h .
sl . s .
sl . s . c .
v . sl . s .
sl . s .
i .
i .
i .
i .
i .
i .
i .
0 .05
d .
Alcohol
Ether
s.
v. s. h.
v. s.
v. sl. s.
v. s.
s.
s.
i.
0.0117
116
∞
s .
∞30
∞
∞36
s .
∞
∞
s .
v . s .
s .
230020 cc .
s .
v . s .
0 .122
v . s .
∞
s .
s .
v . s .
∞
s .
s .
∞
s .
s .
s .
s .
i .
i .
s .
s .
∞
s .
i .
∞
s .
s .
s .
∞
s .
∞30
∞
∞36
∞
∞
s .
v . s .
s .
s .
50020 cc .
s .
500020 cc .
∞
s .
s .
v . s .
∞
s .
∞
∞
s .
s .
s .
s .
i .
s .
s .
∞
i .
∞
s .
s .
s .
s .
∞
∞
s .
∞
∞
∞
s .
s .
s .
s .
s . h .
s .
v . s .
s .
2-33
Dibenzothiazyl-disulfide (2-,2′-)
Dibensoyl methane
Dibensyl-amine
-aniline
ketone
phthalate (o-)
succinate
Dibromo-benzene (o-)
(m-)
(p-)
-diphenyl (4-,4′-)
Dibutyl-adipate (n-)
(i-)
-amine (n-)
(i-)
-p-aminophenol (s-)
-aniline (n-)
carbonate (n-)
(i-)
(s-)
ether (n-)
(i-)
(s-)
ketone (n-)
(i-)
malate (l-)(n-)
oxalate (n-)
phthalate (n-)
tartrate (d-)(n-)
(d-)(i-)
Dichloro-acetic acid
-acetone (αα-)
-aniline (2-,5-)
-anthraquinone (1-,3-)
(1-,4-)
(1-,5-)
(1-,6-)
(1-,8-)
(2-,3-)
(2-,6-)
(2-,7-)
-benzene (o-)
(m-)
(p-)
-butane (n-)(1-,4-)
-diphenyl (4-,4′-)
-ethane (1-,2-)
-naphthalene (β-)(1-,4-)
(γ-)(1-,5-)
-nitrobenzene (2-,5-)
-pentane (1-,5-)
-phenol (2-,4-)
Dichloramine T (p-)
Dicyandiamide
Diethanolamine
Diethyl adipate
-amine
-aminophenol (m-)
-aniline
sulfonic acid (m-)
carbonate
diethyl malonate
Diethyl dimethyl malonate
glutarate
ketone
malonate
-malonic acid
-naphthylamine (α-)
(β-)
oxalate
phthalate (o-)
sulfate
sulfide
(C6H4NSC)2S2
(C6H5CO)2CH2
(C6H5CH2)2NH
C6H5N(CH2C6H5)2
(C6H5CH2)2CO
C6H4(CO2CH2C6H5)2
(⋅CH2CO2CH2C6H5)2
C6H4Br2
C6H4Br2
C6H4Br2
BrC6H4⋅C6H4Br
(⋅CH2CH2CO2C4H9)2
(⋅CH2CH2CO2C4H9)2
(C2H5CH2CH2)2NH
[(CH3)2CHCH2]2NH
(C4H9)2N⋅C6H4OH
C6H5N(C4H9)2
CO(OC4H9)2
CO(OC4H9)2
CO(OC4H9)2
(C2H5CH2CH2)2O
[(CH3)2CHCH2]2O
[C2H5(CH3)CH]2O
(C2H5CH2CH2)2CO
[(CH3)2CHCH2]2CO
C2H4O(CO2C4H9)2
(⋅CO2C4H9)2
C6H4(CO2C4H9)2
(CHOHCO2C4H9)2
(CHOHCO2C4H9)2
Cl2CH⋅CO2H
Cl2CHCOCH3
Cl2C6H3NH2
C6H4:(CO)2:C6H2Cl2
C6H4:(CO)2:C6H2Cl2
C6H3Cl:(CO)2:C6H3Cl
C6H3Cl:(CO)2:C6H3Cl
C6H3Cl:(CO)2:C6H3Cl
C6H4:(CO)2:C6H2Cl2
C6H3Cl:(CO)2:C6H3Cl
C6H3Cl:(CO)2:C6H3Cl
C6H4Cl2
C6H4Cl2
C6H4Cl2
ClCH2(CH2)2CH2Cl
ClC6H4⋅C6H4Cl
ClCH2⋅CH2Cl
C10H6Cl2
C10H6Cl2
Cl2C6H3NO2
ClCH2(CH2)3CH2Cl
Cl2C6H3OH
CH3C6H4SO2NCl2
H2N⋅C(:NH)⋅NH⋅CN
HN(CH2CH2OH)2
(⋅CH2CH2CO2C2H5)2
(C2H5)2NH
(C2H5)2N⋅C6H4⋅OH
(C2H5)2NC6H5
(C2H5)2NC6H4SO3H
OC(OC2H5)2
(C2H5)2C(CO2C2H5)2
(CH3)2C(CO2C2H5)2
CH2(CH2CO2C2H5)2
(C2H5)2CO
CH2(CO2C2H5)2
(C2H5)2C(CO2H)2
C10H7N(C2H5)2
C10H7N(C2H5)2
(⋅CO2C2H5)2
C6H4(CO2C2H5)2
O2S(OC2H5)2
(C2H5)2S
332 .49
224 .25
197 .28
273 .37
210 .27
346 .38
298 .33
235 .90
235 .90
235 .90
312 .00
258 .35
258 .35
129 .24
129 .24
221 .34
205 .34
174 .24
174 .24
174 .24
130 .23
130 .23
130 .23
142 .24
142 .24
246 .30
202 .25
278 .34
262 .30
262 .30
128 .94
126 .97
162 .02
277 .10
277 .10
277 .10
277 .10
277 .10
277 .10
277 .10
277 .10
147 .00
147 .00
147 .00
127 .01
223 .10
98 .96
197 .06
197 .06
192 .00
141 .04
163 .00
240 .11
84 .08
105 .14
202 .25
73 .14
165 .23
149 .23
229 .30
118 .13
216 .27
188 .22
188 .22
86 .13
160 .17
160 .17
199 .29
199 .29
146 .14
222 .24
154 .18
90 .19
cr.
rhb./al.
col. oil
pr./al.
cr.
pr./al.
lf./al.
col. lq.
col. lq.
pl./al.
mn. pr.
col. lq.
col . lq .
col . lq .
col . lq .
lq .
lq .
col . lq .
col . lq .
col . lq .
lq .
lq .
lq .
lq .
oil
lq .
col . lq .
col . lq .
pr .
cr .
lq .
lq .
nd .
yel . nd .
yel . nd .
yel . nd .
yel . nd .
yel . nd .
yel . nd .
yel . nd .
yel . nd .
col . lq .
col . lq .
col . mn .
lq .
pr .
col . lq .
nd ./al .
lf ./al .
tri ./al .
col . lq .
nd .
cr .
mn . pl .
pr .
col . lq .
col . lq .
rhb .
oil
cr .
col . lq .
col . lq .
col . lq .
syrup
col . lq .
col . lq .
pr ./aq .
col . oil
col . oil
col . lq .
col . lq .
col . lq .
col . lq .
1.50
1.028 25/25
1.956 20/4
1.952 20/4
2.26118
1.897
0.965 20/4
0 .950 25
0 .768 20/20
0 .74125/4
180
78
−26
70–1
34–5
42–3
45–6
1.8
−6.9
87–8
164–5
−38
−20
−70
0 .924 20/4
0 .91915
0 .769 20/20
0 .76215
0 .756 21
0 .82718/4
0 .805 21/4
1 .038 20/4
0 .986 20/4
1 .045 21
1 .09815
1 .03175/4
1 .560 25/25
1 .23415
1 .305 20/4
1 .288 20/4
1 .458 21
1 .442 0/4
1 .256 20/20
1 .300 76/4
1 .669 22
1 .094 25/4
1 .383 60/25
1 .4014
1 .09720/4
1 .00920/4
0 .712 15/15
0 .934 20/4
0 .975 20/4
0 .985 20/4
0 .994 25/25
1 .025 21
0 .816 19/4
1 .055 20/4
1 .005
1 .026
1 .079 20/4
1 .121 25/25
1 .172 25/4
0 .837 20/4
−98
−5 .9
−29 .6
22–2 .5
73–4
9 .7(−4)
50
208–9
187 .5
251
203–4
202–3
268–70
282
210–11
−17 .6
−24 .8
53
−38 .7
148
−35 .3
67–8
107
54 .6
45
83
207–8
28
−21
−38 .9
78
−34 .4
270 d .
−43
−24
−42
−49 .8
125
−40 .6
−25
−99 .5
d.
219–2118
268–71250
>300
330.6
27412
23814
221–2
219755
218.6758
355–60
18314
278–80
159761
139–40
17010
262 .8
207740
190
178–80
142 .4
122 .5
121
187 .7
168 .1
170–118
245 .5
340
200–318
323–5
194 .4
120
251
179
172766
174764
161–3
315–9
83 .7
286–7 740
subl .
266
180–1
209–10
d .
270 748
239–41761
55 .5759
276–80
216
126759
230
196 .7
237
101 .7
198 .9
d . 170–80
285–90
318
186
298–9
210
92–3 754
i.
i.
i.
i.
i.
v. sl. s.
i.
i.
i.
i.
i.
i.
i .
∞
v . sl . s .
i .
i .
i .
i .
<0 .05
i .
i .
i .
<0 .06
v . sl . s .
i .
0 .04 25
i .
v . sl . s .
∞
v . sl . s .
v . sl . s .
i .
i .
i .
i .
i .
i .
i .
i .
i .
i .
i .
i .
0 .90
i .
i .
i .
i .
0 .45 20
sl . s .
2 .318
∞
0 .4380
v . s .
s .
1 .412
s .
i .
i .
i .
0 .88 20
4 .7 20
2 .08 20
65 16
i .
i .
v . sl . s .
i .
i .
0 .3120
4.420
s.
v. s. h.
s.
s.
s.
s.
s.
s.
s.
1.6
v. sl. s. h.
∞
s.
s.
s.
s.
7125
∞
s .
∞
s .
∞
s .
∞
∞
∞
∞
s .
∞
∞
∞
∞
v . s .
∞
s .
∞
s .
∞
∞
s .
s .
i .
v . sl . s .
sl . s .
∞
s .
s .
∞
v . sl . s .
sl . s .
sl . s .
∞
s .
v . s .
∞
s .
v . s .
v . sl . s .
∞
v . sl . s .
s .
v . s . h .
s .
v . s .
425
∞
s .
v . s .
1 .318
∞
s .
∞
0 .0118
v . sl . s .
s .
∞
s .
s .
∞
∞
∞
v . s .
∞
∞
v . s .
∞
∞
∞
∞
s .
∞
∞
∞
∞
s .
∞
∞
v . s .
∞
∞
∞
∞
∞
∞
s .
(Continued )
2-34
TABLE 2-2 Physical Properties of Organic Compounds (Continued )
Name
tartrate (d-)
-toluidine (o-)
(m-)
(p-)
Diethyleneglycol dinitrate
Difluorodichloromethane
Diglycerol
Dihydroxy-dinaphthyl (α-)
(-2,-2′,-1,-1′)
-diphenyl (4-,4′-)
-ethyl formal (β-)
-naphthalene (1-,5-)
(1-,8-)
Dimethoxy-benzene (p-)
-diphenylamine (4-,4′-)
-ethyl adipate
Dimethyl adipate
-amine
-aminoasobenzene (p-)
-aminoethanol
-aminophenol (m-)
-aniline
sulfonic acid (m-)
(p-)
carbonate
ether
-formamide
fumarate
glutarate
glyoxime
-naphthalene (1-,4-)
(2-,3-)
-naphthylamine (α-)
(β-)
oxalate
phthalate (o-)
sulfate
sulfide
tartrate (d-)
-vinyl-ethenyl carbinol
Dinaphthyl (αα-)
-methane (αα′-)
(β,β′-)
Dinitro-anisole (1-)(2-,4-)
-benzene (o-)
(m-)
(p-)
sulfonic acid (2-,4-)(1-)
-benzoic acid (2-,4-)
(3-,5-)
-benzophenone (4-,4′-)
-diphenyl (4-,4′-)
(2-,4′-)
-naphthalene (1-,5-)
(1-,8-)
Dinitro-phenol (2-,3-)
(2-,4-)
(2-,6-)
-salicylic acid (3-,5-)
-stilbene (4-,4′-)
-toluene (2-,4-)
(3-,4-)
(3-,5-)
Dioxane
Dipentene
Formula
(CHOH⋅CO2C2H5)2
CH3⋅C6H4⋅N(C2H5)2
CH3⋅C6H4⋅N(C2H5)2
CH3⋅C6H4⋅N(C2H5)2
O(CH2CH2ONO2)2
F2CCl2
[(HO)2C3H5]2O
(HO⋅C10H6⋅)2
(HO⋅C10H6⋅)2
(HO⋅C6H4⋅)2
CH2(OCH2CH2OH)2
C10H6(OH)2
C10H6(OH)2
(CH3O)2C6H4
HN(C6H4OCH3)2
(CH2)4(CO2C2H4OCH3)2
[(CH2)2CO2CH3]2
(CH3)2NH
C6H5N:N⋅C6H4N(CH3)2
(CH3)2NCH2CH2OH
(CH3)2NC6H4OH
(CH3)2NC6H5
(CH3)2NC6H4SO3H
(CH3)2NC6H4SO3H⋅H2O
OC(OCH3)2
CH3OCH3
HCON(CH3)2
(:CHCO2CH3)2
(CH2)3(CO2CH3)2
(CH3⋅C:NOH)2
C10H6(CH3)2
C10H6(CH3)2
C10H7N(CH3)2
C10H7N(CH3)2
(⋅CO2CH3)2
C6H4(CO2CH3)2
(CH3O)2SO2
(CH3)2S
(CHOH⋅CO2CH3)2
(CH3)2COH⋅C⋮C⋅CH:CH2
C10H7⋅C10H7
(C10H7)2CH2
(C10H7)2CH2
CH3OC6H3(NO2)2
C6H4(NO2)2
C6H4(NO2)2
C6H4(NO2)2
(NO2)2C6H3SO3H⋅3H2O
(NO2)2C6H3CO2H
(NO2)2C6H3CO2H
(NO2C6H4)2CO
(NO2C6H4)2
(NO2C6H4)2
C10H6(NO2)2
C10H6(NO2)2
(NO2)2C6H3OH
(NO2)2C6H3OH
(NO2)2C6H3OH
(NO2)2C6H2(OH)CO2H⋅H2O
(NO2C6H4CH:)2
(NO2)2C6H3CH3
(NO2)2C6H3CH3
(NO2)2C6H3CH3
O < (CH2⋅CH2)2 > O
C10H16
Formula
weight
206 .19
163 .26
163 .26
163 .26
196 .12
120 .91
166 .17
286 .32
286 .32
186 .21
136 .15
160 .17
160 .17
138 .16
229 .27
262 .30
174 .19
45 .08
225 .29
89 .14
137 .18
121 .18
201 .24
219 .26
90 .08
46 .07
73 .09
144 .13
160 .17
116 .12
156 .22
156 .22
171 .24
171 .24
118 .09
194 .18
126 .13
62 .13
178 .14
110 .15
254 .33
268 .35
268 .35
198 .13
168 .11
168 .11
168 .11
302 .22
212 .12
212 .12
272 .21
244 .20
244 .20
218 .17
218 .17
184 .11
184 .11
184 .11
246 .13
270 .24
182 .13
182 .13
182 .13
88 .11
136 .23
Form and
color
Specific
gravity
Melting
point, °C
Boiling
point, °C
lq.
lq .
lq .
lq .
lq .
gas
lq .
pl ./al .
nd ./al .
rhb ./al .
lq .
pr ./aq .
nd .
lf .
cr .
lq .
col . lq .
col . lq .
yel ./al .
col . lq .
nd .
yel . lq .
cr .
pr .
col . lq .
gas
lq .
col . tri .
lq .
col . cr .
lq .
lf ./al .
col . oil
col . cr .
col . mn .
col . lq .
col . oil
oil
cr .
lq .
lf ./al .
pr ./al .
nd ./al .
col . mn .
col . mn .
col . rhb .
col . mn .
pr .
cr ./aq .
mn . pr .
col . nd .
nd ./al .
mn .
nd .
rhb .
yel . mn .
yel . rhb .
yel . rhb .
pl ./aq .
yel . lf .
nd .
nd .
mn . pr .
col . lq .
col . lq .
1.204 20/4
17
0 .924 15 .5
1 .377 25/4
1 .486 −30
280
208–9755
231–2
228–9
−11 .3
−155
1 .25
1 .154 25
1 .053 55/55
1 .075 15 .6
1 .063 20/4
0 .680 0/4
0 .887
20/4
0 .956 20/4
1 .070 20/4
0 .94525
1 .08915 .6
1 .016 20/4
1 .042 20
1 .03970/70
1 .14854
1 .18925/25
1 .3520/4
0 .84621/4
1 .32820/4
0 .887 20/4
1 .341 20
1 .5918
1 .575 20/4
1 .625 18
1 .445
1 .474
1 .681 20
1 .683 24
1 .321 71
1 .259 111
1 .277 111
1 .033 20/4
0 .865 18
300
218
270–2
−5 .3
258–60
140
56
103
10–1
−96
116–7
85
2 .5
d . 266
257
0 .5
−138 .5
−58 .3
102
−37
240–6
<−18
104
46
54
−26 .8
−83 .2
61 .5
160
109
92
94–5
117–8
89 .8
173–4
106–8
179–80
204–5
189
233
93 .5
216
170–2
144–5
114–5
63–4
173 d .
210–6
70
60–1
92–3
9 .5–10 .5
−29 .2
220–3010
subl .
subl .
264
d .
212 .6
145–502
11518
7 .4
d .
135756
265–8
193
89–90
−23 .7
152 .8
192
13050
264–6
265767
274 .5711
304–5
163 .3
280734
188 .3
37 .3
280
150
240–412
>360
319774
300–2
299777
subl .
subl .
d .
subl .
300
subl .
101 .1
178
Solubility in 100 parts
Water
sl. s.
i .
i .
i .
i .
5 .7 cc .26
s . h .
i .
i .
sl . s .
∞
sl . s .
sl . s . h .
v . sl . s .
i .
5
i .
v . s .
i .
∞
sl . s . h .
i .
s .
s . h .
i .
3700 cc .18
∞
i .
20
0 .06
i .
i .
i .
i .
6
0 .43
v . sl . s .
i .
s .
620
i .
i .
i .
sl . s . h .
0 .01 c .
0 .399
0 .18100
s .
1 .8525
s h .
i .
i .
i .
i .
i .
sl . s .
0 .5 c .
s . h .
s . c .
i .
0 .0322
i .
sl . s .
∞
i .
Alcohol
Ether
∞
s .
s .
∞
s .
s .
s .
s .
i .
v . s .
v . s .
v . s .
s .
s .
v . s .
v . s .
s .
v . s .
v . s .
v . s .
s .
s .
s .
s .
s .
s .
s .
s .
v . sl . s .
∞
s .
v . sl . s .
∞
s .
sl . s .
sl . s .
v . s .
v . s .
sl . s .
s .
s .
s .
s .
s .
s .
∞
s .
20015
∞
s .
s . h .
0 .8 c .
s .
1 .520
1 .921
320
0 .1821
s .
s .
v . s .
s .
v . s .
v . sl . s .
sl . s .
20
1 .5
v . s . h .
0 .2 c .
v . s . h .
420
s . h .
v . s .
v . sl . s .
1 .215
v . s .
v . s . h .
s .
v . s .
v . sl . s .
916
s . h .
s .
s .
s .
2-35
Diphenyl
-amine
carbonate
-chloroarsine
-ethane
ether
guanidine
-methane
phenylenediamine (p-)
succinate
sulfide
sulfone
urea (uns .)
Diphenylene oxide
Dipropyl adipate (n-)
-amine (n-)
(i-)
aniline (n-)
carbonate (n-)
ether (n-)
(i-)
ketone (n-)
(i-)
oxalate (n-)
(i-)
Disalicylal ethylenediamine
Ditolyl guanidine (o-)
Divinyl acetylene
Docosane (n-)
Dodecane (n-)
Dulcitol
Durene (1-,2-,4-,5-)
Elaidic acid
Eosine
Ephedrine (l-)
Epichlorhydrin (α-)
Epidichlorohydrin (α-)
Erythritol (dl-)
tetranitrate
Ethane
Ethanol-amine
formamide
Ether
Ethyl abietate
acetate
acetoacetate
alcohol
-amine
hydrochloride
aniline
sulfonic acid (m-)
anisate (p-)
anthranilate (o-)
benzene
benzoate
-benzyl-aniline
bromide
butyrate (n-)
(i-)
caprate (n-)
Ethyl caproate (n-)
caprylate (n-)
chloride
chloroacetate
chlorocarbonate
cinnamate (trans-)
cyanoacetate
formate
furoate (α)
heptoate
hypochlorite
iodide
lactate
C6H5⋅C6H5
C6H5NHC6H5
CO(OC6H5)2
(C6H5)2AsCl
(C6H5CH2⋅)2
C6H5OC6H5
(C6H5NH)2C:NH
(C6H5)2CH2
(C6H5NH)2C6H4
(⋅CH2CO2C6H5)2
(C6H5)2S
(C6H5)2SO2
(C6H5)2NCONH2
< (C6H4)2O
(⋅CH2CH2CO2C3H7)2
(C2H5CH2)2NH
[(CH3)2CH]2NH
C6H5N(C3H7)2
CO(OCH2C2H5)2
(C2H5CH2)2O
[(CH3)2CH]2O
(C2H5CH2)2CO
[(CH3)2CH]2CO
(CO2CH2C2H5)2
[CO2CH(CH3)2]2
[HOC6H4CH:NCH2⋅]2
(C7H7NH)2C:NH
(H2C:CH⋅C⋮)2
CH3(CH2)20CH3
CH3(CH2)10CH3
CH2OH(CHOH)4CH2OH
(CH3)4C6H2
C8H17CH:CH(CH2)7CO2H
C20H8O5Br4
C6H5CHOHCH(CH3)NHCH3
C2H3O⋅CH2Cl
CH2:CCl⋅CH2Cl
CH2OH(CHOH)2CH2OH
C4H6(ONO2)4
CH3CH3
HOCH2CH2NH2
HCONHCH2CH2OH
(CH3CH2)2O
C19H29CO2C2H5
CH3CO2C2H5
CH3COCH2CO2C2H5
CH3CH2OH
C2H5NH2
C2H5NH2⋅HCl
C6H5NHC2H5
C2H5NHC6H4SO3H
CH3OC6H4CO2C2H5
NH2C6H4CO2C2H5
C6H5⋅C2H5
C6H5CO2C2H5
C6H5N(C2H5)CH2C6H5
C2H5Br
C2H5CH2CO2C2H5
(CH3)2CHCO2C2H5
CH3(CH2)8CO2C2H5
CH3(CH2)4CO2C2H5
CH3(CH2)6CO2C2H5
CH3CH2Cl
ClCH2CO2C2H5
ClCO2CH2CH3
C6H5CH:CHCO2C2H5
CH2(CN)CO2C2H5
HCO2CH2CH3
OC4H3CO2C2H5
CH3(CH2)5CO2C2H5
ClOCH2CH3
CH3CH2I
CH3CH(OH)CO2C2H5
154 .21
169 .22
214 .22
264 .58
182 .26
170 .21
211 .26
168 .23
260 .33
270 .28
186 .27
218 .27
212 .25
168 .19
230 .30
101 .19
101 .19
177 .29
146 .18
102 .17
102 .17
114 .19
114 .19
174 .19
174 .19
268 .31
239 .32
78 .11
310 .60
170 .33
182 .17
134 .22
282 .46
647 .89
165 .23
92 .52
110 .97
122 .12
302 .11
30 .07
61 .08
89 .09
74 .12
330 .50
88 .11
130 .14
46 .07
45 .08
81 .54
121 .18
201 .24
180 .20
165 .19
106 .17
150 .17
211 .30
108 .97
116 .16
116 .16
200 .32
144 .21
172 .26
64 .51
122 .55
108 .52
176 .21
113 .11
74 .08
140 .14
158 .24
80 .51
155 .97
118 .13
col. mn.
col. mn.
nd./al.
rhb.
col. pr.
col. rhb.
mn ./al .
col . pr .
cr .
lf ./al .
col . lq .
nd ./aq .
rhb .
lf ./al .
col . lq .
col . lq .
col . lq .
yel . oil
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
cr .
cr .
lq .
cr .
lq .
mn .
mn .
lf ./al .
col . cr .
cr ./et .
lq .
col . lq .
tet . pr .
lf ./al .
col . gas
col . oil
lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
col . lq .
mn .
lq .
nd ./aq .
lq .
cr .
col . lq .
col . lq .
yel . oil
col . lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lf .
col . lq .
yel . lq .
col . lq .
oil
0.992 73/4
1.160 20/20
1.272 14
1.583 40
0.978 50/50
1.073 20
1 .001 26/4
1 .119 15/15
1 .248 25/4
1 .276
20/4
0 .979
0 .739 20/4
0 .722 22
0 .910 20
0 .968 22
0 .744 21/0
0 .725 21/0
0 .822 20/4
0 .806 20/4
1 .038 0/0
1 .34
1 .1020/4
0 .776 20/4
0 .778 44/4
0 .751 20/4
1 .466 15
0 .838 81/4
0 .851 79/4
1 .183 25/25
1 .204 25
1 .451 20/4
−88
0 .546
1 .022 20
1 .169 25
0 .708 25/4
1 .020 20/20
0 .901 20/4
1 .025 20/4
0 .789 20/4
0 .689 15/15
1 .216
0 .963 20/4
1 .103 25/25
1 .117 20/4
0 .867 20/4
1 .052 15/15
1 .034 18 .5
1 .431 20/4
0 .879 20/4
0 .871 20/4
0 .859 28
0 .873 20/20
0 .878 17
0 .917 6/6
1 .159 20/4
1 .138 20/4
1 .049 20/4
1 .062 20/4
0 .923 20/4
1 .117 21/4
0 .872 20/20
1 .013 −6/4
1 .933 20/4
1 .030 25/4
69–70
52.9
80
43–4
52–3
27
147–8
26–7
152
122–3
<−40
128–9
189
86–7
−20 .3
−39 .6
−61
−122
−60
−32 .6
−51 .7
254.9
302
302–6
d. 327
284
259
d . > 170
265
330
296–7
379
287–8
143–510
110–1
83 .5743
245 .4
168 .2
91
69
144 .2
123 .7
213 .5
190
125–6
178–9
44 .5
−9 .6
189
79–80
51–2
40
−25 .6
126
61
−172
10 .5
<−40
−116 .3
−82 .4
−45
−112
−80 .6
108–9
−63 .5
d . 294
7–8
13
−94 .4
−34 .6
−117 .8
−93 .3
−88 .2
−20
−67 .5
−45
−139
−26
−80 .6
12
−22 .5
−79
34
−66 .1
expl .
−105
85
224 .515
214 .5
290–53
193–5
288100
255
117756
94
329–31
expl .
−88 .6
171757
d .
34 .6
2004
77 .1
180755
78 .4
16 .6
204
269–70
266–8
136 .2
211–2
28510
38 .4
120–1
110–1
244 .6758
165–6736
207–8753
13
144
94–5
271
208753
54760
195766
187–8
36752
72 .4
155
i.
0.0325
i.
0.2 d.
i.
v. sl. s.
v . sl . s .
i .
i .
i .
i .
sl . s . h .
v . sl . s .
i .
i .
s .
s .
i .
v . sl . s .
sl . s .
0 .2
0 .43
v . sl . s .
d . h .
0 .0328
v . sl . s .
i .
i .
i .
3 .215
i .
i .
i .
5
<5
i .
60
i . c .
4 .7 cc .20
∞
∞
7 .520
i .
8 .515
1317
∞
∞
24017
i .
2 .1515
i .
v . sl . s .
0 .0115
0 .0820
i .
1 .060
0 .6825
sl . s .
0 .00220
i .
i .
0 .450
i .
d .
i .
225
1118
i .
0 .02920
0 .420
∞
1020
5619.5
v. s.
20
s.
s.
920
v . s .
s . h .
s . h .
s .
s . h .
s .
∞
s .
s .
6.620
s.
s.
s.
v. s.
∞
sl . s .
v . s .
s .
∞
s .
v . s .
s .
∞
s .
∞
∞
∞
∞
∞
∞
∞
∞
s . h .
s .
4 h .
v . s .
v . sl . s .
s .
v . s .
s .
500
∞
∞
sl . s . c .
s .
150 cc .
∞
v . s .
v . s .
i .
s .
v . s .
s .
∞
∞
i .
s .
1
∞
∞
∞
∞
v . s .
∞
s .
s .
∞
∞
18
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
i .
∞
s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
(Continued )
2-36
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
laurate
mercaptan
methacrylate
naphthylamine (α-)
naphthyl ether (α-)
nitrate
nitrite
oleate
palmitate
pelargonate
propionate
salicylate (o-)
stearate
toluate (o-)
(m-)
toluene sulfonate (p-)
toluidine (o-)
(p-)
urea
valerate (n-)
(i-)
Ethylal
Ethylene
bromide
bromohydrin
chlorobromide
chlorohydrin
diamine
oxide
Ethylidene diacetate
Eugenol (1-,4-,3-)
(i-)(1-,3-,4-)
Fenchyl alcohol (dl-)
(d-)(α-)
(i-)(l-)
Ferric dimethyl-dithiocarbamate
Fluorene
Fluorescein
Fluoro-dichloromethane
-trichloromethane
Formaldehyde
(m-)
(p-)
Formamide
Formanilide
Formic acid
Fructose
Fuchsin
Fulminic acid
Fumaric acid (trans-)
Furfural
Furfuran
Furfuryl acetate
alcohol
butyrate
propionate
Furoic acid
G-acid, K salt (2-)(6-,8-)
Na salt (2-)(6-,8-)
Galactose (d-)(α-)
Gallic acid (3-,4-,5-)
Gamma acid (2-,8-,6-)
Geraniol
Glucose (d-)(α-)
(d-)(β-)
Glucuronic acid
Glutam(in)ic acid (dl-)
Formula
CH3(CH2)10CO2C2H5
CH3CH2SH
CH2:C(CH3)CO2C2H5
C10H7NHC2H5
C10H7OC2H5
C2H5ONO2
C2H5ONO
C17H33CO2C2H5
CH3(CH2)14CO2C2H5
CH3(CH2)7CO2C2H5
CH3CH2CO2C2H5
HOC6H4CO2C2H5
CH3(CH2)16CO2C2H5
CH3⋅C6H4CO2C2H5
CH3⋅C6H4CO2C2H5
CH3⋅C6H4SO3C2H5
CH3⋅C6H4NHC2H5
CH3⋅C6H4NHC2H5
C2H5NH⋅CO⋅NH2
CH3(CH2)3CO2C2H5
(CH3)2CH(CH2)CO2C2H5
CH2(OC2H5)2
H2C:CH2
BrCH2⋅CH2Br
BrCH2⋅CH2OH
ClCH2⋅CH2Br
ClCH2⋅CH2OH
H2NCH2⋅CH2NH2
< (CH2)2 > O
CH3CH(O2CCH3)2
C3H5⋅C6H3(OH)OCH3
C3H5⋅C6H3(OCH3)OH
C10H17OH
C10H17OH
C10H17OH
Fe[SSCN(CH3)2]3
(C6H4)2 > CH2
C20H12O5
FCHCl2
Cl3CF
HCHO
(CH2O)3
(CH2O)x⋅xH2O
HCONH2
HCONHC6H5
HCO2H
CH2OH(CHOH)3COCH2OH
C20H19N3HCl
C:NOH
HO2CCH:CHCO2H
C4H3O⋅CHO
C4H4O
CH3CO2CH2C4H3O
C4H3O⋅CH2OH
C3H7CO2CH2⋅C4H3O
C2H5CO2CH2⋅C4H3O
C4H3O⋅CO2H
HOC10H5(SO3K)2
HOC10H5(SO3Na)2
C5H11O5⋅CHO
(HO)3C6H2CO2H⋅H2O
C10H5(NH2)(OH)SO3H
C9H15CH2OH
C5H11O5⋅CHO
C6H12O6⋅H2O
CHO(CHOH)4CO2H
[⋅CHNH2(CH2)2⋅](CO2H)2
Formula
weight
228 .37
62 .13
114 .14
171 .24
172 .22
91 .07
75 .07
310 .51
284 .48
186 .29
102 .13
166 .17
312 .53
164 .20
164 .20
200 .25
135 .21
135 .21
88 .11
130 .18
130 .18
104 .15
28 .05
187 .86
124 .96
143 .41
80 .51
60 .10
44 .05
146 .14
164 .20
164 .20
154 .25
154 .25
154 .25
416 .49
166 .22
332 .31
102 .92
137 .37
30 .03
90 .08
(30 .03)
45 .04
121 .14
46 .03
180 .16
337 .85
43 .02
116 .07
96 .08
68 .07
140 .14
98 .10
168 .19
154 .16
112 .08
380 .48
348 .26
180 .16
188 .13
239 .25
154 .25
180 .16
198 .17
194 .14
147 .13
Form and
color
Specific
gravity
Melting
point, °C
Boiling
point, °C
oil
lq .
col . lq .
oil
cr .
col . lq .
lq .
oil
col . nd .
col . lq .
col . lq .
col . lq .
col . cr .
lq .
lq .
pr ./al .
lq .
lq .
nd .
col . lq .
col . lq .
lq .
col . gas
col . lq .
col . lq .
lq .
col . lq .
col . lq .
lq .
col . lq .
oil
oil
col . cr .
col . pr .
col . cr .
cr .
cr ./al .
yel . red
gas
col . lq .
gas
wh .
amor .
lq .
mn .
col . lq .
nd ./aq .
red
0.868 13/4
0 .839 20/4
0 .913 15 .6
1 .060 20/4
1 .061 20/20
1 .100 25/4
0 .900 15 .5
0 .867 25
0 .858 25/4
0 .866 17 .5
0 .891 20/4
1 .136 15/4
0 .848 36 .3
1 .032 25/25
1 .030 20/20
1 .166 48/4
0 .948 25/4
0 .942 25/4
1 .213 18
0 .877 20
0 .867 20/4
0 .824 25/4
0 .57−102/4
2 .180 20/4
1 .772 20/4
1 .689 19
1 .213 20/4
0 .900 20/20
0 .887 7/4
1 .061 12
1 .070 15/15
1 .091 15/15
0 .935 40
0 .964 20/4
0 .961
−10.7
−121
269
36–7
118
303723
276 .4
87–8
17
216–815
19110
227–8757
99 .1
233–4
20110
227
231750
221 .3
215–6
217
col . pr .
lq .
col . lq .
col . oil
oil
col . lq .
col . lq .
mn . pr .
cr .
cr .
pr .
mn ./aq .
cr .
col . lq .
rhb .
cr .
cr .
cr ./aq .
1 .203 0/4
1 .4260
1 .494 17 .2
0 .815 −20
1 .1765
1 .139 20/4
1 .147 15/15
1 .220 20/4
1 .669 17 .5
1 .22
20/4
1 .635
1 .159 20/4
0 .937 20/4
1 .118 20/4
1 .129 25/4
1 .053 20/4
1 .109 20/4
5 .5
−102
<−15
24–5
−44 .5
−72 .6
1 .3
33 .4(31)
<−10
33–4
<−15
92
−91 .2
−99 .3
−66 .5
−169
10
−16 .6
−69
8 .5
−111 .3
18 .85
10 .3
−10
35
45–7
61–2
d . 100–30
115–6
d . > 290
−127
−92
64
150–60
2
47
8 .6
95–105
d . >200
286–7
−38 .7
133–4
1 .694 4/4
15
0 .883
1 .544 25
1 .562 18/4
1 .460
145 .5
135
89
−103 .9
131 .5
150 .3
106 .7
128 .8
117 .2
13 .5747
168740
253 .5
267 .5
201
201–2
201–2
ign . >150
293–5
14 .5
24 .9
−21
114 .5759
subl .
193
216120
100 .8
290
161 .7760
31–2756
175–7
169 .5752
212–3
195–6
230–2
165 .5
d . 220
<−15
146
150
154
199 d .
230
d .
Solubility in 100 parts
Water
i.
1 .5
i .
i .
i .
1 .355
v . sl . s .
i .
i .
i .
2 .420
i .
i .
i .
i .
i .
i .
i .
v . s .
0 .2425
0 .1720
918
26 cc .0
0 .4380
sl . s .
0 .6980
∞
∞
∞
sl . s .
v . sl . s .
v . sl . s .
sl . s .
sl . s .
i .
v . sl . s .
i .
v . sl . s . h .
i .
i .
v . s .
2125
20–3018
∞
sl . s .
∞
v . s .
0 .3
17
0 .7
9 .113
i .
i .
∞
v . sl . s .
v . sl . s .
3 .615
825
3420
10 .30
113
i .
8217 .5
15415
v . s .
1 .5 20
Alcohol
Ether
s.
s .
s .
s .
s .
∞
∞
∞
s .
∞
∞
∞
s .
∞
∞
s .
∞
s .
s .
s .
s .
∞
∞
∞
s .
∞
∞
∞
s .
∞
∞
s .
80
∞
∞
∞
360 cc .
∞
s .
i .
∞
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
∞
0 .3
v . s .
∞
∞
s .
s .
s . h .
s . h .
s .
∞
v . s .
s .
i .
∞
v . s .
∞
818
s .
5 .8
∞
s .
s .
s .
s .
s .
s .
30
s .
s .
∞
v . s .
s .
i .
v . sl . s .
s .
i .
0 .725
∞
s .
s .
s .
∞
∞
s .
0 .640
2815
2 .515
∞
sl . s .
∞
i .
v . sl . s .
v . sl . s .
Glutaric acid
Glycerol
acetate (mono-)
(di-)
nitrate (mono-) (α-)
(β-)
dinitrate (1-,3-)
Glyceryl triacetate
tribenzoate
tributyrate
tricaprate
tricaproate
tricaprylate
trilaurate
trimyristate
trinitrate
trinitrite
trioleate
tripalmitate
tristearate
Glycide
Glycine, Glycocoll
Glycol
diacetate
dibenzoate
dibutyrate
dicaprylate
diformate
dilaurate
dinitrate
dinitrite
dipalmitate
dipropionate
ether
formal
formate (mono-)
Glycolic acid
Guaiacol (o-)
Guanidine
H-acid, Na salt (1-,8-,3-,6-)
Heptacosane (n-)
Heptane (n-)
(i-)
Heptoic acid
aldehyde
Heptyl acetate (n-)
alcohol (n-)
mercaptan
Hexachloro-benzene
-ethane
Hexacosane (n-)
Hexadecane (n-)
Hexaethylbenzene
Hexamethylbenzene
Hexamethylene-diamine
-diisocyanate
-glycol
tetramine
Hexane (n-)
(i-)
(neo-)
2-37
CH2(CH2CO2H)2
CH2OH⋅CHOH⋅CH2OH
C5H10O4
(CH3CO2)2C3H5OH
CH2OH⋅CHOH⋅CH2NO3
CH2OH⋅CHNO3⋅CH2OH
CHOH(CH2ONO2)2
(CH3CO2)3C3H5
(C6H5CO2)3C3H5
(C2H5CH2CO2)3C3H5
[CH3(CH2)8CO2]3C3H5
[CH3(CH2)4CO2]3C3H5
[CH3(CH2)6CO2]3C3H5
[CH3(CH2)10CO2]3C3H5
[CH3(CH2)12CO2]3C3H5
CH2NO3⋅CHNO3⋅CH2NO3
CH2NO2⋅CHNO2⋅CH2NO2
(C17H33CO2)3C3H5
[CH3(CH2)14CO2]3C3H5
[CH3(CH2)16CO2]3C3H5
C2H3O⋅CH2OH
NH2CH2⋅CO2H
CH2OH⋅CH2OH
(CH3CO2CH2⋅)2
(C6H5CO2CH2⋅)2
(C3H7CO2CH2⋅)2
(C7H15CO2CH2⋅)2
(HCO2CH2⋅)2
(C11H23CO2CH2⋅)2
(O2NO⋅CH2⋅)2
(ONO⋅CH2⋅)2
(C15H31CO2CH2⋅)2
(C2H5CO2CH2⋅)2
(HO⋅CH2CH2)2O
< O⋅CH2CH2OCH2 >
HCO2CH2CH2OH
HOCH2CO2H
CH3O⋅C6H4OH
NH:C(NH2)2
C10H8O7NS2Na⋅1½H2O
CH3(CH2)25CH3
CH3(CH2)5CH3
(CH3)2CH(CH2)3CH3
C3H7⋅CH(CH3)⋅C2H5
(CH3)3C⋅CH2⋅C2H5
[(CH3)2CH]2CH2
(CH3)2C(C2H5)2
(C2H5)3CH
(CH3)3C⋅CH(CH3)2
CH3(CH2)5CO2H
CH3(CH2)5CHO
CH3CO2CH2(CH2)5CH3
CH3(CH2)5CH2OH
[(CH3)2CH]2CHOH
(C2H5⋅CH2)2CHOH
CH3CH(SH)⋅C5H11
C6Cl6
CCl3⋅CCl3
CH3(CH2)24CH3
CH3(CH2)14CH3
C6(C2H5)6
C6(CH3)6
NH2(CH2)6NH2
OCN(CH2)6NCO
HO(CH2)6OH
(CH2)6N4
CH3(CH2)4CH3
(CH3)2CH(CH2)2CH3
(CH3)3C⋅C2H5
(CH3)2CH⋅CH(CH3)2
(C2H5)2CHCH3
132 .11
92 .09
134 .13
176 .17
137 .09
137 .09
182 .09
218 .20
404 .41
302 .36
554 .84
386 .52
470 .68
639 .00
723 .16
227 .09
179 .09
885 .43
807 .32
891 .48
74 .08
75 .07
62 .07
146 .14
270 .28
202 .25
314 .46
118 .09
426 .67
152 .06
120 .06
538 .89
174 .19
106 .12
74 .08
90 .08
76 .05
124 .14
59 .07
368 .32
380 .73
100 .20
100 .20
100 .20
100 .20
100 .20
100 .20
100 .20
100 .20
130 .18
114 .19
158 .24
116 .20
116 .20
116 .20
132 .27
284 .78
236 .74
366 .71
226 .44
246 .43
162 .27
116 .20
168 .19
118 .17
140 .19
86 .18
86 .18
86 .18
86 .18
86 .18
col. cr.
col. lq.
col . oil
col . lq .
col . pr .
lf .
oil
col . lq .
nd .
col . lq .
col . cr .
col . lq .
col . lq .
col . nd .
lf .
yel . oil
yel . lq .
col . oil
col . nd .
col . pr .
col . lq .
mn .
col . lq .
col . lq .
rhb ./et .
col . lq .
lq .
lq .
amor .
yel . lq .
lq .
nd .
lq .
lq .
lq .
lq .
nd ./aq .
pr .
col . cr .
cr .
col . cr .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
lq .
mn .
rhb .
cr .
lf .
pr ./al .
pl ./al .
lf .
lq .
nd ./aq .
col . rhb .
col . lq .
lq .
lq .
lq .
lq .
1.429 15
1.260 50/4
1 .20 20/4
1 .178 15/15
1 .4015
1 .4015
1 .4715
1 .16117/4
1 .228 12
1 .032 20/4
0 .921 40/4
0 .987 20/4
0 .954 20/4
0 .894 60/4
0 .885 60/6
1 .601 15
1 .291 10/16
0 .915 15
0 .866 80/4
0 .862 80/4
1 .114 16/16
1 .161
1 .113 19/4
1 .109 14/4
1 .024 0
97.5
17.9
40
58–9
54
<−30
−78
75–6
<−75
31(25)
−25
8 .3(−21)
45–6
56 .5
13 .3(2)
−4
65 .1
70 .8(55)
20020
290
158165
175–640
155–60
155–60
146–815
258–9
d .
305–9
16015
150 sl . d .
24018
310–200 .1
166 sl . d .
232–6 d .
−15 .6
−31
73–4
197 .4
190 .5
>360
240
22
1 .482 21/2
1 .216 0
52–4
−20
<−15
71–2
1 .045 25
1 .118 20/20
1 .060 20/4
1 .199 15/4
−10 .5
1 .140 15/15
79(63)
28 .3
50
0 .780 60/4
0 .684 20/4
0 .679 20/4
0 .687 20/4
0 .674 20/4
0 .675 20/4
0 .693 20/4
0 .698 20/4
0 .690 20/4
0 .918 20
0 .850 20/ℓ
0 .874 16/16
0 .824 20/4
0 .829 20/4
0 .820 20/4
0 .835 20
2 .044 24
2 .091 20/4
0 .779 57/4
0 .774 20/4
0 .831 130/4
1 .0428
0 .659 20/4
0 .654 20/4
0 .649 20/20
0 .662 20/4
0 .664 20/4
59 .5
−90 .6
−118 .2
−119 .4
−125
−119 .4
−135 .0
−118 .7
−25
−10
−42
−34
−37
228–31
186–7
56 .6
18 .5
130
166
42
42
subl .
−94
−153 .7
−98 .2
−129 .8
−118
174
18820
expl . 114
96–8
2600 .1
211–2
244 .8
75–6
180
d .
205
27015
98 .4760
90 .0
91 .8
79 .1
80 .8
86 .0
93 .5
80 .8
221–2
155
191 .5 759
175 756
140
156
174–5 765
309742
186777
26215
287 .5
298 .3
265
204–5
143–420
250
69
60 .2
49 .7
58 .0760
63 .2
63.920
∞
v . s .
s .
7015
7 .1715
i .
i .
i .
i .
i .
i .
i .
0 .1820
d .
i .
i .
i .
∞
23 c .
∞
14 .322
i .
i .
i .
v . sl . s .
i .
0 .9225
i .
i .
sl . s .
∞
∞
∞
∞
1 .715
v . s .
0 .1720
i .
0 .00515
i .
i .
i .
i .
i .
i .
i .
0 .2515
0 .0220
i .
0 .18 25
v . sl . s .
i .
i .
i .
0 .00522
i .
i .
i .
i .
v . s .
d .
s .
8112
0 .01415
i .
i .
i .
i .
v. s.
∞
v . s .
s .
v . s .
v . s .
v . s .
∞
s . h .
s .
s . h .
s .
s .
sl . s . c .
s .
5020
d .
sl . s .
0 .00421
s . h .
∞
0 .1 c .
∞
∞
v. s.
i .
sl . s .
sl . s .
v . sl . s .
sl . s .
v . s .
∞
s .
s .
v . s .
s .
s .
v . s .
v . s .
∞
s .
v . s .
v . s .
s . h .
∞
i .
1 .0
∞
s .
v . s .
v . s .
s .
s . d .
s .
∞
∞
v . s .
∞
s .
s .
∞
i .
9025
v . s .
s .
v . s .
v . s .
sl . s .
s .
s .
s .
s .
s .
s .
s .
s .
∞
s .
∞
∞
s .
∞
∞
∞
∞
∞
∞
∞
∞
s .
∞
s .
∞
∞
s .
v . sl . s . h .
v . s .
v . sl . s .
∞
0 .7525
0 .20
s .
d .
s .
3
5033
s . h .
v . s .
∞
825
v . s .
sl . s . h .
v . sl . s .
∞
s .
s .
s .
s .
(Continued )
2-38
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Hexyl acetate (n-)
alcohol (n-)
formate (n-)
resorcinol (2-,4-)
Hippuric acid
Histidine (l-)
Homophthalic acid (o-)
Hydracrylic acid
Hydro-cyanic acid
-quinone (p-)
Hydroxy-benzaldehyde (p-)
-benzanilide (o-)
-quinoline (2-)(α-)
(8-)(o-)
Indigo
White
Indole
Indoxyl
Iodo-benzene
-phenol (p-)
Iodoform
Ionone (α-)
(β-)
Irone (β-)
Isatin
Isoprene
Ketene
Koch acid (1-)(3-,6-,8-)
Lactic acid (dl-)
anhydride
Lactide (dl-)
Lactose
Lauric acid
Laurone
Lauryl alcohol
Lead tetraethyl
tetramethyl
Lepidine (py-4)
Leucine (l-)
Levulinic acid
Limonene (d- or l-)
Linalool (d- or l-)
Linalyl acetate
Linoleic acid
Maleic acid
anhydride
Malic acid (dl-)
(d- or l-)
Malonic acid
Maltose
Mandelic acid (dl-)
Mannitol (d-)
Mannose (d-)
Margaric acid
Mellitic acid
Menthol (l-)(α-)
Mercapto-benzothiazole (2-)
-thiazoline (2-)
Mercuric cyanide
fulminate
Mesityl oxide
Mesitylene (1-,3-,5-)
Metanilic acid (m-)
Methane
Formula
CH3CO2(CH2)5CH3
CH3(CH2)4CH2OH
(CH3)2CH⋅C(CH3)2OH
(CH3)2COH⋅CH2C2H5
HCO2CH2(CH2)4CH3
CH3(CH2)5C6H3(OH)2
C6H5CONHCH2CO2H
C6H9O2N3
HO2C⋅C6H4⋅CH2CO2H
HOCH2CH2CO2H
HCN
C6H4(OH)2
HO⋅C6H4⋅CHO
HO⋅C6H4⋅CONHC6H5
C9H6N⋅OH
C9H6N⋅OH
[C6H4(CO)(NH)C:]2
C16H12O2N2
C8H7N
C8H6NOH
C6H5I
IC6H4OH
HCI3
C10H16:CHCOCH3
C10H16:CHCOCH3
C14H22O
C6H4 < (CO)(N) > COH
CH2:CH⋅C(CH3):CH2
H2C:CO
C10H4(NH2)S3O9HNa2
CH3CH(OH)CO2H
C6H10O5
C6H8O4
C12H22O11⋅H2O
CH3(CH2)10CO2H
[CH3(CH2)10]2CO
CH3(CH2)10CH2OH
Pb(CH2CH3)4
Pb(CH3)4
C9H6N⋅CH3
(CH3)2CHCH2CH(NH2)CO2H
CH3CO(CH2)2CO2H
C10H16
C10H17OH
CH3CO2C10H17
C17H31CO2H
HO2C⋅CH:CH⋅CO2H
< (⋅CHCO)2 > O
HO2CCH2CH(OH)CO2H
HO2CCH2CH(OH)CO2H
H2C(CO2H)2
C12H22O11⋅H2O
C6H5CH(OH)CO2H
CH2OH(CHOH)4CH2OH
CH2OH(CHOH)4CHO
CH3(CH2)15CO2H
C6(CO2H)6
C10H19OH
< C6H4N:C(SH)S >
< CH2N:C(SH)SCH2 >
Hg(CN)2
Hg(ONC)2⋅½H2O
(CH3)2C:CHCOCH3
C6H3(CH3)3
H2NC6H4SO3H
CH4
Formula
weight
144 .21
102 .17
102 .17
102 .17
130 .18
194 .27
179 .17
155 .15
180 .16
90 .08
27 .03
110 .11
122 .12
213 .23
145 .16
145 .16
262 .26
264 .28
117 .15
133 .15
204 .01
220 .01
393 .73
192 .30
192 .30
206 .32
147 .13
68 .12
42 .04
427 .34
90 .08
162 .14
144 .13
360 .31
200 .32
338 .61
186 .33
323 .44
267 .34
143 .19
131 .17
116 .12
136 .23
154 .25
196 .29
280 .45
116 .07
98 .06
134 .09
134 .09
104 .06
360 .31
152 .15
182 .17
180 .16
270 .45
342 .17
156 .27
167 .25
119 .21
252 .62
293 .63
98 .14
120 .19
173 .19
16 .04
Form and
color
Specific
gravity
col. lq.
col. lq.
lq .
lq .
lq .
col . nd .
rhb .
lf ./aq .
cr ./aq .
syrup
lq .
cr .
nd ./aq .
pr ./al .
pr ./al .
pr .
cr .
gray
lf ./aq .
yel . pr .
col . lq .
nd ./aq .
yel . hex .
col . oil
col . oil
col . oil
yel . red
col . lq .
col . gas
cr .
hyg .
yel . oil
tri ./al .
col . rhb .
col . nd .
pl .
lf .
col . lq .
col . lq .
lq .
cr .
lf .
lq .
col . oil
col . lq .
yel . oil
mn .
cr .
col . cr .
col . cr .
col . tri .
col . nd .
rhb ./aq .
col . rhb .
rhb .
col . pl .
nd ./al .
col . cr .
nd .
cr .
cr .
cr ./aq .
lq .
col . lq .
col . nd .
gas
0.890 0/0
0.820 20/20
0 .821 20/0
0 .809 20/4
0 .898 0
1 .371 20/4
0 .697 18
1 .332 15
1 .129 130
1 .35
1 .824 25/4
1 .857 112
4 .008 17
0 .930 20
0 .944 20
0 .939 20
Melting
point, °C
−51.6
−14
−107
68–70
187–8
d . 287
175–80
−12
170 .3
116–7
135
199–200
75–6
390–2
52
85
−28 .5
93–4
119
0 .681 20/4
200–1
−120
−151
1 .249 15/4
16 .8
10/4
0 .862
1 .525 20
0 .869 50/4
0 .809 69/4
0 .831 24/4
1 .659 18/4
1 .995 20/4
1 .086 20
1 .29318
1 .140 20/20
0 .842 20/4
0 .868 20
0 .895 20
0 .903 18/4
1 .609
1 .5
1 .601 20/4
1 .595 20/4
1 .631 15
1 .540 17
1 .300 20/4
1 .489 20/4
1 .539 20/4
0 .853 60
15/15
0 .890
1 .4220/4
1 .50
4 .003 22
4 .4
0 .858 20/4
0 .865 20/4
0 .415 −164
124 .5
202
48(44)
69–70
24
−136
−27 .5
9–10
295
33 .5
−96 .9
−9 .5
130 .5
57–60
128–9
99–100
130–5 d .
d .
118 .1
166
132
60–1
286–8
42–3
179
106
d . 320
expl .
−59
−45(−52)
d .
−182 .6
Boiling
point, °C
169.2
157.2
120–1
123762
153 .6
1797
d .
d .
25–6
285730
subl .
d .
subl .
266 .6752
subl .
253–4
110
188 .6
d .
subl .
136 .117
14018
14416
subl .
34
−56
12214
d . 250
255757
d .
225100
255–9
152291
110760
261–3
subl .
245–6
177
198–200
220762 d .
229–3016
135 d .
202
150 d .
140 d .
d .
290–53
227100
d .
212
d .
130750
164 .8
−161 .4
Solubility in 100 parts
Water
i.
0.620
v . sl . s .
v . sl . s .
0 .05
0 .420
s .
s . h .
∞
615
1 .3831
v . sl . s . h .
s . h .
v . sl . s . c .
i .
i .
s . h .
s .
0 .03420
sl . s .
0 .0125
sl . s .
sl . s .
v . sl . s .
s . h .
i .
d .
7 .220
∞
v . sl . s .
v . sl . s .
1710
i .
i .
i .
i .
i .
sl . s .
2 .218
v . s .
i .
v . sl . s .
v . sl . s .
i .
7925
16 .380
14426
v . s .
13816
10825
1620
1314
24817
i .
v . s .
0 .04 c .
i .
1 .660
12 .515
0 .0712
320
i .
215
0 .420 cc .
Alcohol
Ether
v. s.
∞
∞
∞
∞
v . s .
s . h .
v . sl . s .
v . s .
v. s.
∞
∞
∞
∞
s .
0 .2518
i .
sl . s .
∞
v . s .
∞
v . s .
s .
v . s .
s .
i .
s .
s . h .
s .
s .
v . s .
1 .517
∞
∞
v . s .
v . s . h .
∞
d .
s .
v . s .
sl . s .
i .
s .
s .
s .
∞
v . s .
13 .625
∞
∞
v . s .
sl . s .
∞
s .
∞
s .
v . sl . s . c .
i .
s .
i . c .
s .
sl . s .
∞
∞
∞
s .
v . s .
∞
s .
∞
∞
7030
v . s .
∞
∞
∞
∞
825
v . s .
v . s .
4225
v . sl . s . c .
s .
0 .0114
v . sl . s .
3228
v . s .
v . s .
s .
v . s .
8 .415
815
i .
s .
i .
i .
v . s .
s .
∞
s .
v . sl . s .
4720 cc .
i .
s .
s .
∞
∞
∞
v . s .
sl . s .
∞
∞
v . sl . s .
10410 cc .
2-39
Methoxy-methoxyethanol
Methyl acetate
acrylic acid (α-)
alcohol
-amine
-amine hydrochloride
aniline
anthracene (α-)
(β-)
anthranilate (o-)
anthraquinone (2-)
benzoate
benzylaniline
bromide
butyrate (n-)
(i-)
caprate
caproate (n-)
caprylate
cellosolve
chloride
chloroacetate
chloroformate
cinnamate
cyclohexane
ethyl carbonate
ethyl ketone
ethyl oxalate
formate
furoate
glucamine
glycolate
heptoate
hypochlorite
iodide
lactate
laurate
mercaptan
methacrylate
myristate
naphthalene (α-)
(β-)
nitrate
nitrite
nonyl ketone (n-)
oleate
orange
palmitate
phosphine
propionate
propyl ketone (n-)
salicylate (o-)
stearate
toluate (o-)
(m-)
(p-)
Methyl toluidine (o-)
(m-)
(p-)
valerate (n-)
(i-)
vinyl ketone
Methylal
Methylene-bis-(phenyl-4-isocyanate)
bromide
chloride
dianiline
iodide
Michler’s hydrol (p-,p′-)
ketone
Morphine
Mucic acid
CH3(OCH2)2CH2OH
CH3CO2CH3
CH2:C(CH3)CO2H
CH3OH
CH3NH2
CH3NH2⋅HCl
C6H5NHCH3
C6H4:(CH)2:C6H3CH3
C6H4:(CH)2:C6H3CH3
NH2C6H4CO2CH3
C6H4:(CO)2:C6H3CH3
C6H5CO2CH3
C6H5N(CH3)CH2C6H5
CH3Br
CH3(CH2)2CO2CH3
(CH3)2CHCO2CH3
CH3(CH2)8CO2CH3
CH3(CH2)4CO2CH3
CH3(CH2)6CO2CH3
CH3OCH2CH2OH
CH3Cl
ClCH2CO2CH3
ClCO2CH3
C6H5CH:CHCO2CH3
CH2 < (CH2CH2)2 > CHCH3
CH3O⋅CO⋅OC2H5
CH3 .CO⋅C2H5
CH3OCO⋅CO2C2H5
HCO2CH3
C4H3O⋅CO2CH3
CH2OH(CHOH)4CH2NHCH3
HOCH2CO2CH3
CH3(CH2)5CO2CH3
ClOCH3
CH3I
CH3CH(OH)CO2CH3
CH3(CH2)10CO2CH3
CH3SH
CH2:C(CH3)CO2CH3
CH3(CH2)12CO2CH3
C10H7CH3
C10H7CH3
CH3ONO2
CH3ONO
CH3(CH2)8COCH3
C17H33CO2CH3
(CH3)2NC6H4N2C6H4SO3Na
CH3(CH2)14CO2CH3
CH3PH2
CH3CH2CO2CH3
CH3COCH2CH2CH3
HO⋅C6H4CO2CH3
CH3(CH2)16CO2CH3
CH3⋅C6H4CO2CH3
CH3⋅C6H4CO2CH3
CH3⋅C6H4CO2CH3
CH3⋅C6H4NHCH3
CH3⋅C6H4NHCH3
CH3⋅C6H4NHCH3
CH3(CH2)3CO2CH3
(CH3)2CHCH2CO2CH3
CH3COCH:CH2
HCH(OCH3)2
(OCN⋅C6H4)2CH2
CH2Br2
CH2Cl2
(C6H5NH)2CH2
CH2I2
[(CH3)2NC6H4]2CHOH
[(CH3)2NC6H4]2CO
C17H19O3N⋅H2O
(⋅CHOHCHOHCO2H)2
106 .12
74 .08
86 .09
32 .04
31 .06
67 .52
107 .15
192 .26
192 .26
151 .16
222 .24
136 .15
197 .28
94 .94
102 .13
102 .13
186 .29
130 .18
158 .24
76 .09
50 .49
108 .52
94 .50
162 .19
98 .19
104 .10
72 .11
132 .11
60 .05
126 .11
195 .21
90 .08
144 .21
66 .49
141 .94
104 .10
214 .34
48 .11
100 .12
242 .40
142 .20
142 .20
77 .04
61 .04
170 .29
296 .49
327 .33
270 .45
48 .02
88 .11
86 .13
152 .15
298 .50
150 .17
150 .17
150 .17
121 .18
121 .18
121 .18
116 .16
116 .16
70 .09
76 .09
250 .25
173 .83
84 .93
198 .26
267 .84
270 .37
268 .35
303 .35
210 .14
lq.
col . lq .
pr .
col . lq .
col . gas
pl ./al .
lq .
lf ./al .
col . lf .
col . lq .
col . nd .
col . lq .
lq .
gas
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
gas
col . lq .
col . lq .
cr .
col . lq .
lq .
col . lq .
lq .
lq .
col . lq .
lq .
lq .
gas
col . lq .
lq .
lq .
gas
lq .
cr ./al .
oil
mn .
lq .
gas
col . oil
oil
red pd .
col . cr .
gas
col . lq .
col . lq .
col . lq .
col . cr .
col . lq .
col . lq .
cr .
lq .
lq .
lq .
lq .
col . lq .
lq .
col . lq .
lq .
col . lq .
col . lq .
cr .
col . lq .
gn .
lf ./al .
pr ./al .
pd .
1.038 25
0 .924 20/4
1 .015 20/4
0 .792 20/4
0 .699 −11
1 .23
0 .989 20/4
1 .047 99 .4
1 .181 0/4
1 .168 19/4
1 .087 25/25
1 .732 0/0
0 .898 20/4
0 .891 20/4
0 .904 0/0
0 .887 18
0 .965 20/4
0 .952 0
1 .236 20/4
1 .236 15
1 .042 36/0
0 .769 20/4
1 .002 27
0 .805 20/4
1 .156 0/0
0 .974 20/4
1 .179 21/4
<−70
−98 .7
15–16
−97–8
−92 .5
226–8
−57
86
207
24
176–7
−12 .5
9 .2
−93
<−95
−84 .7
−18
−40
−97 .7
−32 .7
33 .4
−126 .3
−14 .5
−85 .9
−99 .8
18
1 .168
0 .881 15/4
2 .279 20/4
1 .090 19
0 .896 0
0 .950 15 .6
1 .025 14/4
0 .994 40/4
1 .203 25
0 .991 15
0 .828 20/20
0 .879 18
−64 .4
5
−121
−48
18–9
−19
35–6
expl .
13 .5
30–1
20/4
0 .915
0 .812 15/15
1 .182 25/25
1 .073 15
1 .066 15
0 .973 15
0 .935 55/4
0 .895 15/4
0 .881 20/4
0 .836 20/4
0 .866 15/4
1 .222 30
2 .495 20/4
1 .336 20/4
3 .325 20/4
1 .317
−87 .5
−77 .8
−8 .3
38–9
<−50
33–4
−91
−104 .8
−52 .8
−96 .7
65
5 .7
96–7
174
254 d .
206–14
167.5
57 .1
161–3
64 .7
−6 .7 758
23015
195 .5
135 .5 15
subl .
198–9
305–6
4 .5 758
102 .3
92 .6
223–4
149 .5
192–4
124–5
−24
130740
71–2
263
101
109 .2
79 .6
173 .7
32
181 .3
151 .2
172–3
12726
42 .4
144 .8
14818
5 .8752
100 .3
295715
244 .6
241–2
65
−12
228
190–110
19615
−14759
79 .7
102
222 .2
21515
213
215
217
206–7
206–7
211761
127 .3
116 .7764
81
42–3
210–213
98 .5756
40–1
208–9 d .
180 d .
>360 d .
∞
3322
s . h .
∞
v . s .
v . s .
0 .0125
i .
i .
sl . s .
i .
0 .0230
i .
v . sl . s .
1 .7
v . sl . s .
i .
i .
i .
∞
28016 cc .
v . sl . s .
d .
i .
i .
i .
3510
i .
3020
i .
∞
∞
∞
v . s .
23 h .
s .
∞
∞
∞
i .
∞
v . sl . s .
s .
s .
∞
s .
s .
∞
∞
∞
∞
∞
∞
v . s .
∞
∞
v . s .
s .
∞
∞
v . s .
∞
∞
v . sl . s .
s .
s .
∞
s .
s .
∞
∞
∞
∞
∞
∞
v . s .
∞
∞
v . s .
s .
∞
∞
v . s .
∞
s .
∞
s .
v . s .
v . s .
v . s .
v . s .
s .
s .
s .
∞
v . s .
v . s .
s .
s .
s .
∞
s .
sl . s .
∞
∞
∞
s .
∞
s .
∞
∞
∞
s .
∞
v . s .
∞
∞
∞
∞
∞
v . s .
∞
∞
∞
∞
∞
∞
d .
∞
∞
s .
∞
s . h .
sl . s .
sl . s .
i .
∞
∞
i .
1 .815
∞
i .
s .
i .
i .
i .
i .
sl . s .
i .
i .
0 .2 c .
i .
i .
0 .520
v . sl . s .
0 .0730
i .
i .
i .
i .
i .
i .
i .
v . sl . s .
v . sl . s .
>85
33
d .
1 .170
220
i .
1 .420
i .
i .
0 .0220
0 .3314
∞
∞
s .
∞
s .
v . sl . s .
s .
i .
(Continued )
2-40
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Mustard gas
Myricyl alcohol
Myristic acid
Myristyl alcohol
Naphthalene
disulfonic acid (1-,5-)
(1-,6-)
sulfonic acid (α-)
(β-)
Naphthasultam (1-,8-)
disulfonate Na (1-,8-)
(2-,4-)
Naphthoic acid (α-)
(β-)
Naphthol (α-)
(β-)
sulfonic acid (α-)(1-,2-)
(β-)(2-,6-)
Naphthyl acetate (α-)
(β-)
amine (α-)
(β-)
amine hydrochloride (α-)
(β-)
amine sulfonic acid (1-,4-)
(1-,5-)
(1-,7-)
(1-,8-)
(2-,5-)
(2-,6-)
(2-,7-)
isocyanate (α-)
Nicotine
Nicotinic acid (3-)
(i-)(4-)
Nitro-acetanilide (p-)
-acetophenone (m-)
-aminoanisole (4-,1-,2-)
(5-,1-,2-)
(3-,1-,4-)
-aminophenol (4-,2-,1-)
-aniline (o-)
(m-)
(p-)
-anisole (o-)
(p-)
-anthraquinone (α-)
-anthraquinone sulfonic acid (1-,5-)
-benzal chloride (m-)
-benzaldehyde (m-)
Nitro-benzene
-benzidine (2-)
-benzoic acid (o-)
(m-)
(p-)
-benzyl alcohol (m-)
-benzyl bromide (p-)
-chlorotoluene (1-,2-,6-)
-cresol (1-,3-,4-)
-cymene (1-,2-,4-)
-dimethylaniline (o-)
(m-)
(p-)
-diphenyl (o-)
(p-)
-diphenylamine (o-)
-guanidine
Formula
(ClCH2⋅CH2)2S
C31H63OH(?)
CH3(CH2)12CO2H
CH3(CH2)12CH2OH
C10H8
C10H6(SO3H)2
C10H6(SO3H)2
C10H7SO3H⋅2H2O
C10H7SO3H⋅H2O
C10H7O2NS
C10H5O8NS3Na2⋅2H2O
C10H4O8NS3Na3⋅8½H2O
C10H7CO2H
C10H7CO2H
C10H7OH
C10H7OH
HO⋅C10H6SO3H
HO⋅C10H6SO3H
CH3CO2C10H7
CH3CO2C10H7
C10H7NH2
C10H7NH2
C10H7NH2⋅HCl
C10H7NH2⋅HCl
NH2⋅C10H6⋅SO3H
NH2⋅C10H6⋅SO3H⋅H2O
NH2⋅C10H6⋅SO3H⋅H2O
NH2⋅C10H6⋅SO3H⋅H2O
NH2⋅C10H6⋅SO3H
NH2⋅C10H6⋅.SO3H⋅H2O
NH2⋅C10H6⋅SO3H⋅H2O
C10H7N:CO
C10H14N2
C5H4NCO2H
C5H4NCO2H
CH3CONHC6H4NO2
CH3COC6H4NO2
NO2⋅C6H3(OCH3)NH2
NO2⋅C6H3(OCH3)NH2
NO2⋅C6H3(OCH3)NH2
NO2⋅C6H3(NH2)OH
NO2⋅C6H4NH2
NO2⋅C6H4NH2
NO2⋅C6H4NH2
CH3OC6H4NO2
CH3OC6H4NO2
C6H4:(CO)2:C6H3NO2
NO2⋅C14H6O2⋅SO3H
NO2⋅C6H4⋅CHCl2
NO2⋅C6H4CHO
C6H5NO2
NH2C6H4C6H3(NH2)NO2
NO2⋅C6H4⋅CO2H
NO2⋅C6H4⋅CO2H
NO2⋅C6H4⋅CO2H
NO2⋅C6H4⋅CH2OH
NO2⋅C6H4CH2Br
CH3⋅C6H3(NO2)Cl
CH3⋅C6H3(NO2)OH
CH3⋅C6H3(NO2)CH(CH3)2
NO2⋅C6N4N(CH3)2
NO2⋅C6H4N(CH3)2
NO2⋅C6H4N(CH3)2
C6H5⋅C6H4NO2
C6H5⋅C6H4NO2
C6H5⋅NH⋅C6H4NO2
H2NC(NH)NHNO2
Formula
weight
159 .08
452 .84
228 .37
214 .39
128 .17
288 .30
288 .30
244 .26
226 .25
205 .23
445 .35
584 .43
172 .18
172 .18
144 .17
144 .17
224 .23
224 .23
186 .21
186 .21
143 .19
143 .19
179 .65
179 .65
223 .25
241 .26
241 .26
241 .26
223 .25
241 .26
241 .26
169 .18
162 .23
123 .11
123 .11
180 .16
165 .15
168 .15
168 .15
168 .15
154 .12
138 .12
138 .12
138 .12
153 .14
153 .14
253 .21
333 .27
206 .03
151 .12
123 .11
229 .23
167 .12
167 .12
167 .12
153 .14
216 .03
171 .58
153 .14
179 .22
166 .18
166 .18
166 .18
199 .21
199 .21
214 .22
104 .07
Form and
color
Specific
gravity
Melting
point, °C
Boiling
point, °C
oil
cr.
col. lf.
cr.
pl./al.
lf.
cr.
cr.
cr.
nd.
cr.
lf.
nd.
mn.
mn.
mn.
pl./aq.
lf.
nd./al.
nd./al.
rhb.
lf./aq.
nd.
lf.
nd.
cr.
cr.
cr.
cr.
cr.
cr.
col. lq.
oil
nd ./al .
nd ./aq .
rhb .
nd .
red nd .
yel . nd .
red
or . pr .
yel . rhb .
yel . rhb .
yel . mn .
col . cr .
pr ./al .
nd .
yel . cr .
mn .
nd ./aq .
yel . lq .
red nd .
tri ./aq .
mn .
yel . mn .
cr .
nd ./al .
cr .
yel .
oil
yel . oil
red mn .
yel . nd .
rhb .
nd ./al .
or . cr .
nd ./aq .
1.275 20/4
0.777 95
0.853 70/4
0.824 38/4
1.145 20/4
13–4
88
57–8
38
80.2
d.
d. 125
90
125
177–8
217
1.077 100/4
1.224 4
1.217 4
1.123 25/25
1.061 98/4
160–1
184
96
122–3
>250
125
46–9
69–70
50
111–2
250.5100
16715
217.9
300
>300
278–80
285–6
300.8
306.1
subl.
d.
1.18
1.009 20/4
1 .207 156
1 .211 156
15
1 .442
1 .43
1 .437 14
1 .254 20/4
1 .233 20
1 .205
18/4
1 .575 4/4
1 .494 4/4
1 .550 22/4
89/4
1 .240
1 .067 20/4
1 .179 20/4
1 .313 17
1 .44
<−80
235 .2
317
215–6
80–1
118
139–40
123
142–3
71 .5
114
146–7
9 .4
54
230
65
58
5 .7
143
147 .5
140–1
240–2
27
99–100
37 .5
32
60–1
163–4
37
113–4
75–6
246–7
269–70
246730
subl .
d .
202
284 .1
306 .4
331 .7
272–3
274
2707
16423
210 .9
subl .
175–803
238
12522
15215
151–380
280–5
320
340
Solubility in 100 parts
Water
0.0725
i.
i.
<0.02
0.00325
10220
16420
v. s.
7730
s. h.
v. s.
v. s.
v. sl. s. h.
0.00725
sl. s. h.
0.07425
v. s. h.
v. s.
sl. s. h.
i.
0.17 c.
v. s. h.
3.820
v. s.
0.2100
sl. s.
0.4625
0.42100
0.08
0.38100
0.28100
d.
s.
s . h .
s . h .
s . h .
i .
i .
sl . s .
sl . s . c .
s . h .
0 .1120
0 .0819
0 .1730
0 .0630
i .
s .
i .
1 .95112
0 .1920
sl . s . h .
0 .6520
0 .24165
0 .0215
Alcohol
Ether
s.
v. sl. s.
v. s.
sl. s.
9.520
s.
s.
v. s.
s.
v. s.
v. s.
s.
v. s.
i.
i.
sl. s.
sl. s.
s.
sl. s.
s. h.
s.
v. s.
v. s.
v. s.
s.
s.
v. s.
s.
s.
v. s.
i.
s.
s.
v. s.
v. s.
i.
s.
s.
v. s.
s.
s.
i.
s.
∞
s . h .
sl . s . h .
s .
s .
s .
s.
∞
v . sl . s .
v . sl . s .
s .
s .
v . s .
v . s .
7 .120
5 .820
∞
v . s .
sl . s .
i .
v . s . h .
v . s . h .
v . s .
s .
v . s .
v . s .
7 .920
6 .120
∞
v . s .
v . sl . s .
i .
v . s .
v . s .
∞
2811
3112
0 .910
2211
2510
2 .218
219
v . s .
i .
i .
v . sl . s .
i .
v . sl . s .
i .
i .
i .
i .
v . s .
v . s .
v . s .
s .
s . h .
s .
sl . s . c .
v . s .
s .
9100
sl . s .
v . sl . s .
v . s .
v . s .
2-41
-naphthalene (α-)
(β-)
-phenol (o-)
(m-)
(p-)
-phenol sulfonic acid (1-,4-,2-)
(1-,2-,4-)
-phthalic acid (3-)
(4-)
-toluene (o-)
(m-)
(p-)
-toluene sulfonic acid (1-,4-,2-)
-toluidine (4-,1-,2-)
(3-,1-,4-)
Nitron
Nitroso-dimethylaniline (p-)
-naphthol (β-)(1-)
Nonadecane (n-)
Nonane (n-)
Octadecane (n-)
Octane (n-)
(iso-)
Octyl acetate (n-)
(sec-)
alcohol (n-)
(sec-)
Octylene (n-)
Oleic acid
Orcinol (1-,3-,5-)
Oxalic acid
Palmitic acid
Pelargonic acid
Penta-chloroethane
-decane (n-)
-erythritol
Pentandiol
Pentane (n-)
(i-)
(neo-)
Phenacetin
Phenanthrene
Phenetidine (o-)
(p-)
Phenetole
Phenol
-phthalein
-sulfonic acid (o-)
Phenyl acetaldehyde
acetic acid
-acetylene
aniline (o-)
(p-)
Phenyl-ethyl alcohol
-glycine
-hydrazine
-hydrazine sulfonic acid (p-)
isocyanate
-methylpyrazolone (3-)(N-)
-mustard oil
naphthalene (α-)
(β-)
naphthylamine (α-)
(β-)
phenol (o-)
(p-)
propyl alcohol (γ-)
quinoline (2-)(α-)
(8-)(0-)
salicylate, salol
stearate
urethane
C10H7NO2
C10H7NO2
NO2⋅C6H4⋅OH
NO2⋅C6H4⋅OH
NO2⋅C6H4⋅OH
HO⋅C6H3(NO2)SO3H⋅3H2O
HO⋅C6H3(NO2)SO3H⋅3H2O
NO2⋅C6H3(CO2H)2
NO2⋅C6H3(CO2H)2
CH3⋅C6H4NO2
CH3⋅C6H4NO2
CH3⋅C6H4NO2
CH3⋅C6H3(NO2)SO3H⋅2H2O
NO2⋅C6H3(CH3)NH2
NO2⋅C6H3(CH3)NH2
C20H16N4
ON⋅C6H4N(CH3)2
ON⋅C10H6OH
CH3(CH2)17CH3
CH3(CH2)7CH3
CH3(CH2)16CH3
CH3(CH2)6CH3
(CH3)3CCH2CH(CH3)2
CH3CO2CH2(CH2)6CH3
CH3CO2CH(CH3)C6H13
CH3(CH2)6CH2OH
CH3(CH2)5CH(OH)CH3
CH3(CH2)5CH:CH2
C8H17CH:CH(CH2)7CO2H
(HO)2C6H3⋅CH3
HO2C⋅CO2H⋅2H2O
CH3(CH2)14CO2H
CH3(CH2)7CO2H
CHCl2⋅CCl3
CH3(CH2)13CH3
C(CH2OH)4
HOCH2(CH2)3CH2OH
CH3(CH2)3CH3
(CH3)2CHCH2CH3
(CH3)2C(CH3)2
C2H5OC6H4NHCOCH3
< (C6H4CH)2 >
C2H5O⋅C6H4⋅NH2
C2H5O⋅C6H4⋅NH2
C2H5O⋅C6H5
C6H5OH
C20H14O4
HO⋅C6H4SO3H⋅¾H2O
C6H5CH2CHO
C6H5CH2CO2H
C6H5C:CH
C6H5⋅C6H4⋅NH2
C6H5⋅C6H4⋅NH2
C6H5CH2CH2OH
C6H5NHCH2CO2H
C6H5NH⋅NH2
H2NNHC6H4SO3H
C6H5N:CO
C4H5ON2⋅C6H5
C6H5N:CS
C10H7⋅C6H5
C10H7⋅C6H5
C10H7NHC6H5
C10H7NHC6H5
C6H5⋅C6H4OH
C6H5⋅C6H4OH
C6H5(CH2)3OH
C6H5⋅C9H6N
C6H5⋅C9H6N
HO⋅C6H4CO2C6H5
CH3(CH2)16CO2C6H5
C6H5NHCO2C2H5
173 .17
173 .17
139 .11
139 .11
139 .11
273 .22
273 .22
211 .13
211 .13
137 .14
137 .14
137 .14
253 .23
152 .15
152 .15
312 .37
150 .18
173 .17
268 .52
128 .26
254 .49
114 .23
114 .23
172 .26
172 .26
130 .23
130 .23
112 .21
282 .46
124 .14
126 .07
256 .42
158 .24
202 .29
212 .41
136 .15
104 .15
72 .15
72 .15
72 .15
179 .22
178 .23
137 .18
137 .18
122 .16
94 .11
318 .32
187 .69
120 .15
136 .15
102 .13
169 .22
169 .22
122 .16
151 .16
108 .14
188 .20
119 .12
174 .20
135 .19
204 .27
204 .27
219 .28
219 .28
170 .21
170 .21
136 .19
205 .25
205 .25
214 .22
360 .57
165 .19
yel./al.
col./al.
yel. mn.
col. mn.
yel. pr.
nd.
nd./aq.
yel./aq.
yel. cr.
yel. lq.
lq .
rhb .
pl ./aq .
yel . mn .
red mn .
yel . lf .
gn . tri .
brn . pr .
cr .
col . lq .
cr .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
col . nd .
pr ./bz .
col . mn .
col . pl .
col . oil
col . lq .
col . lq .
cr .
lq .
col . lq .
col . lq .
col . lq .
col . mn .
pl ./al .
oil
lq .
col . lq .
col . nd .
col . rhb .
cr .
lq .
lf .
col . lq .
cr .
lf .
col . oil
cr .
yel . oil
cr ./al .
lq .
pr ./aq .
col . lq .
waxy
lf ./al .
pr ./al .
rhb .
nd .
nd .
oil
nd .
lq .
rhb ./al .
cr .
pl ./al .
1.223 62
45
1.295
1.485 20
1.479 20
20/4
1.163
1 .160 18/4
1 .139 55/55
1 .365 15
1 .312 17
0 .777 32/4
0 .718 20/4
0 .775 28/4
0 .703 20/4
0 .692 20/4
0 .885 0/4
0 .863 14/4
0 .827 20/4
0 .822 20/4
0 .721 18/4
0 .854 78/4
1 .290 4
1 .653 19/4
0 .849 70/4
0 .906 20/4
1 .671 25/4
0 .770 20/4
0 .994 20/4
0 .630 18/4
0 .621 19
0 .613 20/4
1 .179 25
1 .061 15
0 .967 20/4
1 .071 25/4
1 .299 25/4
1 .025 20
1 .081 80/4
0 .930 20/4
1 .023 18/4
1 .097 23/4
1 .096 20/4
1 .138
15/15
1 .17
1 .18
1 .008 20/4
1 .250 20/4
1 .106
30/4
59–60
79
44–5
96–7
113–4
d. 110
51.5
222
164–5
−4.1
15–16
51 .9
130
105–7
116–7
189–90 d .
86–7
109 .5
32
−53 .7
28
−56 .5
−107 .4
−38 .5
−16
−38 .6
14
107–8
101 .5
63–4
12 .5
−22
10
262
−129 .7
−160 .0
−20
134–5
99–100
<−21
3–4
−30 .2
42–3
261–2
50 d .
76–7
−43
45–6
50–2
127
19 .6
286
128
−21
45
102 .5
62
107–8
56–7
164–5
<−18
86
42–3
52
52–3
304
16515
214.5
19470
subl.
222.3
230–1
237 .7
330
150 .5759
317
125 .7
99 .3760
210
195
194–5
179–80
126
285–6100
287–90
subl .
271 .5100
253–4
162
270 .5
27630
239 .4
36 .3
27 .95
9 .5
d .
340
228–9
254–5
172
181 .4
193–4
265 .5
142–3
299760
302
219–21750
243 .5
166769
19117
219–20
336–7
345–6
335258
399 .5
275
305–8
235–7
363
283187
172–312
26715
237–8
i.
i.
1.08100
1.3520
1.625
v. s.
v. s.
2.0525
v. s.
0.0780
0 .0580
0 .0480
47 .728
v . sl . s .
sl . s . h .
i .
i .
0 .120
i .
i .
i .
0 .00216
i .
i .
i .
0 .05425
0 .09625
i .
i .
v . s .
s .
i .
v . sl . s .
0 .0520
i .
5 .615
∞
0 .03616
i .
i .
0 .720
i .
i .
i .
i .
8 .215
0 .220
v . s .
v . sl . s .
1 .6620
i .
v . sl . s .
s . h .
1 .620
s .
sl . s . h .
0 .612
d .
120
i .
i .
i .
0 .0860
0 .460
i .
i .
sl . s .
sl . s .
sl . s .
0 .01525
i .
i . c .
s.
v. s.
v. s.
v. s.
v. s.
v. s.
v. s.
v. s. h.
v. s.
∞
∞
8 .615
v . s .
s .
s .
s . h .
s .
2 .418
sl . s .
sl . s .
sl . s .
sl . s .
sl . s .
s .
s .
∞
∞
∞
∞
v . s .
s .
920
s .
∞
v . s .
v . sl . s .
s.
v. s.
v. s.
s.
v. s.
sl. s.
sl. s.
s.
∞
∞
80 .815
v . s .
s .
v . sl . s .
s .
s .
s .
s .
s .
s .
s .
s .
∞
∞
∞
∞
v . s .
1 .3
s .
s .
∞
v . s .
i .
∞
∞
s .
40 h .
10 h .
s .
s .
∞
∞
1025
v . s .
∞
v . s .
∞
s .
s .
s .
s .
∞
sl . s .
d .
v . s . h .
s .
v . s .
sl . s .
s .
v . s . h .
s .
s .
∞
s . h .
s .
v . s .
∞
∞
s .
1 .625
v . s .
s .
s .
∞
∞
5 .9 c .
s .
s .
∞
v . s .
∞
s .
s .
∞
sl . s .
∞
v . s .
v . sl . s .
s .
v . s .
sl . s .
s .
v . s . h .
s .
s .
∞
s .
s .
s .
(Continued )
2-42
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Phenylene-diamine (o-)
(m-)
(p-)
Phloroglucinol (1-,3-,5-)
Phorone
Phosgene
Phthalic acid (o-)
(m-)(iso-)
anhydride (o-)
nitrile (o-)
Phthalide
Phthalimide (o-)
Picoline (α-)
(β-)
(γ-)
Picramic acid (1-,2-,4-,6-)
Picric acid (2-,4-,6-)
Picryl chloride (2-,4-,6-)
Pinacol
Pinacoline
Pinene (α-)(dl-)
hydrochloride
Pinol (dl-)
Piperidine
carboxylic acid (α-)(dl-)
Piperidinium pentamethylene dithiocarbamate
Propane
Propionic acid
aldehyde
anhydride
Propyl acetate (n-)
(i-)
alcohol (n-)
(i-)
amine (n-)
(i-)
aniline (n-)
benzoate (n-)
(i-)
bromide (n-)
(i-)
n-butyrate (n-)
i-butyrate (n-)
n-butyrate (i-)
i-butyrate (i-)
chloride (n-)
(i-)
Propyl formate (n-)
(i-)
furoate (n-)
lactate (n-)
(i-)
mercaptan (n-)
(i-)
propionate (n-)
(i-)
thiocyanate (i-)
n-valerate (n-)
i-valerate (n-)
i-valerate (i-)
Propylene
bromide
chlorohydrin
chloride
glycol
oxide
Protocatechuic acid (3-,4-)
Formula
C6H4(NH2)2
C6H4(NH2)2
C6H4(NH2)2
C6H3(OH)3⋅2H2O
[(CH3)2C:CH]2CO
OCCl2
C6H4(CO2H)2
C6H4(CO2H)2
C6H4 < (CO)2 > O
C6H4(CN)2
C6H4(CH2)(CO) > O
C6H4 < (CO)2 > NH
C5H4N⋅CH3
C5H4N⋅CH3
C5H4N⋅CH3
HO⋅C6H2(NH2)(NO2)2
HO⋅C6H2(NO2)3
ClC6H2(NO2)3
[(CH3)2C⋅OH]2
CH3COC(CH3)3
C10H16
C10H17Cl
C10H16O
CH2 < (CH2CH2)2 > NH
HO2C⋅CH < (CH2CH2)2 > NH
(CH2)5CS2H⋅HN(CH2)5
CH3CH2CH3
CH3CH2CO2H
CH3CH2CHO
(CH3CH2CO)2O
CH3CO2CH2CH2CH3
CH3CO2CH(CH3)2
CH3CH2CH2OH
(CH3)2CHOH
CH3CH2CH2NH2
(CH3)2CHNH2
C6H5NHCH2CH2CH3
C6H5CO2CH2CH2CH3
C6H5CO2CH(CH3)2
CH3CH2CH2Br
(CH3)2CHBr
C2H5CH2CO2CH2C2H5
(CH3)2CHCO2CH2C2H5
C2H5CH2CO2CH(CH3)2
(CH3)2CHCO2CH(CH3)2
CH3CH2CH2Cl
(CH3)2CHCl
HCO2CH2CH2CH3
HCO2CH(CH3)2
C4H3O⋅CO2C3H7
CH3CH(OH)CO2CH2C2H5
CH3CH(OH)CO2CH(CH3)2
CH3CH2CH2SH
(CH3)2CHSH
C2H5CO2CH2C2H5
C2H5CO2CH(CH3)2
(CH3)2CH⋅CNS
CH3(CH2)3CO2CH2C2H5
(CH3)2CHCH2CO2C3H7
(CH3)2CHCH2CO2C3H7
CH3CH:CH2
CH3CHBrCH2Br
CH3CHClCH2OH
CH3CHClCH2Cl
CH3CH(OH)CH2OH
CH3(CHCH2)O
(HO)2C6H3CO2H⋅H2O
Formula
weight
Form and
color
108 .14
108 .14
108 .14
162 .14
138 .21
98 .92
166 .13
166 .13
148 .12
128 .13
134 .13
147 .13
93 .13
93 .13
93 .13
199 .12
229 .10
247 .55
118 .17
100 .16
136 .23
172 .69
152 .23
85 .15
129 .16
232 .43
44 .10
74 .08
58 .08
130 .14
102 .13
102 .13
60 .10
60 .10
59 .11
59 .11
135 .21
164 .20
164 .20
122 .99
122 .99
130 .18
130 .18
130 .18
130 .18
78 .54
78 .54
88 .11
88 .11
154 .16
132 .16
132 .16
76 .16
76 .16
116 .16
116 .16
101 .17
144 .21
144 .21
144 .21
42 .08
201 .89
94 .54
112 .99
76 .09
58 .08
172 .14
lf./aq.
rhb.
mn.
rhb.
yel. pr.
gas
mn./aq.
nd./aq.
rhb.
cr.
nd./aq.
cr./et.
col. lq.
col . lq .
lq .
red nd .
yel . rhb .
yel . mn .
col . nd .
col . lq .
col . lq .
lf .
lq .
lq .
cr .
cr .
gas
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
col . lq .
lq .
lq .
col . lq .
col . lq .
lq .
lq .
col . lq .
col . lq .
gas
col . lq .
col . lq .
col . lq .
col . oil
col . lq .
nd ./aq .
Specific
gravity
1.139 15/15
0.885 20/4
1.392 19/4
1.593 20/4
1.527
4
1.164
99/4
0.950 15/4
0 .961 15/4
0 .957 15/4
1 .763 20/4
1 .797 20
0 .967 15
0 .800 16
0 .878 20/4
0 .953 20/20
0 .860 20/4
1 .13
0 .585 −45/4
0 .992 20/4
0 .807 20/4
1 .012 20/4
0 .886 20/4
0 .874 20/20
0 .804 20/4
0 .78920/4
0 .718 20/20
0 .694 15/4
0 .949 18
1 .021 25/25
1 .010 25/25
1 .353 20/4
1 .310 20/4
0 .879 15
0 .884 0/4
0 .865 18
0 .869 0/4
0 .890 20/4
0 .859 20
0 .901 20/4
0 .873 20/4
1 .075 26/4
0 .836 25/4
0 .809 25/4
0 .883 20/4
0 .893 0
0 .963 20
0 .874 15
0 .863 20/4
0 .854 17
0 .609 −47/4
1 .933 20/4
1 .103 20
1 .159 20/20
1 .040 19 .4
0 .831 20/20
1 .542 4/4
Melting
point, °C
Boiling
point, °C
103–4
62.8
140
117
28
−104
208
330
130.8
141
73(65)
238
−70
256–8
284–7
267
subl.
197.2743
8.2756
d.
subl.
284.5
169
121 .8
83
43(38)
−52 .5
−55
131–2
−9
264
175
−187 .1
−22
−81
−45
−92 .5
−73 .4
−127
−85 .8
−83
−101
−51 .6
−109 .9
−89
−95 .2
−122 .8
−117
−92 .9
−112
−130 .7
−76
−70 .7
−185
−55 .5
<−70
199 d .
290
subl.
128.8
143 .5
143 .1
expl .
d .
171–2789
106 .2
154–6
207–8
183–4
106
−42 .2
141 .1
49 .5740
168 .8780
101 .6
88 .4
97 .8
82 .5
49–50761
33–4
222
231
218 .5
70 .8
60
142 .7
134–5
128
120 .8
46 .4
36 .5
81 .3
68–71751
211
122–3150
167 .5
67–8
58–60
122–3
109–11750
152–3754
67 .5
155 .9
142756
−48749
141 .6
133–4
96 .8
188–9
35
Solubility in 100 parts
Water
73381
35.125
669107
1.1325
0.150
v. sl. s.
0.7025
0.2100
v. sl. s.
sl. s. c.
v. sl. s.
0.0425
v. s.
∞
∞
0 .1422
1 .2320
0 .01815
sl . s . c .
2 .515
v . sl . s .
i .
Alcohol
Ether
v. s.
v. s.
s.
v. s.
s.
v. s.
s.
s.
v. s.
s.
1218
s.
s.
0.6815
s.
5
∞
∞
∞
s .
620
4 .817
v . s .
s .
s .
33
s .
∞
sl. s.
s. h.
∞
∞
∞
sl . s .
113
717
v . s .
s .
∞
s .
s .
∞
s .
628
6 .518 cc .
∞
2020
d .
1 .616
320
∞
∞
∞
∞
i .
i .
i .
0 .2520
0 .3220
0 .1717
v . sl . s .
v . sl . s .
v . sl . s .
0 .2720
0 .3120
12 .222
2 .122
v . sl . s .
s .
s .
v . sl . s .
v . sl . s .
0 .5625
0 .625
i .
i .
i .
s .
∞
∞
d .
∞
∞
∞
∞
∞
∞
v . s .
s .
s .
∞
∞
∞
v . s .
∞
∞
∞
∞
∞
∞
s .
s .
s .
s .
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
s .
s .
s .
∞
∞
∞
∞
∞
∞
44 .6 cc .
0 .2520
s .
0 .2720
∞
3320
1 .8214
1200 cc .
s .
s .
v . s .
∞
∞
v . s .
v . s .
s .
v . s .
8
∞
s .
∞
∞
∞
∞
∞
∞
v . s .
s .
s .
∞
∞
∞
2-43
Pulegol (iso-)(d-)
Pulegone
Pyrazole
Pyrazoline
Pyrazolone
Pyrene
Pyridazine
Pyridine
Pyrocatechol (o-)
Pyrogallol (1-,2-,3-)
Pyrone
Pyrrole
Pyrrolidine
Pyrroline
Pyruvic acid
Quercitrin
Quinaldine (py-2)
Quinoline
(iso-)
-diol (1-,3-)
Quinone (p-)
R-acid Ca salt (2-)(3-,6-)
K salt
Na salt
Raffinose
Resorcinol (m-)
Retene
Rhamnose (β-)
Ricinoleic acid
Rosaniline
Rosolic acid
Saccharin
Safrole (1-,3-,4-)
(iso-)(1-,3-,4-)
Salicylic acid (o-)
aldehyde (o-)
Saligenin
Schaeffer’s salt, Ca
K
Na
Semicarbazide
hydrochloride
Skatole (3-)
Sodium methylate
Sorbitol
Sorbose (d- or l-)
Starch
Stearic acid
amide
Styrene
Suberic acid
Succinic acid
Sucrose
Sulfanilic acid (p-)
Sylvestrene (d-)
Tartaric acid (meso-)
(racemic)
(d- or l-)
Tartronic acid
Terephthalic acid (p-)
Terpin hydrate (cis-)
Terpineol (α-)(d- or l-)
(dl-)
Terpinyl acetate (α-)(dl-)
Tetrabromo-ethane (sym)
(uns)
Tetrachloro-ethane (sym)
(uns)
-ethylene
Tetracosane (n-)
Tetradecane (n-)
Tetraethyl-thiuram disulfide
C10H17OH
C10H16O
—NH⋅N:CH⋅CH:CH—
—NH⋅N:CH⋅CH2CH2—
—NH⋅CO⋅CH2CH:N—
C16H10
N2 < (CHCH)2 >
CH < (CHCH)2 > N
C6H4(OH)2
C6H3(OH)3
CO < (CHCH)2 > O
< (CH:CH)2 > NH
< (CH2⋅CH2)2 > NH
< (CH⋅CH2)2 > NH
CH3COCO2H
C21H20O11⋅2H2O
CH3⋅C9H6N
C9H7N
C9H7N
—C6H4CH:C(OH)N:C(OH)—
CO < (CHCH)2 > CO
HOC10H5(SO3)2Ca
HOC10H5(SO3K)2
HOC10H5(SO3Na)2
C18H32O16⋅5H2O
C6H4(OH)2
C18H18
CH3(CHOH)4CHO⋅H2O
C17H32(OH)CO2H
C20H21ON3
C20H16O3
C6H4(CO)(SO2) > NH
CH2:CHCH2⋅C6H3:O2CH2
CH3⋅CH:CH⋅C6H3:O2CH2
HO⋅C6H4⋅CO2H
HO⋅C6H4⋅CHO
HO⋅C6H4⋅CH2OH
(HOC10H6SO3)2Ca⋅5H2O
HOC10H6SO3K
HOC10H6SO3Na
NH2⋅CO⋅NH⋅NH2
NH2⋅CO⋅NH⋅NH3Cl
CH3⋅C8H6N
CH3ONa
[CH2OH(CHOH)2]2
C6H12O6
(C6H10O5)x
CH3(CH2)16CO2H
CH3(CH2)16CONH2
C6H5CH:CH2
HO2C(CH2)6CO2H
HO2C(CH2)2CO2H
C12H22O11
H2N⋅C6H4⋅SO3H
C10H16
(CHOHCO2H)2
(CHOHCO2H)2⋅H2O
(CHOHCO2H)2
CH(OH)(CO2H)2⋅½H2O
C6H4(CO2H)2
C10H20O2⋅H2O
C10H18O
C10H18O
CH3CO2⋅C10H17
Br2CH⋅CHBr2
Br3C⋅CH2Br
Cl2CH⋅CHCl2
Cl3C⋅CH2Cl
Cl2C:CCl2
CH3(CH2)22CH3
CH3(CH2)12CH3
[(C2H5)2NCS]2S2
154 .25
152 .23
68 .08
70 .09
84 .08
202 .25
80 .09
79 .10
110 .11
126 .11
96 .08
67 .09
71 .12
69 .11
88 .06
484 .41
143 .19
129 .16
129 .16
161 .16
108 .09
342 .36
380 .48
348 .26
594 .51
110 .11
234 .34
182 .17
298 .46
319 .40
304 .34
183 .18
162 .19
162 .19
138 .12
122 .12
124 .14
576 .60
262 .32
246 .21
75 .07
111 .53
131 .17
54 .02
182 .17
180 .16
162 .14
284 .48
283 .49
104 .15
174 .19
118 .09
342 .30
173 .19
136 .23
150 .09
168 .10
150 .09
129 .07
166 .13
190 .28
154 .25
154 .25
196 .29
345 .65
345 .65
167 .85
167 .85
165 .83
338 .65
198 .39
296 .54
col. lq.
col. lq.
nd ./et .
lq .
nd .
yel . pr .
lq .
col . lq .
nd ./aq .
nd .
cr .
lq .
lq .
lq .
col . lq .
yel . nd .
lq .
lq .
pl .
cr .
yel . mn .
cr .
cr .
cr .
cr ./aq .
col . rhb .
lf ./al .
col . mn .
lq .
col . nd .
red lf .
mn .
col . mn .
col . lq .
mn .
col . oil
rhb ./aq .
cr .
cr .
cr .
pr ./al .
pr .
lf .
pd .
cr .
rhb .
amor .
mn .
col . cr .
col . lq .
nd ./aq .
col . mn .
col . mn .
col . cr .
lq .
cr .
tri .
mn .
pr ./aq .
cr .
rhb .
col . cr .
col . cr .
lq .
col . lq .
col . lq .
col . lq .
lq .
col . lq .
cr .
col . lq .
cr .
0.911 20/4
0.932 20/20
70
1 .277 0/4
1 .107 20/4
0 .982 20/4
1 .344 4
1 .453 4
1 .190 40 .3
0 .948 20/4
0 .852 22 .5
0 .910 20/4
1 .267 20/4
1 .059 20/4
1 .095 20
1 .099 21/4
1 .318 20/4
1 .465 0
1 .272 15
1 .1316
1 .47120/4
0 .954 16
1 .100 20/4
1 .122 20/4
1 .443 20/4
1 .153 25/4
1 .161 25
1 .654 15
1 .5021
0 .847 69 .3
0 .903 20/4
1 .266 25/4
1 .572 25/4
1 .588 15
0 .863 20/4
1 .737
1 .697 20/4
1 .760 20/4
1 .510
0 .935 15
0 .935 20/20
0 .966 20/4
2 .964 20/4
2 .875 20/4
1 .600 20/4
1 .588 20/4
1 .624 15/4
0 .779 51/4
0 .765 20/4
1 .17
165
149–50
−8
−42
104–5
133–4
32 .5
13 .6
182–5
−1
−15
24 .6
237
115 .7
119
110 .7
98–9
126
4–5
186 d .
308–10 d .
225–8
11 .2
6–7
159
−7
86–7
96
173 d .
95
d . 300
110–2
165
d .
70–1
108–9
−31
140–4
189–90
170–86 d .
d . > 280
86–9 10
224754
186–8
144
subl . d .
>360
208
115–6
240–5
309
215–7
131
87–8
90–1
165
244–5750
237 .1747
240 .5763
subl .
d . 130
276 .5
390–4
226–810
subl .
233–4
252–3
21120
196 .5
subl .
265–6755
291110
25112
145–6
279100
235 d .
176–7
159–60
205–6
168–70
d . 155–8
subl .
117
38–40
35
< −50
−1 .0
0
−36
−19
51 .1
5 .5
70
d .
subl .
d .
219–21
218–9752
220 d .
15154
10413
146 .3
129–30
120 .8
324
252 .5
v. sl. s.
i.
s .
∞
s .
i .
∞
∞
45 .120
40 13
v . sl . s .
i .
∞
v . s .
∞
0 .04 20
v . sl . s .
6
sl . s .
v . sl . s .
sl . s . h .
30 .6 25
29 .5 25
25 .2 25
14 .3 20
14712
i .
60 .8 21
i .
v . sl . s .
0 .1225
0 .4 25
i .
i .
0 .223
1 .7 86
6 .615
4 .7620
3 .4625
6 .2925
v . s .
v . s .
0 .05 c .
d .
v . s .
5517
i .
0 .0325
i .
v . sl . s .
0 .1416
6 .820
1790
0 .810
12015
20 .620
13920
v . s .
0 .001 c .
0 .415
i .
i .
i .
i .
20
0 .29
i .
0 .0220
i .
i .
∞
s .
∞
v . s .
3 h .
s .
∞
v . s .
s .
s .
s .
∞
∞
∞
s .
∞
s .
0 .120
v . s .
69 h .
∞
s .
sl . s .
v . sl . s .
v . s .
s .
s .
v . s .
s .
v . s .
s .
∞
∞
∞
sl . s .
s .
∞
s .
s .
∞
sl . s .
v . s . h .
3 .1 c .
s .
∞
4915
∞
v . s .
v . s .
v . s . h .
i .
∞
i .
sl . s .
1 .05 c .
∞
∞
5115
∞
v . s .
v . s .
sl . s .
s .
i .
i .
s .
v . s . h .
sl . s .
i .
220
s . h .
∞
s .
9 .915
0 .9
v . sl . s .
i .
6g
s . h:
∞
0 .815
1 .215
i .
v . sl . s .
20
2515
v . s .
sl . s . h .
1015
v . s .
v . s .
20
∞
s .
∞
∞
∞
v . s .
0 .09
0 .415
i .
i .
115
v . s .
v . s .
∞
∞
∞
∞
s .
v . s .
(Continued )
2-44
TABLE 2-2
Physical Properties of Organic Compounds (Continued )
Name
Tetrafluoro-ethylene
Tetrahydro-furan
-furfuryl alcohol
-pyran
Tetralin
Tetramethyl-thiuram disulfide
Tetryl (2-,4-,6-)
Theobromine
Thio-acetic acid
-aniline (4-,4′-)
-carbanilide
-naphthol (β-)
-phenol
-salicylic acid (o-)
-urea
Thiophene
Thymol (5-,2-,1-)
Tolidine (0-)(3-,3′-,4-,4′-)
Toluene
sulfonic acid (o-)
(p-)
sulfonic amide (p-)
sulfonic chloride (p-)
Toluic acid (o-)
(m-)
(p-)
Toluidine (o-)
(m-)
(p-)
hydrochloride (o-)
sulfonic acid (1-,2-,3-)
Toluylenediamine (1-,2-,4-)
Tolylene diisocyanate (1-,2-,4-)
Trehalose
Triamylamine (n-)
(i-)
Tributyl-amine (n-)
phosphite
Trichloro-acetic acid
-benzene (s-)(1-,3-,5-)
-ethane (1-,1-,1-)
-ethylene
-phenol
Tricosane (n-)
Tricresyl phosphate (o-)
Tridecane (n-)
Triethanol amine
Triethyl-amine
-benzene (1-,3-,5-)
(1-,2-,4-)
borate
citrate
Triethylene glycol
Trifluoro-chloromethane
-chloroethylene
-trichloroethane
Trimethoxybutane (1-,3-,3-)
Trimethylamine
Trimethylene bromide
chloride
glycol
Formula
Formula
weight
F2C:CF2
—CH2(CH2)2CH2⋅O—
C4H7O⋅CH2OH
—CH2(CH2)3CH2⋅O—
—C6H4CH2(CH2)2CH2—
[(CH3)2NCS]2S2
(NO2)3C6H2⋅N(CH3)NO2
C7H8O2N4
CH3⋅CO⋅SH
(NH2⋅C6H4)2S
(C6H5⋅NH)2CS
C10H7⋅SH
C6H5⋅SH
HS⋅C6H4⋅CO2H
NH2⋅CS⋅NH2
< (CH:CH)2 > S
(CH3)(C3H7)C6H3OH
[CH3(NH2)C6H3]2
C6H5⋅CH3
CH3⋅C6H4SO3H⋅2H2O
CH3⋅C6H4SO3H⋅H2O
CH3⋅C6H4SO2NH2
CH3⋅C6H4⋅SO2Cl
CH3⋅C6H4⋅CO2H
CH3⋅C6H4⋅CO2H
CH3⋅C6H4⋅CO2H
CH3⋅C6H4⋅NH2
CH3⋅C6H4⋅NH2
CH3⋅C6H4⋅NH2
CH3⋅C6H4⋅NH3Cl
CH3(NH2)C6H3SO3H
CH3⋅C6H3(NH2)2
CH3⋅C6H3(NCO)2
C12H22O11⋅2H2O
[CH3(CH2)3CH2]3N
[(CH3)2CH(CH2)2]3N
[CH3(CH2)2CH2]3N
[CH3(CH2)3O]3P
Cl3C⋅CO2H
C6H3Cl3
Cl3C⋅CH3
Cl2C:CHCl
Cl3C6H2OH
CH3(CH2)21CH3
OP(OC6H4CH3)3
CH3(CH2)11CH3
(HOCH2CH2)3N
(CH3CH2)3N
(C2H5)3C6H3
(C2H5)3C6H3
B(OCH2CH3)3
HOC3H4(CO2C2H5)3
(⋅CH2OCH2CH2OH)2
CF3Cl
F2C:CFCl
Cl2CF⋅CClF2
CH2(OCH3)CH2C(OCH3)2CH3
(CH3)3N
BrCH2CH2CH2Br
ClCH2CH2CH2Cl
HOCH2CH2CH2OH
100 .02
72 .11
102 .13
86 .13
132 .20
240 .43
287 .14
180 .16
76 .12
216 .30
228 .31
160 .24
110 .18
154 .19
76 .12
84 .14
150 .22
212 .29
92 .14
208 .23
190 .22
171 .22
190 .65
136 .15
136 .15
136 .15
107 .15
107 .15
107 .15
143 .61
187 .22
122 .17
174 .16
378 .33
227 .43
227 .43
185 .35
250 .31
163 .39
181 .45
133 .40
131 .39
197 .45
324 .63
368 .36
184 .36
149 .19
101 .19
162 .27
162 .27
145 .99
276 .28
150 .17
104 .46
116 .47
187 .38
148 .20
59 .11
201 .89
112 .99
76 .09
Form and
color
Specific
gravity
Melting
point, °C
Boiling
point, °C
gas
col. lq.
col. lq.
lq .
col . lq .
cr .
yel . mn .
rhb .
yel . lq .
nd ./aq .
rhb ./al .
cr ./al .
col . lq .
yel . nd .
rhb ./al .
col . lq .
cr .
lf .
col . lq .
cr .
mn .
mn .
tri .
cr ./aq .
pr ./aq .
cr ./aq .
col . lq .
col . lq .
cr .
mn . pr .
cr .
rhb .
lq .
rhb ./al .
lq .
col . lq .
col . lq .
lq .
cr .
nd .
lq .
col . lq .
nd .
lf .
lq .
col . lq .
col . lq .
col . oil
lq .
lq .
lq .
oil
col . lq .
gas
gas
lq .
lq .
gas
lq .
lq .
oil
1.58−78
0.88821/4
1.05020/4
0 .88120/4
0 .97318/4
1 .29
1 .5719
−142.5
−65
−76.3
65–6
177–8743
88
206764
1 .07410
24
1 .3
−31
155–6
130 .5
330
< −17
108
154
81
23/4
1 .074
1 .40520/4
1 .07015/4
0 .97225/25
20/4
0 .866
1 .062115/4
1 .054112/4
20/4
0 .999
0 .98920/4
1 .04620/4
164
180–2
−30
51 .5
128–9
−95
d .
104–5
137
69
104–5
110–1
179–80
−16 .3
−31 .5
44–5
218–20
99
1 .2328
expl .
93
d .
286–8
168–9
subl .
d .
84
232752
110 .8
128 .80
146–70
134 .510
259751
263
274–5
199 .7
203 .3
200 .3
242
283–5
134 .520
97
20/4
0 .786
0 .77820/20
0 .92520/4
1 .61746/15
1 .32526/4
1 .46620/20
1 .49075/4
0 .77948/4
0 .75720/4
1 .12620/20
0 .72920/20
0 .86120/4
0 .88217/4
0 .86420/20
1 .13720/4
1 .12520/20
1 .726−130
1 .57620/4
0 .932
0 .662 −5
1 .987 15/4
1 .201 15
1 .060 20/4
58
63 .5
−73
68–9
47 .7
−6 .2
20–1
−114 .8
−5
−182
−157 .5
−35
−124
−34 .4
240–5
235
216 .5761
122–312
195 .5754
208 .5764
74 .1
87 .2
246
23415
234
277–9150
89 .4
215
217–8755
120
294
290
−80
−27 .9
47 .6
63–525
3 .5
167 .5
123–5
214
Solubility in 100 parts
Water
0.0130
s.
∞
s .
i .
i .
i .
0 .0615
s .
sl . s . h .
i .
v . sl . s .
v . sl . s .
sl . s . h .
9 .213
i .
0 .0919
v . sl . s .
0 .0516
v . s .
v . s .
0 .29
i .
2 .17100
1 .6100
1 .3100
1 .525
sl . s .
0 .7421
s .
0 .9711
s . h .
d .
s . h .
i .
i .
i .
i .
12025
i .
i .
0 .125
0 .0925
i .
i .
i .
∞
∞ > 190
i .
i .
d .
i .
∞
d .
i .
d .
4119
0 .1730
0 .2725
∞
Alcohol
Ether
s.
∞
s.
∞
s .
s .
s . h .
0 .06 c .
∞
s .
v . s .
v . s .
v . s .
s .
s .
s .
v . s .
s .
s .
s .
s .
7 .45
s .
v . s .
v . s .
v . s .
∞
∞
v . s .
sl . s .
s .
0 .03 h .
∞
s .
v . s .
v . s .
∞
s .
d .
sl . s . h .
sl . s .
v . s .
s .
∞
s .
v . s .
v . s .
∞
∞
v . s .
s .
i .
s .
∞
s .
sl . s .
∞
∞
v . s .
s .
v . s .
∞
∞
s .
s .
v . s .
sl . s .
∞
s .
s .
∞
∞
∞
v . sl . s .
∞
∞
s .
s .
s .
∞
s .
s .
s .
∞
∞
v . s .
Trinitro-benzene (1-,3-,5-)
-benzoic acid (2-,4-,6-)
-tert-butylxylene
-naphthalene (α-)(1-,3-,5-)
(β-)(1-,3-,8-)
(γ-)(1-,4-,5-)
-phenol (2-,3-,6-)
-toluene (β-)(2-,3-,4-)
(γ-)(2-,4-,5-)
(α-)(2-,4-,6-)
Trional
Triphenyl-arsine
carbinol
guanidine (α-)
methane
methyl
phosphate
Tripropylamine (n-)
Undecane (n-)
Urea
nitrate
Uric acid
Valeric acid (n-)
(i-)
aldehyde (n-)
(i-)
amide (n-)
(i-)
Vanillic acid (3-,4-,1-)
alcohol (3-,4-,1-)
hyl-thiuram disulfide
Vanillin (3-,4-,1-)
Veratrole (o-)
Vinyl acetate
(poly-)
acetic acid
acetylene
alcohol
(poly-)
chloride
propionate
Xylene (o-)
(m-)
(p-)
sulfonic acid (1-,4-,2-)
Xylidine (1:2)(3-)
(1:2)(4-)
(1:3)(2-)
(1:3)(4-)
(1:3)(5-)
(1:4)(2-)
Xylose (l-)(+)
Xylylene dichloride (p-)
Zinc diethyl
dimethyl
dimethyl-dithiocarbamate
note: °F = 9⁄5°C + 32 .
C6H3(NO2)3
(NO2)3C6H2CO2H
(NO2)3C6(CH3)2C4H9
C10H5(NO2)3
C10H5(NO2)3
C10H5(NO2)3
(NO2)3C6H2OH
CH3C6H2(NO2)3
CH3C6H2(NO2)3
CH3C6H3(NO2)3
(C2H5SO2C2H4)2
(C6H5)3As
(C6H5)3COH
C6H5N:C(NHC6H5)2
(C6H5)3CH
(C6H5)3C . . .
OP(OC6H5)3
(CH3CH2CH2)3N
CH3(CH2)9CH3
H2N⋅CO⋅NH2
CO(NH2)2⋅HNO3
C5H4O3N4
C2H5CH2CH2CO2H
(CH3)2CHCH2CO2H
C2H5CH2CH2CHO
(CH3)2CHCH2CHO
C2H5CH2CH2CONH2
(CH3)2CHCH2CONH2
CH3O(OH)C6H3CO2H
CH3O(OH)C6H3CH2OH
[(C2H5)2NCS]2S2
CH3O(OH)C6H3CHO
C6H4(OCH3)2
CH3CO2CH:CH2
(CH3CO2CH:CH2)x
CH2:CH⋅CH2CO2H
CH2:CH⋅C:CH
CH2:CHOH
(CH2:CHOH)x
CH2:CHCl
C2H5CO2CH:CH2
C6H4(CH3)2
C6H4(CH3)2
C6H4(CH3)2
(CH3)2C6H3SO3H⋅2H2O
(CH3)2C6H3NH2
(CH3)2C6H3NH2
(CH3)2C6H3NH2
(CH3)2C6H3NH2
(CH3)2C6H3NH2
(CH3)2C6H3NH2
CH2OH(CHOH)3CHO
C6H4(CH2Cl)2
Zn(CH2CH3)2
Zn(CH3)2
Zn[S2CN(CH3)2]2
213 .10
257 .11
297 .26
263 .16
263 .16
263 .16
229 .10
227 .13
227 .13
227 .13
242 .36
306 .23
260 .33
287 .36
244 .33
243 .32
326 .28
143 .27
156 .31
60 .06
123 .07
168 .11
102 .13
102 .13
86 .13
86 .13
101 .15
101 .15
168 .15
154 .16
296 .54
152 .15
138 .16
86 .09
(86 .09)
86 .09
52 .07
44 .05
(44 .05)
62 .50
100 .12
106 .17
106 .17
106 .17
222 .26
121 .18
121 .18
121 .18
121 .18
121 .18
121 .18
150 .13
175 .06
123 .53
95 .48
305 .84
col. rhb.
rhb./aq.
nd./al.
rhb.
cr./al.
yel. cr.
nd.
cr.
yel. pl.
cr./al.
pl./al.
pl.
cr.
rhb./al.
cr.
col. cr.
pr./al.
col. lq.
col . lq .
col . pr .
col . mn .
cr .
col . lq .
col . lq .
lq .
col . lq .
mn . pl .
mn .
nd ./aq .
mn ./aq .
cr .
mn .
cr .
col . lq .
col . lq .
gas
gas
lq .
col . lq .
col . lq .
col . lq .
col . lf .
lq .
pr .
lq .
lq .
oil
oil
nd .
mn .
col . lq .
col . lq .
1.688 20/4
1.620 20/4
1.620 20/4
1.654
1.199 85/4
1.306
1.188 20/4
1.13
1.014 99/4
1.206 58/4
0.757 20/4
0 .741 20/4
1 .335 20/4
1 .893 20
0 .939 20/4
0 .931 20/20
0 .819 11
0 .803 17
1 .023
0 .965 20/4
1 .17
1 .056
1 .091 15/15
0 .932 20/4
1 .1920
1 .013 15/15
0 .705 1 .5
1 .320
0 .908 25/25
20/4
0 .881
0 .867 17/4
0 .861 20/4
0 .991 15
1 .076 17 .5
0 .980 15
0 .978 20/4
0 .972 20/4
0 .979 21/4
1 .535 0
1 .417 0
1 .182 18
1 .386 11
2 .0040/4
121
210–20 d.
110
122–3
218–9
148–9
117–8
112
104
80.8
76
59–60
162.5
144–5
93.4
145–7
49–50
−93.5
−25 .6
132 .7
152 d .
d .
−34 .5
−37 .6
−92
−51
106
135–7
207
115
70
81–2
22 .5
< −60
100–25
−39
d . >200
−160
−25
−47 .4
13 .2
86
< −15
49–50
15 .5
153–4
100 .5
−28
−40
248–50
d.
expl.
expl.
expl.
d.
>360
>360
d.
359754
d.
24511
156.5
194 .5
d .
187
176
103 .4
92 .5
232
subl .
d .
285
207 .1
72–3
163
5 .5
−12
93–5
144
139 .3
138 .5
1490 .1
223
224–6
216–7
213–4
221–2
215789
240–5 d .
118
46
0.0315
2.0524
i.
i.
0.02100
i.
s. h.
i.
i.
0.0120
0.315
i.
i.
i.
i.
i.
i.
v. sl. s.
i .
10017
v . s . h .
0 .06 h .
3 .316
4 .220
v . sl . s .
sl . s .
v . s .
s .
0 .1214
v . s . h .
i .
114
v . sl . s .
220
i .
s .
0 .670 .6
s .
sl . s .
v . sl . s .
i .
i .
i .
s .
v . sl . s .
v . sl . s .
v . sl . s .
v . sl . s .
v . sl . s .
v . sl . s .
11720
i .
d .
d .
i .
1.918
1.518
sl. s.
s.
0.0523
0.1119
v. s.
sl. s. c.
s. h.
1.522
50
s.
v. s.
40
v. s. h.
sl. s. h.
15525
∞
∞
2020
s .
i .
∞
∞
s .
s .
v . s .
s .
v . s .
v . s .
s.
i .
∞
∞
s .
s .
v . s .
s .
v . s .
v . s .
v . s .
s .
∞
v . s .
s .
∞
∞
∞
s .
v . s .
s .
s .
s .
∞
∞
v . s .
s .
s .
v . sl . s .
s .
d .
d .
i .
v . sl . s .
0.1315
0.419
v. s.
s.
v. s.
533
6.615
v. s.
v. s.
v. s.
v. s.
∞
∞
sl . s .
2-45
2-46
PHYSICAL AnD CHEMICAL DATA
VAPOR PRESSURES
VAPOR PRESSURES OF PURE SUBSTAnCES
TABLE 2-3 Vapor Pressure of Water Ice from 0 to -40çC
Vapor pressure
t, °C
0
−0 .5
−1 .0
−1 .5
−2 .0
−2 .5
−3 .0
−3 .5
−4 .0
−4 .5
−5 .0
−5 .5
−6 .0
−6 .5
−7 .0
−7 .5
−8 .0
−8 .5
−9 .0
−9 .5
−10 .0
−10 .5
−11 .0
−11 .5
−12 .0
−12 .5
−13 .0
Vapor pressure
Vapor pressure
mmHg
kPa
t, °C
mmHg
kPa
t, °C
mmHg
kPa
4 .584
4 .399
4 .220
4 .049
3 .883
3 .724
3 .571
3 .423
3 .281
3 .145
3 .013
2 .887
2 .766
2 .649
2 .537
2 .429
2 .325
2 .225
2 .130
2 .038
1 .949
1 .865
1 .783
1 .705
1 .630
1 .558
1 .489
0 .6112
0 .5865
0 .5627
0 .5398
0 .5177
0 .4965
0 .4761
0 .4564
0 .4375
0 .4193
0 .4018
0 .3849
0 .3687
0 .3532
0 .3382
0 .3238
0 .3100
0 .2967
0 .2839
0 .2717
0 .2599
0 .2486
0 .2377
0 .2273
0 .2173
0 .2077
0 .1985
−13 .5
−14 .0
−14 .5
−15 .0
−15 .5
−16 .0
−16 .5
−17 .0
−17 .5
−18 .0
−18 .5
−19 .0
−19 .5
−20 .0
−20 .5
−21 .0
−21 .5
−22 .0
−22 .5
−23 .0
−23 .5
−24 .0
−24 .5
−25 .0
−25 .5
−26 .0
−26 .5
1 .423
1 .359
1 .298
1 .240
1 .184
1 .130
1 .079
1 .029
0 .9822
0 .9370
0 .8937
0 .8522
0 .8125
0 .7745
0 .7381
0 .7034
0 .6701
0 .6383
0 .6078
0 .5787
0 .5509
0 .5243
0 .4989
0 .4747
0 .4515
0 .4294
0 .4083
0 .1897
0 .1812
0 .1731
0 .1653
0 .1578
0 .1507
0 .1438
0 .1372
0 .1310
0 .1249
0 .1191
0 .1136
0 .1083
0 .1033
0 .09841
0 .09377
0 .08934
0 .08510
0 .08104
0 .07716
0 .07345
0 .06991
0 .06652
0 .06329
0 .06020
0 .05725
0 .05443
−27 .0
−27 .5
−28 .0
−28 .5
−29 .0
−29 .5
−30 .0
−30 .5
−31 .0
−31 .5
−32 .0
−32 .5
−33 .0
−33 .5
−34 .0
−34 .5
−35 .0
−35 .5
−36 .0
−36 .5
−37 .0
−37 .5
−38 .0
−38 .5
−39 .0
−39 .5
−40 .0
0 .3881
0 .3688
0 .3505
0 .3330
0 .3162
0 .3003
0 .2851
0 .2706
0 .2568
0 .2437
0 .2311
0 .2192
0 .2078
0 .1970
0 .1867
0 .1769
0 .1676
0 .1587
0 .1503
0 .1423
0 .1347
0 .1274
0 .1206
0 .1140
0 .1078
0 .1019
0 .0963
0 .05174
0 .04918
0 .04673
0 .04439
0 .04216
0 .04004
0 .03801
0 .03608
0 .03424
0 .03249
0 .03082
0 .02923
0 .02771
0 .02627
0 .02490
0 .02359
0 .02235
0 .02116
0 .02004
0 .01897
0 .01796
0 .01699
0 .01607
0 .01520
0 .01437
0 .01359
0 .01284
source: Formulation of Wagner, Saul, and Pruss, J. Phys. Chem. Ref. Data, 23, 515
(1994), implemented in Harvey, Peskin, and Klein, NIST/ASME Steam Properties, NIST
Standard Reference Database 10, Version 2 .2, National Institute of Standards and Technology, Gaithersburg, Md ., 2000 . This source provides data down to 190 K (−83 .15°C) . A
formula extending to 110 K may be found in Murphy and Koop, Q. J. R. Meteorol. Soc., 131,
1539 (2005) .
TABLE 2-4 Vapor Pressure of Supercooled Liquid Water
from 0 to -40çC*
Vapor pressure
Vapor pressure
Vapor pressure
t, °C
mmHg
kPa
t, °C
mmHg
kPa
t, °C
mmHg
kPa
0
−0.5
−1.0
−1.5
−2.0
−2.5
−3.0
−3.5
−4.0
−4.5
−5.0
−5.5
−6.0
−6.5
−7.0
−7.5
−8.0
−8.5
−9.0
−9.5
−10.0
−10.5
−11.0
−11.5
−12.0
−12.5
−13.0
4.584
4.421
4.262
4.108
3.959
3.816
3.676
3.542
3.411
3.285
3.163
3.046
2.932
2.822
2.715
2.612
2.513
2.417
2.324
2.235
2.149
2.065
1.985
1.907
1.832
1.760
1.690
0.6112
0.5894
0.5682
0.5477
0.5279
0.5087
0.4901
0.4722
0.4548
0.4380
0.4218
0.4061
0.3909
0.3762
0.3620
0.3483
0.3351
0.3223
0.3099
0.2980
0.2865
0.2753
0.2646
0.2542
0.2442
0.2346
0.2253
−13.5
−14.0
−14.5
−15.0
−15.5
−16.0
−16.5
−17.0
−17.5
−18.0
−18.5
−19.0
−19.5
−20.0
−20.5
−21.0
−21.5
−22.0
−22.5
−23.0
−23.5
−24.0
−24.5
−25.0
−25.5
−26.0
−26.5
1.623
1.558
1.495
1.435
1.377
1.321
1.267
1.215
1.165
1.117
1.070
1.026
0.9827
0.9414
0.9016
0.8633
0.8265
0.7911
0.7571
0.7244
0.6930
0.6628
0.6337
0.6059
0.5791
0.5534
0.5288
0.2163
0.2077
0.1993
0.1913
0.1836
0.1761
0.1689
0.1620
0.1553
0.1489
0.1427
0.1367
0.1310
0.1255
0.1202
0.1151
0.1102
0.1055
0.1009
0.0965
0.0923
0.08836
0.08449
0.08078
0.07721
0.07379
0.07050
−27.0
−27.5
−28.0
−28.5
−29.0
−29.5
−30.0
−30.5
−31.0
−31.5
−32.0
−32.5
−33.0
−33.5
−34.0
−34.5
−35.0
−35.5
−36.0
−36.5
−37.0
−37.5
−38.0
−38.5
−39.0
−39.5
−40.0
0.5051
0.4824
0.4606
0.4397
0.4197
0.4005
0.3820
0.3644
0.3475
0.3313
0.3158
0.3009
0.2867
0.2731
0.2600
0.2476
0.2356
0.2242
0.2133
0.2029
0.1929
0.1834
0.1743
0.1656
0.1573
0.1494
0.1419
0.06734
0.06431
0.06141
0.05862
0.05595
0.05339
0.05094
0.04858
0.04633
0.04417
0.04210
0.04012
0.03822
0.03640
0.03467
0.03300
0.03141
0.02989
0.02844
0.02705
0.02572
0.02445
0.02324
0.02208
0.02098
0.01992
0.01891
∗source: Murphy and Koop, Q. J. R. Meteorol. Soc., 131, 1552 (2005) . The formula in
the reference extends down to 123 K (−150 .15°C), although in practice pure liquid
water cannot be supercooled below about 235 K .
Unit Conversions For this subsection, the following unit conversions
are applicable: °F = 9⁄5°C + 32 .
To convert millimeters of mercury to pounds-force per square inch, multiply by 0 .01934 . To convert cubic feet to cubic meters, multiply by 0 .02832 .
To convert bars to pounds-force per square inch, multiply by 14 .504 . To convert bars to kilopascals, multiply by 1 × 102 .
Additional References Additional vapor-pressure data may be
found in major thermodynamic property databases, such as those produced by the AIChE’s DIPPR program (aiche .org/dippr), NIST’s Thermodynamics Research Center (trc .nist .gov), the Dortmund Databank
(ddbst .de), and the Physical Property Data Service (ppds .co .uk) . Additional sources include the NIST Chemistry Webbook (webbook .nist
.gov/chemistry/); Boublik, T ., V . Fried, and E . Hala, The Vapor Pressures of
Pure Substances, 2d ed ., Elsevier, Amsterdam, 1984; Bruce Poling, JohnPrausnitz, and John O’Connell, The Properties of Gases and Liquids, 5th ed .,
McGraw-Hill, New York, 2001; Vapor Pressure of Chemicals (subvolumes A,
B, and C), vol . IV/20 in Landolt-Bornstein: Numerical Data and Functional
Relationships in Science and Technology—New Series, Springer-Verlag, Berlin,
1999–2001 . The most recent work on water may be found at The International Association for the Properties of Water and Steam website http://
iapws .org .
TABLE 2-5 Vapor Pressure (MPa) of Liquid Water
from 0 to 100çC
t, °C
0 .01
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Pvp, MPa
t, °C
Pvp, MPa
t, °C
Pvp, MPa
0 .00061165
0 .00065709
0 .00070599
0 .00075808
0 .00081355
0 .00087258
0 .00093536
0 .0010021
0 .0010730
0 .0011483
0 .0012282
0 .0013130
0 .0014028
0 .0014981
0 .0015990
0 .0017058
0 .0018188
0 .0019384
0 .0020647
0 .0021983
0 .0023393
0 .0024882
0 .0026453
0 .0028111
0 .0029858
0 .0031699
0 .0033639
0 .0035681
0 .0037831
0 .0040092
0 .0042470
0 .0044969
0 .0047596
0 .0050354
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
0 .0053251
0 .0056290
0 .0059479
0 .0062823
0 .0066328
0 .0070002
0 .0073849
0 .0077878
0 .0082096
0 .0086508
0 .0091124
0 .0095950
0 .010099
0 .010627
0 .011177
0 .011752
0 .012352
0 .012978
0 .013631
0 .014312
0 .015022
0 .015762
0 .016533
0 .017336
0 .018171
0 .019041
0 .019946
0 .020888
0 .021867
0 .022885
0 .023943
0 .025042
0 .026183
0 .027368
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
0 .028599
0 .029876
0 .031201
0 .032575
0 .034000
0 .035478
0 .037009
0 .038595
0 .040239
0 .041941
0 .043703
0 .045527
0 .047414
0 .049367
0 .051387
0 .053476
0 .055635
0 .057867
0 .060173
0 .062556
0 .065017
0 .067558
0 .070182
0 .072890
0 .075684
0 .078568
0 .081541
0 .084608
0 .087771
0 .091030
0 .094390
0 .097852
0 .10142
From E . W . Lemmon, M . O . McLinden, and D . G . Friend, “ Thermophysical Properties
of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database
Number 69, Eds . P . J . Linstrom and W . G . Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg, Md . (http://webbook .nist .gov) and Wagner, W .,
and A ., Pruss, “The IAPWS Formulation 1995 for the Thermodynamic Properties of
Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data
31(2):387–535, 2002 .
The website mentioned above allows users to generate their own tables of thermodynamic properties . The user can select the units as well as the temperatures and/or
pressures for which properties are to be generated . The results can then be copied into
spreadsheets or other files .
VAPOR PRESSURES
TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by
Chemical Family
Name
Cmpd. no.
Formula
Paraffins
Methane
Ethane
Propane
Butane
Pentane
Hexane
Heptane
Octane
Nonane
Decane
Undecane
Dodecane
Tridecane
Tetradecane
Pentadecane
Hexadecane
Heptadecane
Octadecane
Nonadecane
Eicosane
2-Methylpropane
2-Methylbutane
2,3-Dimethylbutane
2-Methylpentane
2,3-Dimethylpentane
2,2,3,3-Tetramethylbutane
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
Cyclopropane
Cyclobutane
Cyclopentane
Cyclohexane
Methylcyclopentane
Ethylcyclopentane
Methylcyclohexane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Ethylcyclohexane
193
125
295
31
279
171
160
265
256
74
336
123
327
319
277
169
158
263
254
124
236
202
107
234
114
323
332
333
71
64
69
65
217
134
213
108
109
110
133
CH4
C2H6
C 3H 8
C4H10
C5H12
C6H14
C7H16
C8H18
C9H20
C10H22
C11H24
C12H26
C13H28
C14H30
C15H32
C16H34
C17H36
C18H38
C19H40
C20H42
C4H10
C5H12
C6H14
C6H14
C7H16
C8H18
C8H18
C8H18
C 3H 6
C 4H 8
C5H10
C6H12
C6H12
C7H14
C7H14
C8H16
C8H16
C8H16
C8H16
135
305
36
37
38
70
285
68
177
166
271
260
77
238
205
206
218
219
298
294
29
30
201
C 2H 4
C 3H 6
C4H8
C4H8
C4H8
C5H8
C5H10
C6H10
C6H12
C7H14
C8H16
C9H18
C10H20
C4H8
C5H10
C5H10
C6H10
C6H10
C9H14
C3H4
C4H6
C4H6
C5H8
7
43
288
289
178
180
181
168
C2H2
C4H6
C5H8
C5H8
C6H10
C6H10
C6H10
C7H12
Olefins
Ethylene
Propylene
1-Butene
cis-2-Butene
trans-2-Butene
Cyclopentene
1-Pentene
Cyclohexene
1-Hexene
1-Heptene
1-Octene
1-Nonene
1-Decene
2-Methyl propene
2-Methyl-1-butene
2-Methyl-2-butene
1-Methylcyclopentene
3-Methylcyclopentene
Propenylcyclohexene
Propadiene
1,2-Butadiene
1,3-Butadiene
3-Methyl-1,2-butadiene
Acetylenes
Acetylene
1-Butyne
1-Pentyne
2-Pentyne
3-Hexyne
1-Hexyne
2-Hexyne
1-Heptyne
Name
Cmpd. no.
Formula
Acetylenes
1-Octyne
1-Nonyne
1-Decyne
Methyl acetylene
Vinyl acetylene
Dimethyl acetylene
2-Methyl -1-butene-3-yne
3-Methyl-1-butyne
273
262
79
197
339
105
207
210
C8H14
C9H16
C10H18
C3H4
C4H4
C4H6
C5H6
C5H8
16
325
312
129
343
344
345
243
62
304
330
331
246
321
40
24
290
318
C6H6
C7H8
C8H8
C8H10
C8H10
C8H10
C8H10
C9H10
C9H12
C9H12
C9H12
C9H12
C10H8
C10H12
C10H14
C12H10
C14H10
C18H14
153
1
299
44
278
170
159
264
255
73
CH2O
C2H4O
C3H6O
C4H8O
C5H10O
C6H12O
C7H14O
C8H16O
C9H18O
C10H20O
8
5
222
229
283
284
310
67
144
175
176
226
102
164
165
269
270
20
C3H4O
C3H6O
C4H8O
C5H10O
C5H10O
C5H10O
C6H4O2
C6H10O
C6H12O
C6H12O
C6H12O
C6H12O
C7H14O
C7H14O
C7H14O
C8H16O
C8H16O
C13H10O
156
324
320
322
C4H4O
C4H4S
C4H8O
C4H8S
14
25
52
80
149
Ar
Br2
Cl2
D2
F2
Aromatics
Benzene
Toluene
Styrene
Ethylbenzene
m-Xylene
o-Xylene
p-Xylene
alpha-Methyl styrene
Cumene
Propylbenzene
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
Naphthalene
1,2,3,4-Tetrahydronaphthalene
Butylbenzene
Biphenyl
Phenanthrene
o-Terphenyl
Aldehydes
Formaldehyde
Acetaldehyde
Propionaldehyde
Butyraldehyde
Pentanal
Hexanal
Heptanal
Octanal
Nonanal
Decanal
Ketones
Acrolein
Acetone
Methylethyl ketone
Methylisopropyl ketone
2-Pentanone
3-Pentanone
Quinone
Cyclohexanone
Ethylisopropyl ketone
2-Hexanone
3-Hexanone
Methylisobutyl ketone
Diisopropyl ketone
3-Heptanone
2-Heptanone
2-Octanone
3-Octanone
Benzophenone
Heterocyclics
Furan
Thiophene
Tetrahydrofuran
Tetrahydrothiophene
Elements
Argon
Bromine
Chlorine
Deuterium
Fluorine
(Continued )
2-47
2-48
PHYSICAL AnD CHEMICAL DATA
TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by
Chemical Family (Continued )
Name
Cmpd. no.
Formula
Elements
Hydrogen
Helium-4
Nitrogen
Neon
Oxygen
183
157
249
247
275
H2
He
N2
Ne
O2
194
126
296
297
34
35
281
282
66
173
174
162
163
267
268
258
259
76
337
237
204
21
214
215
216
137
309
32
33
CH4O
C2H6O
C3H8O
C3H8O
C4H10O
C4H10O
C5H12O
C5H12O
C6H12O
C6H14O
C6H14O
C7H16O
C7H16O
C8H18O
C8H18O
C9H20O
C9H20O
C10H22O
C11H24O
C4H10O
C5H12O
C7H8O
C7H14O
C7H14O
C7H14O
C2H6O2
C3H8O2
C4H10O2
C4H10O2
291
59
60
61
C6H6O
C7H8O
C7H8O
C7H8O
112
245
221
120
95
240
228
103
208
225
244
147
143
104
101
235
13
84
142
22
121
C2H6O
C3H6O
C3H8O
C4H8O2
C4H10O
C4H10O
C4H10O
C4H10O2
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O2
C6H14O
C6H14O
C7H8O
C8H18O
C8H18O
C9H12O
C12H10O
155
274
3
9
191
300
CH2O2
C2H2O4
C2H4O2
C3H4O2
C3H4O4
C3H6O2
Alcohols
Methanol
Ethanol
1-Propanol
2-Propanol
1-Butanol
2-Butanol
1-Pentanol
2-Pentanol
Cyclohexanol
1-Hexanol
2-Hexanol
1-Heptanol
2-Heptanol
1-Octanol
2-Octanol
1-Nonanol
2-Nonanol
1-Decanol
1-Undecanol
2-Methyl-2-propanol
3-Methyl-1-butanol
Benzyl alcohol
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Ethylene glycol
1,2-Propylene glycol
1,2-Butanediol
1,3-Butanediol
Phenols
Phenol
m-Cresol
o-Cresol
p-Cresol
Ethers
Dimethyl ether
Methyl vinyl ether
Methylethyl ether
1,4-Dioxane
Diethyl ether
Methylpropyl ether
Methylisopropyl ether
1,1-Dimethoxyethane
Methylbutyl ether
Methylisobutyl ether
Methyl tert-butyl ether
Ethylpropyl ether
Ethylisopropyl ether
1,2-Dimethoxypropane
Di-isopropyl ether
Methyl pentyl ether
Anisole
Dibutyl ether
Ethylhexyl ether
Benzyl ethyl ether
Diphenyl ether
Acids
Formic acid
Oxalic acid
Acetic acid
Acrylic acid
Malonic acid
Propionic acid
Name
Cmpd. no.
Formula
Methacrylic acid
Acetic anhydride
Succinic acid
Butyric acid
Isobutyric acid
2-Methylbutanoic acid
Pentanoic acid
2-Ethyl butanoic acid
Hexanoic acid
Benzoic acid
Heptanoic acid
Phthalic anhydride
Terephthalic acid
2-Ethyl hexanoic acid
Octanoic acid
2-Methyloctanoic acid
Nonanoic acid
Decanoic acid
192
4
313
45
189
203
280
131
172
18
161
293
317
141
266
233
257
75
C4H6O2
C4H6O3
C4H6O4
C4H8O2
C4H8O2
C5H10O2
C5H10O2
C6H12O2
C6H12O2
C7H6O2
C7H14O2
C8H4O3
C8H6O4
C8H16O2
C8H16O2
C9H18O2
C9H18O2
C10H20O2
224
140
196
198
338
127
239
306
232
146
211
302
39
132
200
130
115
119
C2H4O2
C3H6O2
C3H6O2
C4H6O2
C4H6O2
C4H8O2
C4H8O2
C4H8O2
C5H8O2
C5H10O2
C5H10O2
C5H10O2
C6H12O2
C6H12O2
C8H8O2
C9H10O2
C10H10O4
C10H10O4
199
138
106
128
136
190
303
329
94
93
100
122
328
CH5N
C2H5N
C2H7N
C2H7N
C2H8N2
C3H9N
C3H9N
C3H9N
C4H11N
C4H11NO2
C6H15N
C6H15N
C6H15N
154
2
113
195
15
CH3NO
C2H5NO
C3H7NO
C3H7NO
C7H7NO
6
63
10
301
46
19
C2H3N
C2N2
C3H3N
C3H5N
C4H7N
C7H5N
251
248
CH3NO2
C2H5NO2
Acids
Esters
Methyl formate
Ethyl formate
Methyl acetate
Methyl acrylate
Vinyl acetate
Ethyl acetate
Methyl propionate
Propyl formate
Methyl methacrylate
Ethyl propionate
Methyl butyrate
Propyl acetate
Butyl acetate
Ethyl butyrate
Methyl benzoate
Ethyl benzoate
Dimethyl phthalate
Dimethyl terephthalate
Amines
Methyl amine
Ethyleneimine
Dimethyl amine
Ethyl amine
Ethylenediamine
Isopropyl amine
Propyl amine
Trimethyl amine
Diethyl amine
Diethanol amine
Di-isopropyl amine
Dipropyl amine
Triethyl amine
Amides
Formamide
Acetamide
N,N-Dimethyl formamide
N-Methyl acetamide
Benzamide
Nitriles
Acetonitrile
Cyanogen
Acrylonitrile
Propionitrile
Butyronitrile
Benzonitrile
Nitro Compounds
Nitromethane
Nitroethane
VAPOR PRESSURES
2-49
TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by
Chemical Family (Continued )
Name
Cmpd. no.
Formula
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
334
335
C6H3N3O6
C7H5N3O6
227
292
C2H3NO
C7H5NO
231
145
308
307
41
42
287
286
17
72
179
23
167
272
261
78
CH4S
C2H6S
C3H8S
C3H8S
C4H10S
C4H10S
C5H12S
C5H12S
C6H6S
C6H12S
C6H14S
C7H8S
C7H16S
C8H18S
C9H20S
C10H22S
117
111
223
96
230
241
209
C2H6S
C2H6S2
C3H8S
C4H10S
C4H10S
C4H10S
C5H12S
50
51
55
83
90
99
28
56
152
340
326
81
82
88
CCl4
CF4
CHCl3
CH2Br2
CH2Cl2
CH2F2
CH3Br
CH3Cl
CH3F
C2H3Cl
C2H3Cl3
C2H4Br2
C2H4Br2
C2H4Cl2
Isocyanates
Methyl isocyanate
Phenyl isocyanate
Mercaptans
Methyl mercaptan
Ethyl mercaptan
Propyl mercaptan
2-Propyl mercaptan
Butyl mercaptan
sec-Butyl mercaptan
Pentyl mercaptan
2-Pentyl mercaptan
Benzenethiol
Cyclohexyl mercaptan
Hexyl mercaptan
Benzyl mercaptan
Heptyl mercaptan
Octyl mercaptan
Nonyl mercaptan
Decyl mercaptan
Sulfides
Dimethyl sulfide
Dimethyl disulfide
Methylethyl sulfide
Diethyl sulfide
Methylisopropyl sulfide
Methylpropyl sulfide
Methylbutyl sulfide
Cmpd. no.
Formula
1,2-Dichloroethane
1,1-Difluoroethane
1,2-Difluoroethane
Bromoethane
Chloroethane
Fluoroethane
1,1-Dichloropropane
1,2-Dichloropropane
1-Chloropropane
2-Chloropropane
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
Bromobenzene
Chlorobenzene
Fluorobenzene
89
97
98
27
54
151
91
92
57
58
85
86
87
26
53
150
C2H4Cl2
C2H4F2
C2H4F2
C2H5Br
C2H5Cl
C2H5F
C3H6Cl2
C3H6Cl2
C3H7Cl
C3H7Cl
C6H4Cl2
C6H4Cl2
C6H4Cl2
C6H5Br
C6H5Cl
C6H5F
242
212
220
341
148
116
311
CH6Si
CH5ClSi
CH4Cl2Si
C2H3Cl3Si
C2H5Cl3Si
C2H8Si
F4Si
186
49
47
48
250
315
184
185
187
188
12
182
253
252
314
276
316
CHN
CO
CO2
CS2
F3N
F6S
HBr
HCl
HF
H2S
H3N
H4N2
NO
N2 O
O2 S
O3
O3 S
11
139
118
342
Mixture
C2H4O
C2H6OS
H2O
Silanes
Methylsilane
Methylchlorosilane
Methyldichlorosilane
Vinyl trichlorosilane
Ethyltrichlorosilane
Dimethylsilane
Silicon tetrafluoride
Light Gases
Halogenated Hydrocarbons
Carbon tetrachloride
Carbon tetrafluoride
Chloroform
Dibromomethane
Dichloromethane
Difluoromethane
Bromomethane
Chloromethane
Fluoromethane
Vinyl chloride
1,1,2-Trichloroethane
1,1-Dibromoethane
1,2-Dibromoethane
1,1-Dichloroethane
Name
Halogenated Hydrocarbons
Nitro Compounds
Hydrogen cyanide
Carbon monoxide
Carbon dioxide
Carbon disulfide
Nitrogen trifluoride
Sulfur hexafluoride
Hydrogen bromide
Hydrogen chloride
Hydrogen fluoride
Hydrogen sulfide
Ammonia
Hydrazine
Nitric oxide
Nitrous oxide
Sulfur dioxide
Ozone
Sulfur trioxide
Others
Air
Ethylene oxide
Dimethyl sulfoxide
Water
2-50
PHYSICAL AnD CHEMICAL DATA
TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146,
and 2-148
Formula
No.
Name
Ar
Br2
CCl4
CF4
CHCl3
CHN
CH2Br2
CH2Cl2
CH2F2
CH2O
CH2O2
CH3Br
CH3Cl
CH3F
CH3NO
CH3NO2
CH4
CH4Cl2Si
CH4O
CH4S
CH5ClSi
CH5N
CH6Si
CO
CO2
CS2
C2H2
C2H2O4
C2H3Cl
C2H3Cl3
C2H3Cl3Si
C2H3N
C2H3NO
C2H4
C2H4Br2
C2H4Br2
C2H4Cl2
C2H4Cl2
C2H4F2
C2H4F2
C2H4O
C2H4O
C2H4O2
C2H4O2
C2H5Br
C2H5Cl
C2H5Cl3Si
C2H5F
C2H5N
C2H5NO
C2H5NO2
C2H6
C2H6O
C2H6O
C2H6O2
C2H6OS
C2H6S
C2H6S
C2H6S2
C2H7N
C2H7N
C2H8N2
C2H8Si
C2N2
C3H3N
C3H4
C3H4
C3H4O
C3H4O2
C3H4O4
C3H5N
C3H6
C3H6
C3H6Cl2
11
14
25
50
51
55
186
83
90
99
153
155
28
56
152
154
251
193
220
194
231
212
199
242
49
47
48
7
274
340
326
341
6
227
135
81
82
88
89
97
98
1
139
3
224
27
54
148
151
138
2
248
125
112
126
137
118
117
145
111
106
128
136
116
63
10
197
294
8
9
191
301
71
305
91
Air
Argon
Bromine
Carbon tetrachloride
Carbon tetrafluoride
Chloroform
Hydrogen cyanide
Dibromomethane
Dichloromethane
Difluoromethane
Formaldehyde
Formic acid
Bromomethane
Chloromethane
Fluoromethane
Formamide
Nitromethane
Methane
Methyldichlorosilane
Methanol
Methyl mercaptan
Methylchlorosilane
Methyl amine
Methylsilane
Carbon monoxide
Carbon dioxide
Carbon disulfide
Acetylene
Oxalic acid
Vinyl chloride
1,1,2-Trichloroethane
Vinyl trichlorosilane
Acetonitrile
Methyl Isocyanate
Ethylene
1,1-Dibromoethane
1,2-Dibromoethane
1,1-Dichloroethane
1,2-Dichloroethane
1,1-Difluoroethane
1,2-Difluoroethane
Acetaldehyde
Ethylene oxide
Acetic acid
Methyl formate
Bromoethane
Chloroethane
Ethyltrichlorosilane
Fluoroethane
Ethyleneimine
Acetamide
Nitroethane
Ethane
Dimethyl ether
Ethanol
Ethylene glycol
Dimethyl sulfoxide
Dimethyl sulfide
Ethyl mercaptan
Dimethyl disulfide
Dimethyl amine
Ethyl amine
Ethylenediamine
Dimethylsilane
Cyanogen
Acrylonitrile
Methyl acetylene
Propadiene
Acrolein
Acrylic acid
Malonic acid
Propionitrile
Cyclopropane
Propylene
1,1-Dichloropropane
Formula
No.
Name
C3H6Cl2
C3H6O
C3H6O
C3H6O
C3H6O2
C3H6O2
C3H6O2
C3H7Cl
C3H7Cl
C3H7NO
C3H7NO
C3H8
C3H8O
C3H8O
C3H8O
C3H8O2
C3H8S
C3H8S
C3H8S
C3H9N
C3H9N
C3H9N
C4H4
C4H4O
C4H4S
C4H6
C4H6
C4H6
C4H6
C4H6O2
C4H6O2
C4H6O2
C4H6O3
C4H6O4
C4H7N
C4H8
C4H8
C4H8
C4H8
C4H8
C4H8O
C4H8O
C4H8O
C4H8O2
C4H8O2
C4H8O2
C4H8O2
C4H8O2
C4H8O2
C4H8S
C4H10
C4H10
C4H10O
C4H10O
C4H10O
C4H10O
C4H10O
C4H10O
C4H10O2
C4H10O2
C4H10O2
C4H10S
C4H10S
C4H10S
C4H10S
C4H10S
C4H11N
C4H11NO2
C5H6
C5H8
C5H8
C5H8
C5H8
C5H8
C5H8O2
92
5
245
299
140
196
300
57
58
113
195
295
221
296
297
309
223
308
307
190
303
329
339
156
324
29
30
43
105
192
198
338
4
313
46
36
37
38
64
238
44
222
320
45
120
127
189
239
306
322
31
236
34
35
95
237
240
228
32
33
103
41
42
96
230
241
94
93
207
70
201
210
288
289
232
1,2-Dichloropropane
Acetone
Methyl vinyl ether
Propionaldehyde
Ethyl formate
Methyl acetate
Propionic acid
1-Chloropropane
2-Chloropropane
N,N-Dimethyl formamide
N-Methyl acetamide
Propane
Methylethyl ether
1-Propanol
2-Propanol
1,2-Propylene glycol
Methylethyl sulfide
Propyl mercaptan
2-Propyl mercaptan
Isopropyl amine
Propyl amine
Trimethyl amine
Vinyl acetylene
Furan
Thiophene
1,2-Butadiene
1,3-Butadiene
1-Butyne
Dimethyl acetylene
Methacrylic acid
Methyl acrylate
Vinyl acetate
Acetic anhydride
Succinic acid
Butyronitrile
1-Butene
cis-2-Butene
trans-2-Butene
Cyclobutane
2-Methyl propene
Butyraldehyde
Methylethyl ketone
Tetrahydrofuran
Butyric acid
1,4-Dioxane
Ethyl acetate
Isobutyric acid
Methyl propionate
Propyl formate
Tetrahydrothiophene
Butane
2-Methylpropane
1-Butanol
2-Butanol
Diethyl ether
2-Methyl-2-propanol
Methylpropyl ether
Methylisopropyl ether
1,2-Butanediol
1,3-Butanediol
1,1-Dimethoxyethane
Butyl mercaptan
sec-Butyl mercaptan
Diethyl sulfide
Methylisopropyl sulfide
Methylpropyl sulfide
Diethyl amine
Diethanol amine
2-Methyl-1-butene-3-yne
Cyclopentene
3-Methyl-1,2-butadiene
3-Methyl-1-butyne
1-Pentyne
2-Pentyne
Methyl methacrylate
VAPOR PRESSURES
2-51
TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146,
and 2-148 (Continued )
Formula
No.
Name
C5H10
C5H10
C5H10
C5H10
C5H10O
C5H10O
C5H10O
C5H10O
C5H10O2
C5H10O2
C5H10O2
C5H10O2
C5H10O2
C5H12
C5H12
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O
C5H12O2
C5H12S
C5H12S
C5H12S
C6H3N3O6
C6H4Cl2
C6H4Cl2
C6H4Cl2
C6H4O2
C6H5Br
C6H5Cl
C6H5F
C6H6
C6H6O
C6H6S
C6H10
C6H10
C6H10
C6H10
C6H10
C6H10
C6H10O
C6H12
C6H12
C6H12
C6H12O
C6H12O
C6H12O
C6H12O
C6H12O
C6H12O
C6H12O2
C6H12O2
C6H12O2
C6H12O2
C6H12S
C6H14
C6H14
C6H14
C6H14O
C6H14O
C6H14O
C6H14O
C6H14S
C6H15N
C6H15N
C6H15N
C7H5N
C7H5N3O6
C7H5NO
C7H6O2
C7H7NO
69
205
206
285
229
278
283
284
146
203
211
280
302
202
279
143
147
204
208
225
244
281
282
104
209
286
287
334
85
86
87
310
26
53
150
16
291
17
218
68
178
180
181
219
67
65
177
217
66
144
170
175
176
226
39
131
132
172
72
107
171
234
101
173
174
235
179
100
122
328
19
335
292
18
15
Cyclopentane
2-Methyl-1-butene
2-Methyl-2-butene
1-Pentene
Methylisopropyl ketone
Pentanal
2-Pentanone
3-Pentanone
Ethyl propionate
2-Methylbutanoic acid
Methyl butyrate
Pentanoic acid
Propyl acetate
2-Methylbutane
Pentane
Ethylisopropyl ether
Ethylpropyl ether
3-Methyl-1-butanol
Methylbutyl ether
Methylisobutyl ether
Methyl tert-butyl ether
1-Pentanol
2-Pentanol
1,2-Dimethoxypropane
Methylbutyl sulfide
2-Pentyl mercaptan
Pentyl mercaptan
1,3,5-Trinitrobenzene
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
Quinone
Bromobenzene
Chlorobenzene
Fluorobenzene
Benzene
Phenol
Benzenethiol
1-Methylcyclopentene
Cyclohexene
3-Hexyne
1-Hexyne
2-Hexyne
3-Methylcyclopentene
Cyclohexanone
Cyclohexane
1-Hexene
Methylcyclopentane
Cyclohexanol
Ethylisopropyl ketone
Hexanal
2-Hexanone
3-Hexanone
Methylisobutyl ketone
Butyl acetate
2-Ethyl butanoic acid
Ethyl butyrate
Hexanoic acid
Cyclohexyl mercaptan
2,3-Dimethylbutane
Hexane
2-Methylpentane
Di-isopropyl ether
1-Hexanol
2-Hexanol
Methyl pentyl ether
Hexyl mercaptan
Di-isopropyl amine
Dipropyl amine
Triethyl amine
Benzonitrile
2,4,6-Trinitrotoluene
Phenyl isocyanate
Benzoic acid
Benzamide
Formula
C7H8
C7H8O
C7H8O
C7H8O
C7H8O
C7H8O
C7H8S
C7H12
C7H14
C7H14
C7H14
C7H14O
C7H14O
C7H14O
C7H14O
C7H14O
C7H14O
C7H14O
C7H14O2
C7H16
C7H16
C7H16O
C7H16O
C7H16S
C8H4O3
C8H6O4
C8H8
C8H8O2
C8H10
C8H10
C8H10
C8H10
C8H14
C8H16
C8H16
C8H16
C8H16
C8H16
C8H16O
C8H16O
C8H16O
C8H16O2
C8H16O2
C8H18
C8H18
C8H18
C8H18
C8H18O
C8H18O
C8H18O
C8H18O
C8H18S
C9H10
C9H10O2
C9H12
C9H12
C9H12
C9H12
C9H12O
C9H14
C9H16
C9H18
C9H18O
C9H18O2
C9H18O2
C9H20
C9H20O
C9H20O
C9H20S
C10H8
C10H10O4
C10H10O4
C10H12
C10H14
C10H18
No.
Name
325
13
21
59
60
61
23
168
134
166
213
102
159
164
165
214
215
216
161
114
160
162
163
167
293
317
312
200
129
343
344
345
273
108
109
110
133
271
264
269
270
141
266
265
323
332
333
84
142
267
268
272
243
130
62
304
330
331
22
298
262
260
255
233
257
256
258
259
261
246
115
119
321
40
79
Toluene
Anisole
Benzyl alcohol
m-Cresol
o-Cresol
p-Cresol
Benzyl mercaptan
1-Heptyne
Ethylcyclopentane
1-Heptene
Methylcyclohexane
Di-isopropyl ketone
Heptanal
3-Heptanone
2-Heptanone
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Heptanoic acid
2,3-Dimethylpentane
Heptane
1-Heptanol
2-Heptanol
Heptyl mercaptan
Phthalic anhydride
Terephthalic acid
Styrene
Methyl benzoate
Ethylbenzene
m-Xylene
o-Xylene
p-Xylene
1-Octyne
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Ethylcyclohexane
1-Octene
Octanal
2-Octanone
3-Octanone
2-Ethyl hexanoic acid
Octanoic acid
Octane
2,2,3,3-Tetramethylbutane
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
Dibutyl ether
Ethylhexyl ether
1-Octanol
2-Octanol
Octyl mercaptan
alpha-Methyl styrene
Ethyl benzoate
Cumene
Propylbenzene
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
Benzyl ethyl ether
Propenylcyclohexene
1-Nonyne
1-Nonene
Nonanal
2-Methyloctanoic acid
Nonanoic acid
Nonane
1-Nonanol
2-Nonanol
Nonyl mercaptan
Naphthalene
Dimethyl phthalate
Dimethyl terephthalate
1,2,3,4-Tetrahydronaphthalene
Butylbenzene
1-Decyne
(Continued )
2-52
PHYSICAL AnD CHEMICAL DATA
TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146,
and 2-148 (Continued )
Formula
No.
Name
Formula
No.
Name
C10H20
C10H20O
C10H20O2
C10H22
C10H22O
C10H22S
C11H24
C11H24O
C12H10
C12H10O
C12H26
C13H10O
C13H28
C14H10
C14H30
C15H32
C16H34
C17H36
C18H14
C18H38
C19H40
C20H42
Cl2
77
73
75
74
76
78
336
337
24
121
123
20
327
290
319
277
169
158
318
263
254
124
52
1-Decene
Decanal
Decanoic acid
Decane
1-Decanol
Decyl mercaptan
Undecane
1-Undecanol
Biphenyl
Diphenyl ether
Dodecane
Benzophenone
Tridecane
Phenanthrene
Tetradecane
Pentadecane
Hexadecane
Heptadecane
o-Terphenyl
Octadecane
Nonadecane
Eicosane
Chlorine
D2
F2
F3N
F4Si
F6S
HBr
HCl
HF
H2
H2O
H2S
H3N
H4N2
He
NO
N2
N2O
Ne
O2
O2S
O3
O3S
80
149
250
311
315
184
185
187
183
342
188
12
182
157
253
249
252
247
275
314
276
316
Deuterium
Fluorine
Nitrogen trifluoride
Silicon tetrafluoride
Sulfur hexafluoride
Hydrogen bromide
Hydrogen chloride
Hydrogen fluoride
Hydrogen
Water
Hydrogen sulfide
Ammonia
Hydrazine
Helium-4
Nitric oxide
Nitrogen
Nitrous oxide
Neon
Oxygen
Sulfur dioxide
Ozone
Sulfur trioxide
TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K
Cmpd. no.∗
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
CAS
C1
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
52.9107
125.8 1
53.27
67.1818
69.006
46.735
39.63
138.4
46.745
57.3157
21.662
90.483
128.06
42.127
85.474
83.107
77.765
88.513
55.0403
88.404
100.68
68.541
118.02
77.314
108.26
63.749
57.3242
44.7643
39.714
75.572
66.343
103.28
123.22
106.29483
122.552
51.836
72.541
71.704
122.82
101.22
65.382
60.649
77.004
51.648
78.1171
60.6576
47.0169
67.114
45.698
78.441
61.89
71.334
54.144
44.677
146.43
44.555
58.3592
46.854
95.403
210.88
C2
−4643.14
−12,376
−6304.5
−7463.47
−5599.6
−5126.18
−2552.2
−7122.7
−6587.1
−5662.2
−692.39
−4669.7
−9307.7
−1093.1
−11,932
−6486.2
−8455.1
−11,829
−7363.83
−11,769
−11,059
−7886.2
−10,527
−9910.4
−6592
−7130.2
−4931.2
−3907.8
−3769.9
−4621.9
−4363.2
−11,548
−12,620
−9866.35511
−10,236.2
−4019.2
−4691.2
−4563.1
−9253.2
−9255.4
−6262.4
−5785.9
−5054.5
−5301.36
−8924.37
−6404.32
−2839
−4820.4
−1076.6
−6128.1
−2296.3
−3855
−6244.4
−4026
−7792.3
−3521.3
−5111.33
−4445.5
−10,581
−13,928
C3
−4.50683
−14.589
−4.2985
−6.24388
−7.0985
−3.54064
−2.78
−19.638
−3.2208
−5.06221
−0.39208
−11.607
−16.693
−4.1425
−8.3348
−9.2194
−7.7404
−8.6826
−4.50612
−8.9014
−10.709
−6.5804
−13.91
−7.5079
−14.16
−5.879
−5.2244
−3.4016
−2.6407
−8.5323
−7.046
−10.925
−13.986
−11.6553
−14.125
−4.5229
−7.9776
−7.9053
−14.99
−11.538
−6.2585
−5.6113
−8.5665
−4.2559
−7.59929
−5.49286
−3.86388
−7.5303
−4.8814
−8.5766
−7.086
−8.5171
−4.5343
−3.371
−20.614
−3.4258
−5.35261
−3.6533
−10.004
−29.483
C4
2.70E-17
5.0824E-06
8.89E-18
6.86E-18
6.2237E-06
1.40E-17
2.39E-16
0.026447
5.2253E-07
1.51E-17
0.0047574
0.017194
0.014919
0.000057254
1.29E-18
6.9844E-06
4.31E-18
2.32E-19
1.95E-18
1.93E-18
3.06E-18
2.4285E-06
6.4794E-06
2.24E-18
0.016043
5.21E-18
3.08E-17
2.95E-17
6.94E-18
0.000012269
9.4509E-06
4.26E-18
0.000003926
1.08E-17
2.36E-17
4.88E-17
0.000010368
0.000011319
0.00001047
5.9208E-06
1.49E-17
1.59E-17
0.000010161
1.14E-17
7.39E-18
1.13E-17
2.81E-16
0.0091695
0.000075673
6.8465E-06
0.000034687
0.012378
4.70E-18
2.27E-17
0.024578
5.63E-17
2.47E-17
1.33E-17
4.30E-18
0.025182
C5
Tmin, K
P at Tmin
6
2
6
6
2
6
6
1
2
6
1
1
1
2
6
2
6
6
6
6
6
2
2
6
1
6
6
6
6
2
2
6
2
6
6
6
2
2
2
2
6
6
2
6
6
6
6
1
2
2
2
1
6
6
1
6
6
6
6
1
149.78
353.33
289.81
200.15
178.45
229.32
192.4
185.45
286.15
189.63
59.15
195.41
235.65
83.78
403
278.68
258.27
395.45
260.28
321.35
257.85
275.65
243.95
342.2
265.85
242.43
154.25
179.44
136.95
164.25
134.86
220
196.15
183.85
158.45
87.8
134.26
167.62
199.65
185.3
157.46
133.02
147.43
176.8
267.95
161.3
216.58
161.11
68.15
250.33
89.56
172.12
227.95
136.75
207.15
175.45
150.35
155.97
285.39
304.19
5.15E-01
3.36E+02
1.28E+03
4.10E-02
2.79E+00
1.71E+02
1.27E+05
1.03E+01
2.57E+02
2.47E+00
5.64E+03
6.11E+03
2.45E+00
6.87E+04
3.55E+02
4.76E+03
7.68E+00
7.96E+02
5.40E+00
1.49E+00
1.88E-01
2.31E+01
2.98E-01
9.42E+01
5.85E+03
7.84E+00
3.80E-01
2.07E+02
4.47E-01
6.92E+01
6.74E-01
2.93E-04
3.74E-07
2.91E-04
1.24E-06
6.94E-07
2.72E-01
7.45E+01
8.17E-02
1.54E-04
2.35E-03
3.40E-05
1.18E+00
6.97E-01
1.03E+01
9.41E-04
5.18E+05
1.49E+00
1.54E+04
1.12E+03
1.08E+02
1.37E+03
8.45E+00
2.61E-01
5.25E+01
8.84E+02
8.47E-02
9.08E-01
5.86E+00
6.53E+01
Tmax, K
466
761
591.95
606
508.2
545.5
308.3
506
615
540
132.45
405.65
645.6
150.86
824
562.05
689
751
702.3
830
720.15
662
718
773
584.15
670.15
503.8
464
452
425
425.12
680
676
563.1
535.9
419.5
435.5
428.6
575.4
660.5
570.1
554
440
537.2
615.7
585.4
304.21
552
132.92
556.35
227.51
417.15
632.35
460.35
536.4
416.25
503.15
489
705.85
697.55
P at Tmax
5.570E+06
6.569E+06
5.739E+06
4.000E+06
4.709E+06
4.850E+06
6.106E+06
5.020E+06
5.661E+06
4.660E+06
3.793E+06
1.130E+07
4.273E+06
4.896E+06
5.047E+06
4.875E+06
4.728E+06
4.469E+06
4.215E+06
3.357E+06
4.372E+06
3.113E+06
4.074E+06
3.407E+06
1.028E+07
4.520E+06
5.565E+06
6.929E+06
4.361E+06
4.303E+06
3.770E+06
5.202E+06
4.033E+06
4.414E+06
4.190E+06
4.021E+06
4.238E+06
4.100E+06
3.087E+06
2.882E+06
3.973E+06
4.060E+06
4.599E+06
4.410E+06
4.060E+06
3.880E+06
7.384E+06
8.041E+06
3.494E+06
4.544E+06
3.742E+06
7.793E+06
4.529E+06
5.267E+06
5.554E+06
6.759E+06
4.425E+06
4.510E+06
4.522E+06
5.058E+06
2-53
(Continued )
2-54
TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued )
Cmpd. no.∗
Name
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Di-sopropyl amine
Di-sopropyl ether
Di-sopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Formula
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
CAS
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
C1
C2
C3
118.53
102.81
39.0596
85.899
51.087
189.19
85.424
88.184
66.341
67.952
40.608
85.146
93.5742
112.73
126.405
156.23933
68.401
91.91
142.94
18.947
62.711
43.751
86.295
72.227
53.187
77.105
88.31
66.611
92.355
101.6
83.495
65.955
106.38
49.314
136.9
46.705
73.491
84.625
69.132
462.84
41.631
50.868
53.637
62.097
66.592
71.738
77.161
81.184
78.952
78.429
81.045
44.704
82.762
78.335
72.517
63.08
84.39
56.273
66.1795
44.494
−11,957
−8674.6
−3473.98
−4884.4
−5226.4
−14,337
−7944.4
−6624.9
−5198.5
−5187.5
−3179.6
−7843.7
−10,403.8
−9749.6
−14,864.6
−15,212.33492
−7776.9
−10,565
−11,119
−154.47
−6503.5
−5587.7
−7010.3
−7537.6
−6827.5
−8111.1
−8463.4
−5493.1
−6920.4
−6541.6
−6661.4
−6015.6
−13,714
−4949
−6954.3
−5177.4
−4385.9
−5217.4
−3847.7
−18,227
−4668.7
−6036.5
−5251.2
−6174.9
−4999.8
−5302
−5691.1
−6927
−7075.4
−6882.1
−6941.3
−3525.6
−7955.5
−6348.7
−10,415
−4062.3
−5740.6
−7620.6
−9870.41
−5406.7
−13.293
−11.922
−2.48683
−10.883
−4.2278
−24.148
−9.2862
−10.059
−6.8103
−7.0785
−2.8937
−9.2982
−9.79483
−13.245
−13.9067
−18.42393
−6.4637
−9.5957
−17.818
−0.57226
−5.7669
−3.0891
−9.5972
−7.0596
−4.3233
−7.8886
−9.6308
−6.7301
−10.651
−12.247
−9.2386
−6.5509
−11.06
−3.9256
−19.254
−3.5985
−8.1851
−9.871
−7.5868
−73.734
−2.8551
−4.066
−4.5649
−5.715
−6.8387
−7.3324
−8.501
−8.8498
−8.4344
−8.4129
−8.777
−3.4444
−8.8038
−8.5105
−6.755
−6.425
−9.6454
−4.6279
−5.85599
−3.1287
C4
8.70E-18
7.0048E-06
2.86E-17
0.014934
9.76E-18
0.00001074
4.9957E-06
8.2566E-06
0.000006193
6.8165E-06
5.61E-17
5.1788E-06
4.57E-18
7.1266E-06
2.51E-18
8.50E-18
6.38E-18
5.70E-18
0.00001102
0.038899
1.0427E-06
8.2664E-07
6.7794E-06
9.14E-18
2.31E-18
2.7267E-06
4.5833E-06
5.3579E-06
9.1426E-06
0.000012311
6.7652E-06
4.3172E-06
3.26E-18
9.20E-18
0.024508
1.7147E-06
0.000012978
0.00001305
0.000015065
0.092794
0.00063693
1.1326E-06
1.68E-17
1.23E-17
6.6793E-06
6.42E-17
8.0325E-06
0.000005458
4.5035E-06
4.9831E-06
5.5501E-06
5.46E-17
4.2431E-06
6.4311E-06
1.3269E-06
1.51E-16
0.000010073
4.3819E-07
1.47E-18
2.89E-18
C5
Tmin, K
P at Tmin
6
2
6
1
6
2
2
2
2
2
6
2
6
2
6
6
6
6
2
1
2
2
2
6
6
2
2
2
2
2
2
2
6
6
1
2
2
2
2
1
1
2
6
6
2
6
2
2
2
2
2
6
2
2
2
6
2
2
6
6
307.93
177.14
245.25
182.48
279.69
296.6
242
169.67
179.28
138.13
145.59
189.64
285
243.51
304.55
280.05
206.89
247.56
229.15
18.73
210.15
282.85
220.6
175.3
248.39
256.15
326.14
176.19
237.49
178.01
192.5
172.71
301.15
223.35
156.85
169.2
154.56
179.6
136.95
176.85
187.65
204.81
159.95
226.1
240.91
180.96
145.19
239.66
223.16
184.99
188.44
131.65
212.72
160
274.18
122.93
174.88
291.67
413.79
284.95
3.45E+01
4.71E-04
7.44E+04
1.80E+02
5.36E+03
7.65E+01
6.80E+00
1.04E-01
9.07E+00
1.28E-02
7.80E+01
8.24E-03
5.51E+00
1.39E+00
1.45E-01
1.50E-01
2.59E-02
2.59E-02
1.60E-01
1.72E+04
2.64E+00
7.53E+02
2.13E+01
7.14E-04
6.41E+00
6.49E+00
1.23E+03
2.21E+00
2.37E+02
5.93E+00
1.72E+00
8.25E-02
1.02E-01
3.74E+02
3.95E-01
9.93E-02
6.45E+01
1.17E+02
5.43E+01
4.47E-03
6.86E+00
8.21E-01
9.45E-02
4.50E+01
6.12E+03
7.56E+01
1.52E-02
6.06E+01
6.41E+00
8.04E-02
2.07E-01
3.05E+00
1.95E-01
1.26E-02
3.72E-02
4.15E-01
7.86E+00
5.02E+01
1.15E+03
2.53E+03
Tmax, K
704.65
631
400.15
459.93
553.8
650.1
653
560.4
511.7
507
398
664
674
617.7
722.1
688
616.6
696
619.85
38.35
628
650.15
611
584.1
683.95
705
684.75
523
561.6
510
560
572
736.6
496.6
466.7
557.15
386.44
445
351.26
523.1
500.05
576
507.8
543
473.2
437.2
500
591.15
606.15
596.15
615
400.1
649.6
537.3
766
402
503.04
729
777.4
587
P at Tmax
5.151E+06
3.226E+06
5.924E+06
4.991E+06
4.093E+06
4.265E+06
3.989E+06
4.392E+06
4.513E+06
4.799E+06
5.494E+06
3.970E+06
2.600E+06
2.091E+06
2.280E+06
2.308E+06
2.223E+06
2.130E+06
2.363E+06
1.663E+06
6.034E+06
5.375E+06
7.170E+06
2.459E+06
4.070E+06
4.074E+06
4.070E+06
5.106E+06
5.318E+06
6.093E+06
4.239E+06
4.232E+06
4.260E+06
3.674E+06
3.641E+06
3.961E+06
4.507E+06
4.372E+06
5.761E+06
3.199E+06
2.869E+06
3.017E+06
3.773E+06
3.447E+06
4.870E+06
5.258E+06
3.130E+06
2.939E+06
2.939E+06
2.938E+06
5.363E+06
5.274E+06
4.365E+06
2.882E+06
2.779E+06
3.561E+06
5.533E+06
5.648E+06
2.759E+06
5.158E+06
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
59.969
54
137.47
203.66
51.857
73.304
66.824
81.56
89.063
52.923
90.464
57.661
80.208
88.671
53.963
73.51
84.09
66.51
91.944
73.833
122.364
77.523
57.723
57.459
65.551
105.64
86.898
61.6271
42.393
51.915
38.593
41.2744
49.3632
100.3
43.8066
74.738
11.533
156.95
55.3058
87.829
112.372
147.41
153.088
78.463
75.494
65.922
79.858
59.083
156.06
58.7734
104.65
98.3767
135.42149
122.695
107.44
73.155
51.9766
47.091
68.467
133.2
123.71
76.858
12.69
−8585.5
−6018.5
−11,976
−19,441
−2598.7
−7122.3
−6227.6
−5596.9
−7733.7
−7531.7
−10,243
−6346.5
−7203.2
−7012.7
−2443
−7572.7
−10,411
−6019.2
−5293.4
−5817
−13,308.8
−7978.8
−5236.9
−6356.8
−5027.4
−8007
−6646.4
−6095.88
−1103.3
−5439
−3123.34
−2676.65
−3847.87
−10,763
−5131.03
−5417
−8.99
−15,557
−6694.68
−6996.4
−12,660.1
−13,466
−12,618.7
−8077.2
−7896.5
−6189
−8501.8
−6031.8
−15,015
−6529.3
−6995.5
−11,394
−12,288.40621
−10,870
−8528.6
−7242.9
−5104.66
−5104
−7390.5
−7492.9
−7639
−7245.2
−94.896
−5.1538
−4.4981
−16.698
−25.525
−5.1283
−7.1424
−6.41
−9.0779
−9.917
−4.2347
−9.2836
−5.032
−8.6023
−10.045
−5.5643
−7.1435
−8.1976
−6.3332
−11.682
−7.809
−13.5709
−7.7757
−5.2136
−4.9545
−6.6853
−12.477
−9.5758
−5.69714
−4.1203
−4.2896
−2.53014
−3.03914
−4.09834
−10.946
−3.18777
−8.0636
0.6724
−18.966
−4.64122
−9.8802
−12.147
−17.353
−18.7479
−7.9062
−7.5047
−6.3629
−8.1043
−5.3072
−18.941
−5.17151
−12.702
−10.2239
−15.73191
−14.192
−12.679
−7.2569
−4.34844
−3.6371
−6.5456
−18.405
−16.451
−8.22
1.1125
2.00E-18
9.97E-18
8.0906E-06
8.8382E-06
0.000014913
2.8853E-06
1.79E-17
0.000008792
0.000005986
1.1835E-06
5.26E-18
8.25E-18
4.5901E-06
7.4578E-06
0.000019079
1.21E-17
1.65E-18
1.04E-17
0.014902
0.00000632
6.42E-18
1.01E-17
2.30E-17
5.20E-18
6.3208E-06
0.000009
5.96E-17
1.06E-17
0.000057815
8.75E-18
5.30E-17
2.45E-16
4.64E-17
3.8503E-06
2.37819E-06
0.00000747
0.2743
6.4559E-06
5.28E-18
7.2099E-06
4.39E-18
1.13E-17
7.45073E-06
8.05E-18
8.91E-18
2.01E-17
8.15E-18
1.44E-17
6.8172E-06
6.95E-18
0.000012381
3.29E-18
1.27E-17
0.000003871
8.4606E-06
1.27E-17
1.17E-17
0.00051621
7.76E-18
0.022062
0.016495
0.0061557
0.00032915
6
6
2
2
2
2
6
2
2
2
6
6
2
2
2
6
6
6
1
2
6
6
6
6
2
2
6
6
2
6
6
6
6
2
2
2
1
2
6
2
6
6
2
6
6
6
6
6
2
6
2
6
6
2
2
6
6
1
6
1
1
1
2
300.03
210.15
263.57
309.58
90.35
159.05
189.6
192.15
178.2
238.45
258.15
175.15
161.84
134.71
104
284.29
260.15
195.2
160.65
193.55
155.15
180
140
204.15
125.26
199.25
145.65
167.55
53.48
230.94
129.95
131.35
155.15
275.6
281.45
187.55
1.76
295.13
229.8
182.57
265.83
239.15
220
234.15
238.15
154.12
229.92
192.22
291.31
214.93
177.83
269.25
228.55
223
217.35
217.5
133.39
170.05
192.62
141.25
183.65
274.69
13.95
7.09E+00
3.69E+00
6.15E-01
9.26E-03
1.13E+00
4.96E-04
1.43E+00
1.52E+02
3.91E-03
1.69E-01
4.63E-01
1.04E-02
3.57E-04
3.71E-06
1.26E+02
6.78E+02
2.19E-01
9.71E+00
7.79E+00
1.81E+01
1.44E-14
7.60E-04
4.31E-03
9.70E-01
1.14E-03
7.80E-01
1.61E-03
1.96E-02
2.53E+02
1.51E+02
9.43E+00
4.34E+02
4.89E+01
1.04E+00
2.41E+03
5.00E+01
1.46E+03
4.65E-02
2.56E+00
1.83E-01
4.66E-02
1.95E-02
6.55E-03
2.30E+00
3.54E+00
1.86E-03
3.05E-01
8.15E-01
9.23E-02
1.86E+00
9.02E-01
3.17E-01
2.25E-02
7.46E-02
1.45E+00
2.22E+00
5.16E-04
2.20E-01
1.31E-02
3.92E-04
5.40E-01
4.08E+02
7.21E+03
766.8
550
658
768
305.32
514
523.3
456.15
617.15
698
655
571
609.15
569.5
282.34
593
720
537
469.15
508.4
674.6
583
489
567
499.15
546
500.23
559.95
144.12
560.09
375.31
317.42
420
771
588
490.15
5.2
736
620
540.2
677.3
632.3
608.3
606.6
611.4
537.4
645
547
723
594
507.6
660.2
611.3
585.3
587.61
582.82
504
544
623
516.2
549
653.15
33.19
3.097E+06
3.111E+06
1.822E+06
1.175E+06
4.852E+06
6.109E+06
3.850E+06
5.594E+06
3.590E+06
3.203E+06
3.403E+06
2.935E+06
3.041E+06
3.412E+06
5.032E+06
6.290E+06
8.257E+06
6.850E+06
7.255E+06
4.708E+06
2.780E+06
2.460E+06
3.414E+06
3.293E+06
5.492E+06
3.336E+06
3.372E+06
3.321E+06
5.167E+06
4.544E+06
4.980E+06
5.875E+06
6.590E+06
7.751E+06
5.810E+06
5.550E+06
2.284E+05
1.344E+06
3.160E+06
2.719E+06
3.042E+06
3.013E+06
3.000E+06
2.919E+06
2.946E+06
2.921E+06
2.772E+06
3.209E+06
1.411E+06
3.460E+06
3.045E+06
3.309E+06
3.446E+06
3.323E+06
3.286E+06
3.322E+06
3.210E+06
3.540E+06
3.079E+06
3.635E+06
3.530E+06
1.473E+07
1.315E+06
2-55
(Continued )
2-56
TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued )
Cmpd. no.∗
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
Name
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl-1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
Formula
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
CAS
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
C1
29.315
104.27
36.75
59.544
85.584
110.38
136.66
119.172
109.53
39.205
82.718
79.128
61.267
50.242
107.69
75.206
84.828
66.575
71.308
85.383
117.074
93.131
83.927
95.453
60.164
96.344
69.459
71.87
95.984
92.684
134.63
125.1
54.179
55.368
52.732
52.601
79.788
78.586
72.698
79.07
77.184
57.984
80.503
57.612
53.867
45.242
52.82
54.15
107.36
105.7
53.579
61.907
108.43
172.27
78.01
70.717
67.942
83.711
37.205
C2
−2424.5
−3731.2
−3927.1
−4143.8
−3839.9
−10,540
−7201.5
−15,688.8
−10,410
−1324.4
−6904.5
−9523.9
−5618.6
−3811.9
−7027.2
−5082.8
−9334.7
−5213.4
−4976
−9575.4
−10,743.2
−5525.4
−5640.5
−5448.8
−5621.7
−7856.3
−5250
−6885.7
−5401.7
−7080.8
−10,682
−10,288
−7477.2
−5149.8
−5286.9
−5120.3
−5420
−5176.3
−6143.6
−6114.1
−5606.1
−5339.6
−7421.8
−5197.9
−4701
−5324.4
−5437.7
−4337.7
−8085.3
−12,458
−5041.2
−6188.9
−5039.9
−11,589
−4634.1
−6439.7
−5419.1
−6786.9
−2590.3
C3
−1.1354
−15.047
−2.1245
−6.1764
−11.199
−12.262
−18.934
−12.6757
−12.289
−3.4366
−8.8622
−7.7355
−5.6473
−4.2526
−13.916
−8.0919
−8.7063
−6.7693
−7.7169
−8.6164
−13.1654
−11.852
−9.6453
−12.384
−5.53
−11.058
−7.1125
−7.0944
−11.829
−10.695
−16.511
−15.157
−4.22
−5.0136
−4.4509
−4.4554
−9.0702
−8.7501
−7.5779
−8.631
−8.392
−5.2362
−8.379
−5.1269
−4.7052
−3.2551
−4.442
−4.8127
−12.72
−11.234
−4.6404
−5.706
−15.012
−22.113
−8.9575
−6.9845
−6.8067
−9.2526
−2.5993
C4
2.38E-18
0.03134
3.89E-17
0.000014161
0.018848
1.43E-17
0.022255
1.55E-18
0.000003199
0.000031019
7.4664E-06
3.16E-18
2.11E-17
6.53E-17
0.015185
0.000008113
6.17E-18
4.8106E-06
8.7271E-06
5.61E-18
1.17E-17
0.014205
0.000011121
0.015643
1.86E-17
0.000007308
7.93E-17
1.49E-17
0.000018092
8.1366E-06
8.4427E-06
0.000010918
3.52E-18
0.000003222
1.09E-17
1.33E-17
0.000011489
9.1727E-06
5.6476E-06
6.5333E-06
7.8468E-06
2.08E-17
1.81E-17
2.17E-17
2.88E-17
3.04E-18
9.51E-18
4.50E-17
8.3307E-06
4.46E-18
1.94E-17
1.18E-17
0.022725
0.000013703
0.000013413
2.01E-17
4.78E-17
6.6666E-06
6.0508E-06
C5
Tmin, K
P at Tmin
6
1
6
2
1
6
1
6
2
2
2
6
6
6
1
2
6
2
2
6
6
1
2
1
6
2
6
6
2
2
2
2
6
2
6
6
2
2
2
2
2
6
6
6
6
6
6
6
2
6
6
6
1
2
2
6
6
2
2
185.15
158.97
259.83
189.79
187.68
227.15
177.95
409.15
288.15
90.69
175.47
301.15
175.15
170.45
196.32
179.69
260.75
159.53
113.25
193
155.95
135.58
139.39
160.15
157.48
175.3
183.45
187.35
139.05
146.58
299.15
280.15
269.15
130.73
146.62
168.54
182.55
160
186.48
167.23
174.15
188
189.15
256.15
127.93
180.15
171.64
150.18
224.95
240
119.55
176
113.54
298.97
132.81
185.65
133.97
160.17
116.34
2.95E+04
1.35E+04
1.87E+04
3.37E+02
2.29E+04
7.82E-02
7.73E+00
9.97E+01
5.86E+01
1.17E+04
1.11E-01
2.86E+01
1.02E+00
4.15E+02
4.07E+00
1.77E+02
1.81E+00
7.28E-01
1.21E-04
6.94E-05
1.14E-08
2.05E-02
1.94E-02
2.92E+00
2.99E-02
4.61E-03
4.36E+01
1.34E-01
4.12E-01
1.52E-04
2.57E+02
4.56E+01
1.62E+01
2.25E-04
3.98E-03
5.37E-01
2.58E+01
7.85E+00
1.39E+00
2.25E-01
6.88E+00
8.70E+00
6.99E-02
7.28E+03
3.32E-03
2.95E-01
1.80E-01
3.15E+00
1.91E+01
4.19E-04
2.07E-05
6.33E-02
1.21E-02
5.88E+03
6.45E-01
6.34E-01
2.90E-03
4.26E-03
1.43E+01
Tmax, K
363.15
324.65
456.65
461.15
373.53
605
471.85
834
662
190.56
512.5
718
506.55
402.4
536
430.05
693
490
460.4
643
577.2
465
470
492
512.74
593
463.2
554.5
442
572.1
686
614
617
532.7
542
526
483
437.8
535.5
533
487.2
497
574.6
488
464.48
553.4
553.1
469.95
566
694
497.7
546.49
407.8
506.2
417.9
530.6
476.25
565
352.5
P at Tmax
8.463E+06
8.356E+06
5.353E+06
6.487E+06
8.999E+06
3.683E+06
4.540E+06
6.097E+06
4.812E+06
4.590E+06
8.145E+06
4.997E+06
4.695E+06
5.619E+06
4.277E+06
7.414E+06
3.589E+06
3.831E+06
3.366E+06
3.886E+06
3.933E+06
3.465E+06
3.394E+06
4.469E+06
3.377E+06
3.464E+06
4.199E+06
3.480E+06
4.170E+06
3.486E+06
3.994E+06
3.807E+06
3.767E+06
3.759E+06
4.130E+06
4.129E+06
3.964E+06
4.433E+06
4.120E+06
4.261E+06
5.983E+06
3.416E+06
3.272E+06
5.480E+06
3.764E+06
3.792E+06
4.022E+06
7.231E+06
3.674E+06
2.545E+06
3.044E+06
3.041E+06
3.630E+06
3.957E+06
4.004E+06
4.028E+06
3.802E+06
3.972E+06
4.702E+06
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
CH3NO2
N2 O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
56.485
57.1299
51.085
62.964
29.755
75.632
58.282
68.149
57.278
96.512
72.974
182.54
80.3832
109.35
123.374
162.854
213.069
63.313
106.2
114.77
157.68
74.0298
96.084
116.477
144.11083
185.828
63.775
72.382
74.936
78.368
64.612
107.476
51.245
40.067
135.57
28.3041
78.741
93.2079
114.74801
116.828
84.635
44.286
46.994
58.985
67.309
82.805
137.29
72.958
95.444
86.779
126.5
57.069
59.078
84.66416
110.717
64.268
50.8769
54.552
59.9958
115.16
58.398
91.379
43.905
−6954.2
−5200.7
−4271
−8137.5
−271.06
−7202.3
−1084.1
−2257.9
−6089
−4045
−2650
−17,897
−9096.15
−9030.4
−14,215.3
−15,204.55331
−16,246
−7040.4
−10,982
−9430.8
−16,093
−8302.12
−7900.2
−13,300.4
−13,667.15667
−14,520.2
−7711.3
−8054.8
−7155.9
−8855.4
−6802.5
−12,833.4
−1200.2
−2204.8
−13,478
−4657.56
−5420.3
−10,470.5
−10,643.3
−10,453
−7078.4
−5415.1
−4289.5
−6193.1
−6880.8
−5683.8
−7447.1
−10,943
−10,113
−8101.8
−12,551
−3682.7
−3492.6
−8307.24422
−9040
−7298.9
−4931
−7149.4
−6006.16
−8433.9
−5312.7
−8276.8
−3097.8
−4.7889
−5.13976
−4.307
−5.6317
−2.6081
−7.6464
−8.3144
−8.9118
−4.9821
−12.277
−8.261
−22.498
−8.03581
−12.882
−13.5607
−19.42436
−27.6195
−5.8055
−11.696
−13.631
−18.954
−7.19776
−11.003
−12.6746
−16.82611
−23.6236
−5.7359
−7.0002
−7.5843
−7.8202
−6.0261
−11.3837
−6.4361
−2.9351
−16.022
−0.732149
−8.8253
−9.61345
−12.85754
−13.1768
−9.3
−3.0913
−3.7345
−5.2746
−6.4449
−9.4301
−19.01
−6.7902
−10.09
−9.5303
−15.002
−5.5662
−6.0669
−8.57673
−12.676
−5.9109
−4.16673
−4.2769
−5.46004
−13.934
−5.2876
−10.176
−3.4425
2.78E-18
1.65E-17
3.05E-17
2.27E-18
0.000527
1.83E-17
0.044127
0.023233
1.22E-17
0.00002886
9.70E-15
7.4008E-06
4.71E-18
7.8544E-06
3.17E-18
1.07E-17
1.31827E-05
7.58E-18
8.90E-18
8.1918E-06
5.9272E-06
5.31E-18
7.1802E-06
3.98E-18
9.37E-18
1.08854E-05
3.09E-18
5.83E-18
1.71E-17
5.66E-18
1.10E-17
1.34E-18
0.028405
7.75E-16
5.6136E-06
–8.31E-18
9.6171E-06
5.62E-18
1.25E-17
1.07E-17
6.2702E-06
1.86E-18
2.54E-17
7.40E-18
1.01E-17
0.000010767
0.021415
1.09E-18
6.76E-18
6.1367E-06
7.7521E-06
6.5133E-06
0.000010919
7.51E-18
0.000005538
4.85E-18
1.67E-17
1.18E-18
1.70E-17
0.000010346
1.9913E-06
0.000005624
1.00E-16
6
6
6
6
2
6
1
1
6
2
6
2
6
2
6
6
2
6
6
2
2
6
2
6
6
2
6
6
6
6
6
6
1
6
2
6
2
6
6
6
2
6
6
6
6
2
1
6
6
2
2
2
2
6
2
6
6
6
6
2
2
2
6
249.95
164.55
151.15
353.43
24.56
183.63
63.15
66.46
244.6
182.3
109.5
305.04
267.3
219.66
285.55
268.15
238.15
191.91
253.05
223.15
301.31
251.65
216.38
289.65
257.65
241.55
252.85
255.55
171.45
223.95
193.55
462.65
54.36
80.15
283.07
191.59
143.42
239.15
195.56
200
196.29
234.18
108.02
160.75
197.45
167.45
163.83
372.38
314.06
243.15
404.15
136.87
85.47
146.95
185.26
199
165
252.45
180.37
178.15
188.36
173.55
87.89
9.23E+00
4.94E-01
3.37E+00
9.91E+02
4.38E+04
3.18E-02
1.25E+04
1.86E-01
1.47E+02
8.69E+04
2.20E+04
1.59E-02
4.25E+00
4.31E-01
4.58E-02
8.58E-02
3.85E-03
2.04E-02
1.47E-01
4.50E-01
3.39E-02
3.49E+00
2.11E+00
2.76E-01
9.60E-02
3.79E-02
4.68E+00
7.84E+00
2.98E-03
3.05E-02
1.04E-01
1.97E+04
1.48E+02
7.35E-01
1.29E-01
1.16E+00
6.86E-02
3.97E-02
5.47E-04
5.24E-03
7.52E-01
7.34E+01
3.71E-05
1.77E-03
2.01E-01
2.40E+00
2.05E-01
2.93E+01
1.88E+02
4.33E+00
7.90E+02
1.82E+01
1.68E-04
4.27E-07
1.69E-02
2.48E-02
7.54E-01
1.31E+01
1.89E-01
1.71E-02
1.30E+01
1.81E-04
1.17E-03
654
497.1
437
748.4
44.4
593
126.2
234
588.15
309.57
180.15
758
658.5
594.6
710.7
670.9
649.5
593.1
681
598.05
747
638.9
568.7
694.26
652.3
629.8
632.7
627.7
566.9
667.3
574
828
154.58
261
708
566.1
469.7
639.16
588.1
561
561.08
560.95
464.8
584.3
598
481.2
519
869
694.25
653
791
394
369.83
536.8
508.3
636
503.6
600.81
561.3
549.73
496.95
638.35
364.85
3.341E+06
3.286E+06
4.583E+06
4.069E+06
2.665E+06
5.159E+06
3.391E+06
4.500E+06
6.309E+06
7.278E+06
6.516E+06
1.208E+06
2.680E+06
2.305E+06
2.513E+06
2.528E+06
2.540E+06
2.427E+06
2.330E+06
2.619E+06
1.255E+06
2.960E+06
2.467E+06
2.779E+06
2.781E+06
2.749E+06
2.647E+06
2.705E+06
2.663E+06
2.523E+06
2.880E+06
8.203E+06
5.021E+06
5.566E+06
1.474E+06
3.845E+06
3.364E+06
3.630E+06
3.897E+06
3.699E+06
3.706E+06
3.699E+06
3.562E+06
3.537E+06
3.473E+06
4.170E+06
4.020E+06
2.902E+06
6.058E+06
4.063E+06
4.734E+06
5.218E+06
4.213E+06
5.169E+06
4.771E+06
3.130E+06
5.040E+06
4.608E+06
4.260E+06
3.366E+06
4.738E+06
3.202E+06
4.599E+06
2-57
(Continued )
2-58
TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued )
Cmpd. no.∗
Name
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
Formula
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O 2S
F6S
O 3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
CAS
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
C1
C2
104.08
60.43
62.165
212.8
48.651
272.85
105.93
165.977
47.365
29.16
180.99
124.004
110.52
140.47
54.898
137.23
75.881
57.963
93.193
76.945
54.153
137.45
56.55
134.68
78.341
85.301
84.912
83.105
506.33
302
131
182.57122
57.406
55.682
91.432
54.571
73.649
85.099
90.405
88.72
−7535.9
−5276.9
−5624
−15,420
−7289.5
−9548.9
−8685.9
−19,914.4
−4084.5
−2383.6
−12,060
−17,894.4
−14,045
−13,231
−5305.4
−10,620
−6910.6
−5901.5
−7001.5
−6729.8
−6041.8
−12,549
−5681.9
−6055.8
−8019.8
−8215.9
−6722.2
−6903.7
−37,483
−24,324
−11,143
−17,112.47062
−5702.8
−4439.3
−5141.7
−5561.5
−7258.2
−7615.9
−7955.2
−7741.2
C3
−12.348
−5.6572
−5.8595
−28.109
−3.4453
−40.089
−12.42
−18.9344
−3.6469
−1.1342
−22.839
−13.156
−11.861
−16.859
−4.7627
−17.908
−7.9499
−5.2048
−10.738
−8.179
−4.5383
−16.543
−4.9815
−19.415
−8.1458
−9.2166
−9.5157
−9.1858
−69.22
−40.13
−15.855
−22.1251
−5.0307
−5.0136
−10.981
−4.712
−7.3037
−9.3072
−10.086
−9.8693
C5
Tmin, K
P at Tmin
0.000009602
2.60E-17
2.06E-17
0.000021564
1.01E-18
6.37E-15
7.5583E-06
1.91E-18
1.80E-17
2
6
6
2
6
6
2
6
6
7.24E-17
1.18E-18
2.21E-18
6.5877E-06
1.43E-17
0.014506
4.4315E-06
9.13E-18
8.2308E-06
5.3017E-06
4.98E-18
7.1275E-06
1.24E-17
0.028619
3.8971E-06
4.7979E-06
7.2244E-06
6.4703E-06
0.000027381
0.000017403
8.1871E-06
1.13E-17
1.10E-17
1.97E-17
0.000014318
1.07E-17
4.1653E-06
5.5643E-06
5.9594E-06
0.000006077
6
6
6
2
6
1
2
6
2
2
6
2
6
1
2
2
2
2
2
2
2
6
6
6
2
6
2
2
2
2
180.25
142.61
159.95
213.15
388.85
186.35
242.54
460.85
197.67
223.15
289.95
700.15
329.35
279.01
164.65
237.38
176.99
373.96
234.94
178.18
236.5
267.76
158.45
156.08
247.79
229.33
165.78
172.22
398.4
354
247.57
288.45
180.35
173.15
119.36
178.35
273.16
225.3
247.98
286.41
2.11E-01
9.73E-03
6.51E-02
9.29E-05
1.17E+04
2.21E+05
1.06E+01
7.78E+02
1.67E+03
2.30E+05
2.09E+04
2.42E+05
4.14E-01
2.53E-01
1.96E-01
1.33E-01
1.54E-02
8.69E+04
1.86E+02
4.75E-02
4.47E+01
2.51E-01
1.06E-02
9.92E+00
3.71E+00
6.93E-01
1.71E-02
1.68E-02
8.50E+00
9.36E-01
4.08E-01
1.25E-01
7.06E-01
6.69E+01
1.92E-02
3.54E-01
6.11E+02
3.18E+00
2.18E+01
5.76E+02
C4
Tmax, K
538
517
536.6
626
683
259
636
838
430.75
318.69
490.85
883.6
857
693
540.15
720
631.95
568
579.35
591.75
602
675
535.15
433.25
664.5
649.1
543.8
573.5
846
828
639
703.9
519.13
454
432
543.15
647.1
617
630.3
616.2
P at Tmax
4.031E+06
4.752E+06
4.627E+06
6.041E+06
5.925E+06
3.748E+06
3.823E+06
5.001E+06
7.860E+06
3.771E+06
8.192E+06
3.487E+06
2.974E+06
1.569E+06
5.203E+06
3.624E+06
5.117E+06
2.871E+06
5.702E+06
4.080E+06
4.447E+06
1.679E+06
3.037E+06
4.102E+06
3.447E+06
3.211E+06
2.550E+06
2.812E+06
3.410E+06
3.019E+06
1.949E+06
2.119E+06
3.930E+06
4.887E+06
5.749E+06
3.058E+06
2.193E+07
3.528E+06
3.741E+06
3.501E+06
Vapor pressure Ps is calculated by Ps = exp(C1 + C2/T + C3 ln(T) + C4T C5) where Ps is in Pa and T is in K.
∗All substances and their numbers are listed by chemical family in Table 2-6 and by formula in Table 2-7.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016
AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts,
N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
VAPOR PRESSURES
TABLE 2-9
2-59
Vapor Pressures of Inorganic Compounds, up to 1 atm*
Compound
Pressure, mmHg
1
Name
Aluminum
borohydride
bromide
chloride
fluoride
iodide
oxide
Ammonia
heavy
Ammonium bromide
carbamate
chloride
cyanide
hydrogen sulfide
iodide
Antimony
tribromide
trichloride
pentachloride
triiodide
trioxide
Argon
Arsenic
Arsenic tribromide
trichloride
trifluoride
pentafluoride
trioxide
Arsine
Barium
Beryllium borohydride
bromide
chloride
iodide
Bismuth
tribromide
trichloride
Diborane hydrobromide
Borine carbonyl
triamine
Boron hydrides
dihydrodecaborane
dihydrodiborane
dihydropentaborane
tetrahydropentaborane
tetrahydrotetraborane
Boron tribromide
trichloride
trifluoride
Bromine
pentafluoride
Cadmium
chloride
fluoride
iodide
oxide
Calcium
Carbon (graphite)
dioxide
disulfide
monoxide
oxyselenide
oxysulfide
selenosulfide
subsulfide
tetrabromide
tetrachloride
tetrafluoride
Cesium
bromide
chloride
fluoride
iodide
5
10
20
Formula
Al
Al(BH4)3
AlBr3
Al2Cl6
AlF3
AlI3
Al2O3
NH3
ND3
NH4Br
N2H6CO2
NH4Cl
NH4CN
NH4HS
NH4I
Sb
SbBr3
SbCl3
SbCl5
SbI3
Sb4O6
A
As
AsBr3
AsCl3
AsF3
AsF5
As2O3
AsH3
Ba
Be(BH4)2
BeBr2
BeCl2
BeI2
Bi
BiBr3
BiCl3
B2H5Br
BH3CO
B3N3H6
B10H14
B2H6
B5H9
B5H11
B4H10
BBr3
BCl3
BF3
Br2
BrF5
Cd
CdCl2
CdF2
CdI2
CdO
Ca
C
CO2
CS2
CO
COSe
COS
CSeS
C3S2
CBr4
CCl4
CF4
Cs
CsBr
CsCl
CsF
CsI
40
60
100
200
400
760
Melting
point,
°C
1749
−3.9
176.1
152.0
1422
294.5
2665
−68.4
−67.4
320.0
26.7
271.5
−0.5
0.0
331.8
1223
203.5
143.3
114.1
303.5
957
−200.5
518
145.2
70.9
13.2
−84.3
332.5
−98.0
1301
58.6
405
411
411
1271
360
343
−29.0
−95.3
+4.0
1844
+11.2
199.8
161.8
1457
322.0
2766
−57.0
−57.0
345.3
37.2
293.2
+9.6
+10.5
355.8
1288
225.7
165.9
1947
28.1
227.0
171.6
1496
354.0
2874
−45.4
−45.4
370.8
48.0
316.5
20.5
21.8
381.0
1364
250.2
192.2
2056
45.9
256.3
180.2
1537
385.5
2977
−33.6
−33.4
396.0
58.3
337.8
31.7
33.3
404.9
1440
275.0
219.0
660
−64.
97.
192.4
1040
333.8
1085
−195.6
548
167.7
89.2
26.7
−75.5
370.0
−87.2
1403
69.0
427
435
435
1319
392
372
−15.4
−85.5
18.5
368.5
1242
−190.6
579
193.6
109.7
41.4
−64.0
412.2
−75.2
1518
79.7
451
461
461
1370
425
405
0.0
−74.8
34.3
401.0
1425
−185.6
610
220.0
130.4
56.3
−52.8
457.2
−62.1
1638
90.0
474
487
487
1420
461
441
+16.3
−64.0
50.6
142.3
−120.9
+9.6
20.1
−28.1
33.5
−32.4
−123.0
+9.3
−4.5
611
797
1486
640
1341
1207
4373
−100.2
−5.1
−205.7
−61.7
−85.9
28.3
109.9
119.7
23.0
−150.7
509
1072
1069
1025
1055
163.8
−111.2
24.6
34.8
−14.0
50.3
−18.9
−115.9
24.3
+9.9
658
847
1561
688
1409
1288
4516
−93.0
+10.4
−201.3
−49.8
−75.0
45.7
130.8
139.7
38.3
−143.6
561
1140
1139
1092
1124
−99.6
40.8
51.2
+0.8
70.0
−3.6
−108.3
41.0
25.7
711
908
1651
742
1484
1388
4660
−85.7
28.0
−196.3
−35.6
−62.7
65.2
−86.5
58.1
67.0
16.1
91.7
+12.7
−100.7
58.2
40.4
765
967
1751
796
1559
1487
4827
−78.2
46.5
−191.3
−21.9
−49.9
85.6
163.5
57.8
−135.5
624
1221
1217
1170
1200
189.5
76.7
−127.7
690
1300
1300
1251
1280
Temperature, °C
1284
81.3
100.0
1238
178.0
2148
−109.1
1421
−52.2
103.8
116.4
1298
207.7
2306
−97.5
1487
−42.9
118.0
123.8
1324
225.8
2385
−91.9
1555
−32.5
134.0
131.8
1350
244.2
2465
−85.8
1635
−20.9
150.6
139.9
1378
265.0
2549
−79.2
198.3
−26.1
160.4
−50.6
−51.1
210.9
886
93.9
49.2
22.7
163.6
574
−218.2
372
41.8
−11.4
234.5
−10.4
193.8
−35.7
−36.0
247.0
984
126.0
71.4
48.6
203.8
626
−213.9
416
70.6
+11.7
252.0
−2.9
209.8
−28.6
−28.7
263.5
1033
142.7
85.2
61.8
223.5
666
−210.9
437
85.2
+23.5
270.6
+5.3
226.1
−20.9
−20.8
282.8
1084
158.3
100.6
75.8
244.8
729
−207.9
459
101.3
36.0
−117.9
212.5
−142.6
−108.0
242.6
−130.8
984
19.8
325
328
322
1099
261
242
−75.3
−127.3
−45.0
−103.1
259.7
−124.7
1049
28.1
342
346
341
1136
282
264
−66.3
−121.1
−35.3
−98.0
279.2
−117.7
1120
36.8
361
365
361
1177
305
287
−56.4
−114.1
−25.0
290.0
14.0
245.0
−12.6
−12.3
302.8
1141
177.4
117.8
91.0
267.8
812
−204.9
483
118.7
50.0
−2.5
−92.4
299.2
−110.2
1195
46.2
379
384
382
1217
327
311
−45.4
−106.6
−13.2
1684
−13.4
161.7
145.4
1398
277.8
2599
−74.3
−74.0
303.8
19.6
256.2
−7.4
−7.0
316.0
1176
188.1
128.3
101.0
282.5
873
−202.9
498
130.0
58.7
+4.2
−88.5
310.3
−104.8
1240
51.7
390
395
394
1240
340
324
−38.2
−101.9
−5.8
3586
−134.3
−73.8
−222.0
−117.1
−132.4
−47.3
14.0
80.8
−149.5
−40.4
−29.9
−73.1
−20.4
−75.2
−145.4
−32.8
−51.0
455
618
1231
481
1100
926
3828
−124.4
−54.3
−217.2
−102.3
−119.8
−26.5
41.2
90.2
−144.3
−30.7
−19.9
−64.3
−10.1
−66.9
−141.3
−25.0
−41.9
484
656
1286
512
1149
983
3946
−119.5
−44.7
−215.0
−95.0
−113.3
−16.0
54.9
100.0
−138.5
−20.0
−9.2
−54.8
+1.5
−57.9
−136.4
−16.8
−32.0
516
695
1344
546
1200
1046
4069
−114.4
−34.3
−212.8
−86.3
−106.0
−4.4
69.3
−50.0
−184.6
279
748
744
712
738
−30.0
−174.1
341
838
837
798
828
−19.6
−169.3
375
887
884
844
873
−8.2
−164.3
409
938
934
893
923
117.4
−131.6
−8.0
+2.7
−44.3
14.0
−47.8
−131.0
−8.0
−21.0
553
736
1400
584
1257
1111
4196
−108.6
−22.5
−210.0
−76.4
−98.3
+8.6
85.6
96.3
+4.3
−158.8
449
993
989
947
976
127.8
−127.2
−0.4
10.2
−37.4
22.1
−41.2
−127.6
−0.6
−14.0
578
762
1436
608
1295
1152
4273
−104.8
−15.3
−208.1
−70.2
−93.0
17.0
96.0
106.3
12.3
−155.4
474
1026
1023
980
1009
+1.0
289
291
283
1021
−93.3
−139.2
−63.0
60.0
−159.7
−50.2
−90.9
−41.4
−91.5
−154.6
−48.7
−69.3
394
1112
416
1000
∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947).
2050
−77.7
−74.0
520
36
630.5
96.6
73.4
2.8
167
656
−189.2
814
−18
−5.9
−79.8
312.8
−116.3
850
123
490
405
488
271
218
230
−104.2
−137.0
−58.2
99.6
−169
−47.0
−119.9
−45
−107
−126.8
−7.3
−61.4
320.9
568
520
385
851
−57.5
−110.8
−205.0
−138.8
−75.2
+0.4
90.1
−22.6
−183.7
28.5
636
646
683
621
(Continued )
2-60
PHYSICAL AnD CHEMICAL DATA
TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued )
Compound
Pressure, mmHg
1
Name
Chlorine
fluoride
trifluoride
monoxide
dioxide
heptoxide
Chlorosulfonic acid
Chromium
carbonyl
oxychloride
Cobalt chloride
nitrosyl tricarbonyl
Columbium fluoride
Copper
Cuprous bromide
chloride
iodide
Cyanogen
bromide
chloride
fluoride
Deuterium cyanide
Fluorine
oxide
Germanium bromide
chloride
hydride
Trichlorogermane
Tetramethylgermane
Digermane
Trigermane
Gold
Helium
para-Hydrogen
Hydrogen bromide
chloride
cyanide
fluoride
iodide
oxide (water)
sulfide
disulfide
selenide
telluride
Iodine
heptafluoride
Iron
pentacarbonyl
Ferric chloride
Ferrous chloride
Krypton
Lead
bromide
chloride
fluoride
iodide
oxide
sulfide
Lithium
bromide
chloride
fluoride
iodide
Magnesium
chloride
Manganese
chloride
Mercury
Mercuric bromide
chloride
iodide
Molybdenum
hexafluoride
oxide
5
10
20
Formula
Cl2
ClF
ClF3
Cl2O
ClO2
Cl2O7
HSO3Cl
Cr
Cr(CO)6
CrO2Cl2
CoCl2
Co(CO)3NO
CbF5
Cu
Cu2Br2
Cu2Cl2
Cu2I2
C2N2
CNBr
CNCl
CNF
DCN
F2
F2O
GeBr4
GeCl4
GeH4
GeHCl3
Ge(CH3)4
Ge2H6
Ge3H8
Au
He
H2
HBr
HCl
HCN
H2F2
HI
H2O
H2S
HSSH
H2Se
H2Te
I2
IF7
Fe
Fe(CO)5
Fe2Cl6
FeCl2
Kr
Pb
PbBr2
PbCl2
PbF2
PbI2
PbO
PbS
Li
LiBr
LiCl
LiF
LiI
Mg
MgCl2
Mn
MnCl2
Hg
HgBr2
HgCl2
HgI2
Mo
MoF6
MoO3
40
60
100
200
400
760
Melting
point,
°C
−71.7
−120.8
−34.7
−39.4
−29.4
29.1
105.3
2139
108.0
58.0
843
29.0
148.5
2207
951
960
907
−51.8
22.6
−24.9
−97.0
−17.5
−202.7
−165.8
113.2
27.5
−120.3
26.5
−6.3
−20.3
47.9
2521
−270.3
−257.9
−97.7
−114.0
−17.8
−28.2
−72.1
51.6
−91.6
22.0
−74.2
−45.7
116.5
−31.9
2360
50.3
272.5
842
−171.8
1421
745
784
1080
701
1265
1108
1097
1076
1129
1425
993
909
1142
1792
960
261.7
237.8
237.0
261.8
4109
−8.0
955
−60.2
−114.4
−20.7
−26.5
−17.8
44.6
120.0
2243
121.8
75.2
904
44.4
172.2
2325
1052
1077
1018
−42.6
33.8
−14.1
−89.2
−5.4
−198.3
−159.0
135.4
44.4
−111.2
41.6
+8.8
−4.7
67.0
2657
−269.8
−256.3
−88.1
−105.2
−5.3
−13.2
−60.3
66.5
−82.3
35.3
−65.2
−32.4
137.3
−20.7
2475
68.0
285.0
897
−165.9
1519
796
833
1144
750
1330
1160
1178
1147
1203
1503
1049
967
1223
1900
1028
290.7
262.7
256.5
291.0
4322
+4.1
1014
−47.3
−107.0
−4.9
−12.5
−4.0
62.2
136.1
2361
137.2
95.2
974
62.0
198.0
2465
1189
1249
1158
−33.0
46.0
−2.3
−80.5
+10.0
−193.2
−151.9
161.6
63.8
−100.2
58.3
26.0
+13.3
88.6
2807
−269.3
−254.5
−78.0
−95.3
+10.2
+2.5
−48.3
83.0
−71.8
49.6
−53.6
−17.2
159.8
−8.3
2605
86.1
298.0
961
−159.0
1630
856
893
1219
807
1402
1221
1273
1226
1290
1591
1110
1034
1316
2029
1108
323.0
290.0
275.5
324.2
4553
17.2
1082
−33.8
−100.5
+11.5
+2.2
+11.1
78.8
151.0
2482
151.0
117.1
1050
80.0
225.0
2595
1355
1490
1336
−21.0
61.5
+13.1
−72.6
26.2
−187.9
−144.6
189.0
84.0
−88.9
75.0
44.0
31.5
110.8
2966
−268.6
−252.5
−66.5
−84.8
25.9
19.7
−35.1
100.0
−60.4
64.0
−41.1
−2.0
183.0
+4.0
2735
105.0
319.0
1026
−152.0
1744
914
954
1293
872
1472
1281
1372
1310
1382
1681
1171
1107
1418
2151
1190
357.0
319.0
304.0
354.0
4804
36.0
1151
−100.7
−145
−83
−116
−59
−91
−80
1615
Temperature, °C
−118.0
−98.5
−106.7
−143.4
−80.4
−81.6
−45.3
32.0
1616
36.0
−18.4
−23.8
53.5
1768
58.0
+3.2
1628
572
546
−95.8
−35.7
−76.7
−134.4
−68.9
−223.0
−196.1
−45.0
−163.0
−41.3
−73.2
−88.7
−36.9
1869
−271.7
−263.3
−138.8
−150.8
−71.0
−123.3
−17.3
−134.3
−43.2
−115.3
−96.4
38.7
−87.0
1787
194.0
−199.3
973
513
547
479
943
852
723
748
783
1047
723
621
778
1292
126.2
136.5
136.2
157.5
3102
−65.5
734
1795
666
645
610
−83.2
−18.3
−61.4
−123.8
−54.0
−216.9
−186.6
43.3
−24.9
−151.0
−22.3
−54.6
−69.8
−12.8
2059
−271.5
−261.9
−127.4
−140.7
−55.3
−74.7
−109.6
+1.2
−122.4
−24.4
−103.4
−82.4
62.2
−70.7
1957
−6.5
221.8
−191.3
1099
578
615
861
540
1039
928
838
840
880
1156
802
702
877
1434
736
164.8
165.3
166.0
189.2
3393
−49.0
785
−101.6
−139.0
−71.8
−73.1
−59.0
−13.2
64.0
1845
68.3
13.8
−93.3
−134.3
−62.3
−64.3
−51.2
−2.1
75.3
1928
79.5
25.7
86.3
1879
718
702
656
−76.8
−10.0
−53.8
−118.5
−46.7
−214.1
−182.3
56.8
−15.0
−145.3
−13.0
−45.2
−60.1
−0.9
2154
−271.3
−261.3
−121.8
−135.6
−47.7
−65.8
−102.3
11.2
−116.3
−15.2
−97.9
−75.4
73.2
−63.0
2039
+4.6
235.5
700
−187.2
1162
610
648
904
571
1085
975
881
888
932
1211
841
743
930
1505
778
184.0
179.8
180.2
204.5
3535
−40.8
814
−1.3
103.0
1970
777
766
716
−70.1
−1.0
−46.1
−112.8
−38.8
−211.0
−177.8
71.8
−4.1
−139.2
−3.0
−35.0
−49.9
+11.8
2256
−271.1
−260.4
−115.4
−130.0
−39.7
−56.0
−94.5
22.1
−109.7
−5.1
−91.8
−67.8
84.7
−54.5
2128
16.7
246.0
737
−182.9
1234
646
684
950
605
1134
1005
940
939
987
1270
883
789
988
1583
825
204.6
194.3
195.8
220.0
3690
−32.0
851
−84.5
−128.8
−51.3
−54.3
−42.8
+10.3
87.6
2013
91.2
38.5
770
+11.0
121.5
2067
844
838
786
−62.7
+8.6
−37.5
−106.4
−30.1
−207.7
−173.0
88.1
+8.0
−131.6
+8.8
−23.4
−38.2
26.3
2363
−270.7
−259.6
−108.3
−123.8
−30.9
−45.0
−85.6
34.0
−102.3
+6.0
−84.7
−59.1
97.5
−45.3
2224
30.3
256.8
779
−178.4
1309
686
725
1003
644
1189
1048
1003
994
1045
1333
927
838
1050
1666
879
228.8
211.5
212.5
238.2
3859
−22.1
892
−79.0
−125.3
−44.1
−48.0
−37.2
+18.2
95.2
2067
98.3
46.7
801
18.5
133.2
2127
887
886
836
−57.9
14.7
−32.1
−102.3
−24.7
−205.6
−170.0
98.8
16.2
−126.7
16.2
−16.2
−30.7
35.5
2431
−270.6
−258.9
−103.8
−119.6
−25.1
−37.9
−79.8
41.5
−97.9
12.8
−80.2
−53.7
105.4
−39.4
2283
39.1
263.7
805
−175.7
1358
711
750
1036
668
1222
1074
1042
1028
1081
1372
955
868
1088
1720
913
242.0
221.0
222.2
249.0
3964
−16.2
917
735
−11
75.5
1083
504
422
605
−34.4
58
−6.5
−12
−223
−223.9
26.1
−49.5
−165
−71.1
−88
−109
−105.6
1063
−259.1
−87.0
−114.3
−13.2
−83.7
−50.9
0.0
−85.5
−89.7
−64
−49.0
112.9
5.5
1535
−21
304
−156.7
327.5
373
501
855
402
890
1114
186
547
614
870
446
651
712
1260
650
−38.9
237
277
259
2622
17
795
VAPOR PRESSURES
TABLE 2-9
2-61
Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued )
Compound
Pressure, mmHg
1
Name
Neon
Nickel
carbonyl
chloride
Nitrogen
Nitric oxide
Nitrogen dioxide
Nitrogen pentoxide
Nitrous oxide
Nitrosyl chloride
fluoride
Osmium tetroxide (yellow)
(white)
Oxygen
Ozone
Phosgene
Phosphorus (yellow)
(violet)
tribromide
trichloride
pentachloride
Phosphine
Phosphonium bromide
chloride
iodide
Phosphorus trioxide
pentoxide
oxychloride
thiobromide
thiochloride
Platinum
Potassium
bromide
chloride
fluoride
hydroxide
iodide
Radon
Rhenium heptoxide
Rubidium
bromide
chloride
fluoride
iodide
Selenium
dioxide
hexafluoride
oxychloride
tetrachloride
Silicon
dioxide
tetrachloride
tetrafluoride
Trichlorofluorosilane
Iodosilane
Diiodosilane
Disiloxan
Trisilane
Trisilazane
Tetrasilane
Octachlorotrisilane
Hexachlorodisiloxane
Hexachlorodisilane
Tribromosilane
Trichlorosilane
Trifluorosilane
Dibromosilane
Difluorosilane
Monobromosilane
Monochlorosilane
Monofluorosilane
Tribromofluorosilane
Dichlorodifluorosilane
Trifluorobromosilane
5
10
20
Formula
Ne
Ni
Ni(CO)4
NiCl2
N2
NO
NO2
N2O5
N2O
NOCl
NOF
OsO4
OsO4
O2
O3
COCl2
P
P
PBr3
PCl3
PCl5
PH3
PH4Br
PH4Cl
PH4I
P4O6
P4O10
POCl3
PSBr3
PSCl3
Pt
K
KBr
KCl
KF
KOH
KI
Rn
Re2O7
Rb
RbBr
RbCl
RbF
RbI
Se
SeO2
SeF6
SeOCl2
SeCl4
Si
SiO2
SiCl4
SiF4
SiFCl3
SiH3I
SiH2I2
(SiH3)2O
Si3H8
(SiH3)3N
Si4H10
Si3Cl3
(SiCl3)2O
Si2Cl6
SiHBr3
SiHCl3
SiHF3
SiH2Br2
SiH2F2
SiH3Br
SiH3Cl
SiH3F
SiFBr3
SiF2Cl2
SiF3Br
40
60
100
200
400
760
Melting
point,
°C
−251.0
2364
−6.0
866
−209.7
−166.0
−14.7
7.4
−110.3
−46.3
−88.8
71.5
71.5
−198.8
−141.0
−35.6
197.3
349
103.6
21.0
117.0
−118.8
7.4
−52.0
29.3
108.3
510
47.4
126.3
63.8
3714
586
1137
1164
1245
1064
1080
−99.0
289.0
514
1114
1133
1168
1072
554
258.0
−73.9
118.0
147.5
2083
1969
+5.4
−113.3
−33.2
−4.4
79.4
−55.9
+1.6
−1.1
47.4
146.0
75.4
85.4
51.6
−16.4
−118.7
14.1
−107.3
−42.3
−68.5
−122.4
28.6
−70.3
−249.7
2473
+8.8
904
−205.6
−162.3
−5.0
15.6
−103.6
−34.0
−79.2
89.5
89.5
−194.0
−132.6
−22.3
222.7
370
125.2
37.6
131.3
−109.4
17.6
−44.0
39.9
129.0
532
65.0
141.8
82.0
3923
643
1212
1239
1323
1142
1152
−87.7
307.0
563
1186
1207
1239
1141
594
277.0
−64.8
134.6
161.0
2151
2053
21.0
−170.2
−19.3
+10.7
101.8
−43.5
17.8
+14.0
63.6
166.2
92.5
102.2
70.2
−1.8
−111.3
31.6
−98.3
−28.6
−57.0
−115.2
45.7
−58.0
−69.8
−248.1
2603
25.8
945
−200.9
−156.8
+8.0
24.4
−96.2
−20.3
−68.2
109.3
109.3
−188.8
−122.5
−7.6
251.0
391
149.7
56.9
147.2
−98.3
28.0
−35.4
51.6
150.3
556
84.3
157.8
102.3
4169
708
1297
1322
1411
1233
1238
−75.0
336.0
620
1267
1294
1322
1223
637
297.7
−55.2
151.7
176.4
2220
2141
38.4
−100.7
−4.0
27.9
125.5
−29.3
35.5
31.0
81.7
189.5
113.6
120.6
90.2
+14.5
−102.8
50.7
−87.6
−13.3
−44.5
−106.8
64.6
−45.0
−55.9
−246.0
2732
42.5
987
−195.8
−151.7
21.0
32.4
−85.5
−6.4
−56.0
130.0
130.0
−183.1
−111.1
+8.3
280.0
417
175.3
74.2
162.0
−87.5
38.3
−27.0
62.3
173.1
591
105.1
175.0
124.0
4407
774
1383
1407
1502
1327
1324
−61.8
362.4
679
1352
1381
1408
1304
680
317.0
−45.8
168.0
191.5
2287
2227
56.8
−94.8
+12.2
45.4
149.5
−15.4
53.1
48.7
100.0
211.4
135.6
139.0
111.8
31.8
−95.0
70.5
−77.8
+2.4
−30.4
−98.0
83.8
−31.8
−41.7
−248.7
1452
−25
1001
−210.0
−161
−9.3
30
−90.9
−64.5
−134
56
42
−218.7
−251
−104
44.1
590
−40
−111.8
Temperature, °C
−257.3
1810
−255.5
1979
−254.6
2057
−253.7
2143
671
−226.1
−184.5
−55.6
−36.8
−143.4
731
−221.3
−180.6
−42.7
−23.0
−133.4
759
−219.1
−178.2
−36.7
−16.7
−128.7
789
−216.8
−175.3
−30.4
−10.0
−124.0
−132.0
3.2
−5.6
−219.1
−180.4
−92.9
76.6
237
7.8
−51.6
55.5
−120.3
22.0
+15.6
−213.4
−168.6
−77.0
111.2
271
34.4
−31.5
74.0
−114.3
31.3
26.0
−210.6
−163.2
−69.3
128.0
287
47.8
−21.3
83.2
−107.8
41.0
37.4
−207.5
−157.2
−60.3
146.2
306
62.4
−10.2
92.5
−43.7
−91.0
−25.2
384
−28.5
−79.6
−9.0
39.7
424
50.0
−18.3
2730
341
795
821
885
719
745
−144.2
212.5
297
781
792
921
748
356
157.0
−118.6
34.8
74.0
1724
72.4
+4.6
3007
408
892
919
988
814
840
−132.4
237.5
358
876
887
982
839
413
187.7
−105.2
59.8
96.3
1835
−63.4
−144.0
−92.6
−44.1
−134.8
−76.4
−53.0
3.8
−95.8
−49.7
−49.9
−6.2
74.7
17.8
27.4
−8.0
−62.6
−142.7
−40.0
−136.0
−85.7
−104.3
−145.5
−25.4
−110.5
−21.2
−74.0
−1.1
53.0
442
2.0
83.6
16.1
3146
443
940
968
1039
863
887
−126.3
248.0
389
923
937
1016
884
442
202.5
−98.9
71.9
107.4
1888
1732
−34.4
−130.4
−68.3
−47.7
18.0
−88.2
−40.0
−40.4
+4.3
89.3
29.4
38.8
+3.4
−53.4
−138.2
−29.4
−130.4
−77.3
−97.7
−141.2
−15.1
−102.9
−13.3
−68.0
+7.3
67.8
462
13.6
95.5
29.0
3302
483
994
1020
1096
918
938
−119.2
261.0
422
975
990
1052
935
473
217.5
−92.3
84.2
118.1
1942
1798
−24.0
−125.9
−59.0
−33.4
34.1
−79.8
−29.0
−30.0
15.8
104.2
41.5
51.5
16.0
−43.8
−132.9
−18.0
−124.3
−68.3
−90.1
−136.3
−3.7
−94.5
−112.5
−68.9
−68.7
−27.7
46.3
−5.0
+4.0
−30.5
−80.7
−152.0
−60.9
−146.7
−117.8
−153.0
−46.1
−124.7
−252.6
2234
−23.0
821
−214.0
−171.7
−23.9
−2.9
−118.3
−60.2
−100.3
51.7
50.5
−204.1
−150.7
−50.3
166.7
323
79.0
+2.3
102.5
−129.4
−5.0
−61.5
16.1
84.0
481
27.3
108.0
42.7
3469
524
1050
1078
1156
976
995
−111.3
272.0
459
1031
1047
1096
991
506
234.1
−84.7
98.0
130.1
2000
1867
−12.1
−120.8
−48.8
−21.8
52.6
−70.4
−16.9
−18.5
28.4
121.5
55.2
65.3
30.0
−32.9
−127.3
−5.2
−117.6
−57.8
−81.8
−130.8
+9.2
−85.0
−251.9
2289
−15.9
840
−212.3
−168.9
−19.9
+1.8
−114.9
−54.2
−95.7
59.4
59.4
−201.9
−146.7
−44.0
179.8
334
89.8
10.2
108.3
−125.0
+0.3
−57.3
21.9
94.2
493
35.8
116.0
51.8
3574
550
1087
1115
1193
1013
1030
−106.2
280.0
482
1066
1084
1123
1026
527
244.6
−80.0
106.5
137.8
2036
1911
−4.8
−117.5
−42.2
−14.3
64.0
−64.2
−9.0
−11.0
36.6
132.0
63.8
73.9
39.2
−25.8
−123.7
+3.2
−113.3
−51.1
−76.0
−127.2
17.4
−78.6
−132.5
−28.5
22.5
569
2
38
−36.2
1755
62.3
730
790
880
380
723
−71
296
38.5
682
715
760
642
217
340
−34.7
8.5
1420
1710
−68.8
−90
−120.8
−57.0
−1.0
−144.2
−117.2
−105.7
−93.6
−33.2
−1.2
−73.5
−126.6
−131.4
−70.2
−93.9
−82.5
−139.7
−70.5
(Continued )
2-62
PHYSICAL AnD CHEMICAL DATA
TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Trifluorochlorosilane
Hexafluorodisilane
Dichlorofluorobromosilane
Dibromochlorofluorosilane
Silane
Disilane
Silver
chloride
iodide
Sodium
bromide
chloride
cyanide
fluoride
hydroxide
iodide
Strontium
Strontium oxide
Sulfur
monochloride
hexafluoride
Sulfuryl chloride
Sulfur dioxide
trioxide (α)
trioxide (β)
trioxide (γ)
Tellurium
chloride
fluoride
Thallium
Thallous bromide
chloride
iodide
Thionyl bromide
Thionyl chloride
Tin
Stannic bromide
Stannous chloride
Stannic chloride
iodide
hydride
Tin tetramethyl
trimethyl-ethyl
trimethyl-propyl
Titanium chloride
Tungsten
Tungsten hexafluoride
Uranium hexafluoride
Vanadyl trichloride
Xenon
Zinc
chloride
fluoride
diethyl
Zirconium bromide
chloride
iodide
1
5
10
20
Formula
SiF3Cl
Si2F6
SiFCl2Br
SiFClBr2
SiH4
Si2H6
Ag
AgCl
AgI
Na
NaBr
NaCl
NaCN
NaF
NaOH
NaI
Sr
SrO
S
S2Cl2
SF6
SO2Cl2
SO2
SO3
SO3
SO3
Te
TeCl4
TeF6
Tl
TlBr
TlCl
TlI
SOBr2
SOCl2
Sn
SnBr4
SnCl2
SnCl4
SnI4
SnH4
Sn(CH3)4
Sn(CH3)3⋅C2H5
Sn(CH3)3⋅C3H7
TiCl4
W
WF6
UF6
VOCl3
Xe
Zn
ZnCl2
ZnF2
Zn(C2H5)2
ZrBr4
ZrCl4
ZrI4
40
100
200
400
760
Melting
point,
°C
−108.2
−46.7
−29.0
−4.7
−146.3
−66.4
1795
1242
1152
662
1099
1169
1156
1403
1057
1039
1057
−101.7
−41.7
−19.5
+6.3
−140.5
−57.5
1865
1297
1210
701
1148
1220
1214
1455
1111
1083
1111
−91.7
−34.2
−3.2
23.0
−131.6
−44.6
1971
1379
1297
758
1220
1296
1302
1531
1192
1150
1192
−81.0
−26.4
+15.4
43.0
−122.0
−29.0
2090
1467
1400
823
1304
1379
1401
1617
1286
1225
1285
−70.0
−18.9
35.4
59.5
−111.5
−14.3
2212
1564
1506
892
1392
1465
1497
1704
1378
1304
1384
305.5
63.2
−96.8
+7.2
−54.6
+4.0
8.0
21.4
789
287
−73.8
1143
621
612
631
68.3
10.4
1903
116.2
467
43.5
234.2
−96.6
11.7
38.4
57.5
58.0
5007
−27.5
10.4
49.8
−137.7
700
584
1207
47.2
289
268
355
327.2
75.3
−90.9
17.8
−46.9
10.5
14.3
28.0
838
304
−67.9
1196
653
645
663
80.6
21.4
1968
131.0
493
54.7
254.2
−89.2
22.8
50.0
69.8
71.0
5168
−20.3
18.2
62.5
−132.8
736
610
1254
59.1
301
279
369
359.7
93.5
−82.3
33.7
−35.4
20.5
23.7
35.8
910
330
−57.3
1274
703
694
712
99.0
37.9
2063
152.8
533
72.0
283.5
−78.0
39.8
67.3
88.0
90.5
5403
−10.0
30.0
82.0
−125.4
788
648
1329
77.0
318
295
389
399.6
115.4
−72.6
51.3
−23.0
32.6
32.6
44.0
997
360
−48.2
1364
759
748
763
119.2
56.5
2169
177.7
577
92.1
315.5
−65.2
58.5
87.6
109.6
112.7
5666
+1.2
42.7
103.5
−117.1
844
689
1417
97.3
337
312
409
444.6
138.0
−63.5
69.2
−10.0
44.8
44.8
51.6
1087
392
−38.6
1457
819
807
823
139.5
75.4
2270
204.7
623
113.0
348.0
−52.3
78.0
108.8
131.7
136.0
5927
17.3
55.7
127.2
−108.0
907
732
1497
118.0
357
331
431
−142
−18.6
−112.3
−99.3
−185
−132.6
960.5
455
552
97.5
755
800
564
992
318
651
800
2430
112.8
−80
−50.2
−54.1
−73.2
16.8
32.3
62.1
452
224
−37.8
3035
460
430
440
−52.2
−104.5
231.9
31.0
246.8
−30.2
144.5
−149.9
60
Temperature, °C
−144.0
−81.0
−86.5
−65.2
−179.3
−114.8
1357
912
820
439
806
865
817
1077
739
767
2068
183.8
−7.4
−132.7
−95.5
−39.0
−34.0
−15.3
520
−111.3
825
440
−6.7
−52.9
1492
316
−22.7
−140.0
−51.3
−30.0
−12.0
−13.9
3990
−71.4
−38.8
−23.2
−168.5
487
428
970
−22.4
207
190
264
−133.0
−68.8
−68.4
−45.5
−168.6
−99.3
1500
1019
927
511
903
967
928
1186
843
857
847
2198
223.0
+15.7
−120.6
−35.1
−83.0
−23.7
−19.2
−2.0
605
−98.8
931
490
487
502
+18.4
−32.4
1634
58.3
366
−1.0
156.0
−125.8
−31.0
−7.6
+10.7
+9.4
4337
−56.5
−22.0
+0.2
−158.2
558
481
1055
0.0
237
217
297
−127.0
−63.1
−59.0
−35.6
−163.0
−91.4
1575
1074
983
549
952
1017
983
1240
897
903
898
2262
243.8
27.5
−114.7
−24.8
−76.8
−16.5
−12.3
+4.3
650
233
−92.4
983
522
517
531
31.0
−21.9
1703
72.7
391
+10.0
175.8
−118.5
−20.6
+3.8
21.8
21.3
4507
−49.2
−13.8
12.2
−152.8
593
508
1086
+11.7
250
230
311
−120.5
−57.0
−48.8
−24.5
−156.9
−82.7
1658
1134
1045
589
1005
1072
1046
1300
953
952
953
2333
264.7
40.0
−108.4
−13.4
−69.7
−9.1
−4.9
11.1
697
253
−86.0
1040
559
550
567
44.1
−10.5
1777
88.1
420
22.0
196.2
−111.2
−9.3
16.1
34.0
34.2
4690
−41.5
−5.2
26.6
−147.1
632
536
1129
24.2
266
243
329
−112.8
−50.6
−37.0
−12.0
−150.3
−72.8
1743
1200
1111
633
1063
1131
1115
1363
1017
1005
1018
2410
288.3
54.1
−101.5
−1.0
−60.5
−1.0
+3.2
17.9
753
273
−78.4
1103
598
589
607
58.8
+2.2
1855
105.5
450
35.2
218.8
−102.3
+3.5
30.0
48.5
48.4
4886
−33.0
+4.4
40.0
−141.2
673
566
1175
38.0
281
259
344
−30
3370
−0.5
69.2
−111.6
419.4
365
872
−28
450
437
499
VAPOR PRESSURES
2-63
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm*
Pressure, mmHg
Compound
1
Name
Formula
Acenaphthalene
Acetal
Acetaldehyde
Acetamide
Acetanilide
Acetic acid
anhydride
Acetone
Acetonitrile
Acetophenone
Acetyl chloride
Acetylene
Acridine
Acrolein (2-propenal)
Acrylic acid
Adipic acid
Allene (propadiene)
Allyl alcohol (propen-1-ol-3)
chloride (3-chloropropene)
isopropyl ether
isothiocyanate
n-propyl ether
4-Allylveratrole
iso-Amyl acetate
n-Amyl alcohol
iso-Amyl alcohol
sec-Amyl alcohol (2-pentanol)
tert-Amyl alcohol
sec-Amylbenzene
iso-Amyl benzoate
bromide (1-bromo-3-methylbutane)
n-butyrate
formate
iodide (1-iodo-3-methylbutane)
isobutyrate
Amyl isopropionate
iso-Amyl isovalerate
n-Amyl levulinate
iso-Amyl levulinate
nitrate
4-tert-Amylphenol
Anethole
Angelonitrile
Aniline
2-Anilinoethanol
Anisaldehyde
o-Anisidine (2-methoxyaniline)
Anthracene
Anthraquinone
Azelaic acid
Azelaldehyde
Azobenzene
Benzal chloride (α,α-Dichlorotoluene)
Benzaldehyde
Benzanthrone
Benzene
Benzenesulfonylchloride
Benzil
Benzoic acid
anhydride
Benzoin
Benzonitrile
Benzophenone
Benzotrichloride (α,α,α-Trichlorotoluene)
Benzotrifluoride (α,α,α-Trifluorotoluene)
Benzoyl bromide
chloride
nitrile
Benzyl acetate
alcohol
C12H10
C6H14O2
C2H4O
C2H5NO
C8H9NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C8H8O
C2H3OCl
C2H2
C13H9N
C3H4O
C3H4O2
C6H10O4
C3H4
C3H6O
C3H5Cl
C6H12O
C4H5NS
C6H12O
C11H14O2
C7H14O2
C5H12O
C5H12O
C5H12O
C5H12O
C11H16
C12H16O2
C5H11Br
C9H18O2
C6H12O2
C5H11I
C9H18O2
C8H16O2
C10H20O2
C10H18O3
C10H18O3
C5H11NO3
C11H16O
C10H12O
C5H7N
C6H7N
C8H11NO
C8H8O2
C7H9NO
C14H10
C14H8O2
C9H16O4
C9H18O
C12H10N2
C7H6Cl2
C7H6O
C17H10O
C6H6
C6H5ClO2S
C14H10O2
C7H6O2
C14H10O3
C14H12O2
C7H5N
C13H10O
C7H5Cl3
C7H5F3
C7H5BrO
C7H5ClO
C8H5NO
C9H10O2
C7H8O
5
10
20
114.8
−2.3
−65.1
92.0
146.6
+6.3
24.8
−40.5
−26.6
64.0
−35.0
−133.0
165.8
−46.0
27.3
191.0
−108.0
+0.2
−52.0
−23.1
+25.3
−18.2
113.9
+23.7
34.7
30.9
22.1
+7.2
55.8
104.5
+2.1
47.1
+5.4
+21.9
40.1
33.7
54.4
110.0
104.0
28.8
109.8
91.6
+15.0
57.9
134.3
102.6
88.0
173.5
219.4
210.4
58.4
135.7
64.0
50.1
274.5
−19.6
96.5
165.2
119.5
180.0
170.2
55.3
141.7
73.7
−10.3
75.4
59.1
71.7
73.4
80.8
131.2
+8.0
−56.8
105.0
162.0
17.5
36.0
−31.1
−16.3
78.0
−27.6
−128.2
184.0
−36.7
39.0
205.5
−101.0
10.5
−42.9
−12.9
38.3
−7.9
127.0
35.2
44.9
40.8
32.2
17.2
69.2
121.6
13.6
59.9
17.1
34.1
52.8
46.3
68.6
124.0
118.8
40.3
125.5
106.0
28.0
69.4
149.6
117.8
101.7
187.2
234.2
225.5
71.6
151.5
78.7
62.0
297.2
−11.5
112.0
183.0
132.1
198.0
188.1
69.2
157.6
87.6
−0.4
89.8
73.0
85.5
87.6
92.6
148.7
19.6
−47.8
120.0
180.0
29.9
48.3
−20.8
−5.0
92.4
−19.6
−122.8
203.5
−26.3
52.0
222.0
−93.4
21.7
−32.8
−1.8
52.1
+3.7
142.8
47.8
55.8
51.7
42.6
27.9
83.8
139.7
26.1
74.0
30.0
47.6
66.6
60.0
83.8
139.7
134.4
53.5
142.3
121.8
41.0
82.0
165.7
133.5
116.1
201.9
248.3
242.4
85.0
168.3
94.3
75.0
322.5
−2.6
129.0
202.8
146.7
218.0
207.0
83.4
175.8
102.7
12.2
105.4
87.6
100.2
102.3
105.8
40
60
100
200
400
760
197.5
50.1
−22.6
158.0
227.2
63.0
82.2
+7.7
27.0
133.6
+3.2
−107.9
256.0
+2.5
86.1
265.0
−72.5
50.0
−4.5
29.0
89.5
35.8
183.7
83.2
85.8
80.7
70.7
55.3
124.1
186.8
60.4
113.1
65.4
84.4
104.4
97.6
125.1
180.5
177.0
88.6
189.0
164.2
77.5
119.9
209.5
176.7
155.2
250.0
285.0
286.5
123.0
216.0
138.3
112.5
390.0
26.1
174.5
255.8
186.2
270.4
258.0
123.5
224.4
144.3
45.3
147.7
128.0
141.0
144.0
141.7
222.1
66.3
−10.0
178.3
250.5
80.0
100.0
22.7
43.7
154.2
16.1
−100.3
284.0
17.5
103.3
287.8
−61.3
64.5
10.4
44.3
108.0
52.6
204.0
101.3
102.0
95.8
85.7
69.7
145.2
210.2
78.7
133.2
83.2
103.8
124.2
117.3
146.1
203.1
198.1
106.7
213.0
186.1
96.3
140.1
230.6
199.0
175.3
279.0
314.6
309.6
142.1
240.0
160.7
131.7
426.5
42.2
198.0
283.5
205.8
299.1
284.4
144.1
249.8
165.6
62.5
169.2
149.5
161.3
165.5
160.0
250.0
84.0
+4.9
200.0
277.0
99.0
119.8
39.5
62.5
178.0
32.0
−92.0
314.3
34.5
122.0
312.5
−48.5
80.2
27.5
61.7
129.8
71.4
226.2
121.5
119.8
113.7
102.3
85.7
168.0
235.8
99.4
155.3
102.7
125.8
146.0
138.4
169.5
227.4
222.7
126.5
239.5
210.5
117.7
161.9
254.5
223.0
197.3
310.2
346.2
332.8
163.4
266.1
187.0
154.1
277.5
102.2
20.2
222.0
303.8
118.1
139.6
56.5
81.8
202.4
50.8
−84.0
346.0
52.5
141.0
337.5
−35.0
96.6
44.6
79.5
150.7
90.5
248.0
142.0
137.8
130.6
119.7
101.7
193.0
262.0
120.4
178.6
123.3
148.2
168.8
160.2
194.0
253.2
247.9
147.5
266.0
235.3
140.0
184.4
279.6
248.0
218.5
342.0
379.9
356.5
185.0
293.0
214.0
179.0
60.6
224.0
314.3
227.0
328.8
313.5
166.7
276.8
189.2
82.0
193.7
172.8
185.0
189.0
183.0
80.1
251.5
347.0
249.2
360.0
343.0
190.6
305.4
213.5
102.2
218.5
197.2
208.0
213.5
204.7
Temperature, °C
−23.0
−81.5
65.0
114.0
−17.2
1.7
−59.4
−47.0
37.1
−50.0
−142.9
129.4
−64.5
+3.5
159.5
−120.6
−20.0
−70.0
−43.7
−2.0
−39.0
85.0
0.0
+13.6
+10.0
+1.5
−12.9
29.0
72.0
−20.4
21.2
−17.5
−2.5
14.8
+8.5
27.0
81.3
75.6
+5.2
62.6
−8.0
34.8
104.0
73.2
61.0
145.0
190.0
178.3
33.3
103.5
35.4
26.2
225.0
−36.7
65.9
128.4
96.0
143.8
135.6
28.2
108.2
45.8
−32.0
47.0
32.1
44.5
45.0
58.0
168.2
31.9
−37.8
135.8
199.6
43.0
62.1
−9.4
+7.7
109.4
−10.4
−116.7
224.2
−15.0
66.2
240.5
−85.2
33.4
−21.2
+10.9
67.4
16.4
158.3
62.1
68.0
63.4
54.1
38.8
100.0
158.3
39.8
90.0
44.0
62.3
81.8
75.5
100.6
155.8
151.7
67.6
160.3
139.3
55.8
96.7
183.7
150.5
132.0
217.5
264.3
260.0
100.2
187.9
112.1
90.1
350.0
+7.6
147.7
224.5
162.6
239.8
227.6
99.6
195.7
119.8
25.7
122.6
103.8
116.6
119.6
119.8
181.2
39.8
−31.4
145.8
211.8
51.7
70.8
−2.0
15.9
119.8
−4.5
−112.8
238.7
−7.5
75.0
251.0
−78.8
40.3
−14.1
18.7
76.2
25.0
169.6
71.0
75.5
71.0
61.5
46.0
110.4
171.4
48.7
99.8
53.3
71.9
91.7
85.2
110.3
165.2
162.6
76.3
172.6
149.8
65.2
106.0
194.0
161.7
142.1
231.8
273.3
271.8
110.0
199.8
123.4
99.6
368.8
15.4
158.2
238.2
172.8
252.7
241.7
109.8
208.2
130.0
34.0
133.4
114.7
127.0
129.8
129.3
Melting
point,
°C
95
−123.5
81
113.5
16.7
−73
−94.6
−41
20.5
−112.0
−81.5
110.5
−87.7
14
152
−136
−129
−136.4
−80
−117.2
−11.9
93
22.5
−6.2
2.5
5.2
217.5
286
106.5
68
−16.1
−26
174
+5.5
14.5
95
121.7
42
132
−12.9
48.5
−21.2
−29.3
0
−0.5
33.5
−51.5
−15.3
∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947). For information on fuels see Hibbard, N.A.C.A. Research Mem.
E56I21, 1956. For methane see Johnson (ed.), WADD-TR-60-56, 1960.
(Continued )
2-64
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10
Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Benzylamine
Benzyl bromide (α-bromotoluene)
chloride (α-chlorotoluene)
cinnamate
Benzyldichlorosilane
Benzyl ethyl ether
phenyl ether
isothiocyanate
Biphenyl
1-Biphenyloxy-2,3-epoxypropane
d-Bornyl acetate
Bornyl n-butyrate
formate
isobutyrate
propionate
Brassidic acid
Bromoacetic acid
4-Bromoanisole
Bromobenzene
4-Bromobiphenyl
1-Bromo-2-butanol
1-Bromo-2-butanone
cis-1-Bromo-1-butene
trans-1-Bromo-1-butene
2-Bromo-1-butene
cis-2-Bromo-2-butene
trans-2-Bromo-2-butene
1,4-Bromochlorobenzene
1-Bromo-1-chloroethane
1-Bromo-2-chloroethane
2-Bromo-4,6-dichlorophenol
1-Bromo-4-ethyl benzene
(2-Bromoethyl)-benzene
2-Bromoethyl 2-chloroethyl ether
(2-Bromoethyl)-cyclohexane
1-Bromoethylene
Bromoform (tribromomethane)
1-Bromonaphthalene
2-Bromo-4-phenylphenol
3-Bromopyridine
2-Bromotoluene
3-Bromotoluene
4-Bromotoluene
3-Bromo-2,4,6-trichlorophenol
2-Bromo-1,4-xylene
1,2-Butadiene (methyl allene)
1,3-Butadiene
n-Butane
iso-Butane (2-methylpropane)
1,3-Butanediol
1,2,3-Butanetriol
1-Butene
cis-2-Butene
trans-2-Butene
3-Butenenitrile
iso-Butyl acetate
n-Butyl acrylate
alcohol
iso-Butyl alcohol
sec-Butyl alcohol
tert-Butyl alcohol
iso-Butyl amine
n-Butylbenzene
iso-Butylbenzene
sec-Butylbenzene
tert-Butylbenzene
iso-Butyl benzoate
n-Butyl bromide (1-bromobutane)
iso-Butyl n-butyrate
carbamate
Butyl carbitol (diethylene glycol
butyl ether)
n-Butyl chloride (1-chlorobutane)
iso-Butyl chloride
1
5
10
20
29.0
32.2
22.0
173.8
45.3
26.0
95.4
79.5
70.6
135.3
46.9
74.0
47.0
70.0
64.6
209.6
54.7
48.8
+2.9
98.0
23.7
+6.2
−44.0
−38.4
−47.3
−39.0
−45.0
32.0
−36.0
−28.8
84.0
30.4
48.0
36.5
38.7
−95.4
70.0
54.8
59.6
47.8
206.3
70.2
52.0
127.7
107.8
101.8
169.9
75.7
103.4
74.8
99.8
93.7
241.7
81.6
77.8
27.8
133.7
45.4
30.0
−23.2
−17.0
−27.0
−17.9
−24.1
59.5
−18.0
−7.0
115.6
42.5
76.2
63.2
66.6
−77.8
22.0
117.5
135.4
42.0
49.7
50.8
47.5
146.2
65.0
−72.7
−87.6
−85.7
−94.1
67.5
132.0
−89.4
−81.1
−84.0
+2.9
+1.4
+23.5
+20.0
+11.6
+7.2
−3.0
−31.0
48.8
40.5
44.2
39.0
93.6
−11.2
30.0
83.7
95.7
67.7
73.4
60.8
221.5
83.2
65.0
144.0
121.8
117.0
187.2
90.2
118.0
89.3
114.0
108.0
256.0
94.1
91.9
40.0
150.6
55.8
41.8
−12.8
−6.4
−16.8
−7.2
−13.8
72.7
−9.4
+4.1
130.8
74.0
90.5
76.3
80.5
−68.8
34.0
133.6
152.3
55.2
62.3
64.0
61.1
163.2
78.8
−64.2
−79.7
−77.8
−86.4
85.3
146.0
−81.6
−73.4
−76.3
14.1
12.8
35.5
30.2
21.7
16.9
+5.5
−21.0
62.0
53.7
57.0
51.7
108.6
−0.3
42.2
96.4
107.8
81.8
88.3
75.0
239.3
96.7
79.6
160.7
137.0
134.2
205.8
106.0
133.8
104.0
130.0
123.7
272.9
108.2
107.8
53.8
169.8
67.2
54.2
−1.4
+5.4
−5.3
+4.6
−2.4
87.8
0.0
16.0
147.7
90.2
105.8
90.8
95.8
−58.8
48.0
150.2
171.8
69.1
76.0
78.1
75.2
181.8
94.0
−54.9
−71.0
−68.9
−77.9
100.0
161.0
−73.0
−64.6
−67.5
26.6
25.5
48.6
41.5
32.4
27.3
14.3
−10.3
76.3
67.8
70.6
65.6
124.2
+11.6
56.1
110.1
120.5
97.3
104.8
90.7
255.8
111.8
95.4
180.1
153.0
152.5
226.3
123.7
150.7
121.2
147.2
140.4
290.0
124.0
125.0
68.6
190.8
79.5
68.2
+11.5
18.4
+7.2
17.7
+10.5
103.8
+10.4
29.7
165.8
108.5
123.2
106.6
113.0
−48.1
63.6
170.2
193.8
84.1
91.0
93.9
91.8
200.5
110.6
−44.3
−61.3
−59.1
−68.4
117.4
178.0
−63.4
−54.7
−57.6
40.0
39.2
63.4
53.4
44.1
38.1
24.5
+1.3
92.4
83.3
86.2
80.8
141.8
24.8
71.7
125.3
135.5
C4H9Cl
C4H9Cl
−49.0
−53.8
−28.9
−34.3
−18.6
−24.5
−7.4
−13.8
+5.0
−1.9
60
100
200
400
760
107.3
115.6
100.5
267.0
121.3
105.5
192.6
163.8
165.2
239.7
135.7
161.8
131.7
157.6
151.2
301.5
133.8
136.0
78.1
204.5
87.0
77.3
19.8
27.2
15.4
26.2
18.7
114.8
17.0
38.0
177.6
121.0
133.8
116.4
123.7
−41.2
73.4
183.5
207.0
94.1
100.0
104.1
102.3
213.0
121.6
−37.5
−55.1
−52.8
−62.4
127.5
188.0
−57.2
−48.4
−51.3
48.8
48.0
72.6
60.3
51.7
45.2
31.0
8.8
102.6
93.3
96.0
90.6
152.0
33.4
81.3
134.6
146.0
120.0
129.8
114.2
281.5
133.5
118.9
209.2
177.7
180.7
255.0
149.8
176.4
145.8
172.2
165.7
316.2
146.3
150.1
90.8
221.8
97.6
89.2
30.8
38.1
26.3
37.5
29.9
128.0
28.0
49.5
193.2
135.5
148.2
129.8
138.0
−31.9
85.9
198.8
224.5
107.8
112.0
117.8
116.4
229.3
135.7
−28.3
−46.8
−44.2
−54.1
141.2
202.5
−48.9
−39.8
−42.7
60.2
59.7
85.1
70.1
61.5
54.1
39.8
18.8
116.2
107.0
109.5
103.8
166.4
44.7
94.0
147.2
159.8
140.0
150.8
134.0
303.8
152.0
139.6
233.2
198.0
204.2
280.4
172.0
198.0
166.4
194.2
187.5
336.8
165.8
172.7
110.1
248.2
112.1
107.0
47.8
55.7
42.8
54.5
46.5
149.5
44.7
66.8
216.5
156.5
169.8
150.0
160.0
−17.2
106.1
224.2
251.0
127.7
133.6
138.0
137.4
253.0
156.4
−14.2
−33.9
−31.2
−41.5
161.0
222.0
−36.2
−26.8
−29.7
78.0
77.6
104.0
84.3
75.9
67.9
52.7
32.0
136.9
127.2
128.8
123.7
188.2
62.0
113.9
165.7
181.2
161.3
175.2
155.8
326.7
173.0
161.5
259.8
220.4
229.4
309.8
197.5
222.2
190.2
218.2
211.2
359.6
186.7
197.5
132.3
277.7
128.3
126.3
66.8
75.0
61.9
74.0
66.0
172.6
63.4
86.0
242.0
182.0
194.0
172.3
186.2
−1.1
127.9
252.0
280.2
150.0
157.3
160.0
160.2
278.0
181.0
+1.8
−19.3
−16.3
−27.1
183.8
243.5
−21.7
−12.0
−14.8
98.0
97.5
125.2
100.8
91.4
83.9
68.0
50.7
159.2
149.6
150.3
145.8
212.8
81.7
135.7
186.0
205.0
184.5
198.5
179.4
350.0
194.3
185.0
287.0
243.0
254.9
340.0
223.0
247.0
214.0
243.0
235.0
382.5
208.0
223.0
156.2
310.0
145.0
147.0
86.2
94.7
81.0
93.9
85.5
196.9
82.7
106.7
268.0
206.0
219.0
195.8
213.0
+15.8
150.5
281.1
311.0
173.4
181.8
183.7
184.5
305.8
206.7
18.5
−4.5
−0.5
−11.7
206.5
264.0
−6.3
+3.7
+0.9
119.0
118.0
147.4
117.5
108.0
99.5
82.9
68.6
183.1
172.8
173.5
168.5
237.0
101.6
156.9
206.5
231.2
13.0
+5.9
24.0
16.0
40.0
32.0
58.8
50.0
77.8
68.9
Temperature, °C
Formula
C7H9N
C7H7Br
C7H7Cl
C16H14O2
C7H8Cl2Si
C9H12O
C13H12O
C8H7NS
C12H10
C15H14O2
C12H20O2
C14H24O2
C11H18O2
C14H24O2
C13H22O2
C22H42O2
C2H3BrO2
C7H7BrO
C6H5Br
C12H9Br
C4H9BrO
C4H7BrO
C4H7Br
C4H7Br
C4H7Br
C4H7Br
C4H7Br
C6H4BrCl
C2H4BrCl
C2H4BrCl
C6H3BrCl2O
C8H9Br
C8H9Br
C4H8BrClO
C8H15Br
C2H3Br
CHBr3
C10H7Br
C12H9BrO
C5H4BrN
C7H7Br
C7H7Br
C7H7Br
C6H2BrCl3O
C8H9Br
C 4H 6
C 4H 6
C4H10
C4H10
C4H10O2
C4H10O3
C4H8
C4H8
C4H8
C4H5N
C6H12O2
C7H12O2
C4H10O
C4H10O
C4H10O
C4H10O
C4H11N
C10H14
C10H14
C10H14
C10H14
C11H14O2
C4H9Br
C8H16O2
C5H11NO2
C8H18O3
40
84.2
100.0
16.8
24.4
14.8
10.3
112.4
37.5
−89.0
−102.8
−101.5
−109.2
22.2
102.0
−104.8
−96.4
−99.4
−19.6
−21.2
−0.5
−1.2
−9.0
−12.2
−20.4
−50.0
22.7
14.1
18.6
13.0
64.0
−33.0
+4.6
Melting
point,
°C
−4
−39
39
69.5
29
61.5
49.5
12.5
−30.7
90.5
−100.3
−133.4
−111.2
−114.6
16.6
−16.6
68
−45.0
−138
8.5
5.5
95
−28
39.8
28.5
+9.5
−108.9
−135
−145
77
−130
−138.9
−105.4
−98.9
−64.6
−79.9
−108
−114.7
25.3
−85.0
−88.0
−51.5
−75.5
−58
−112.4
65
−123.1
−131.2
VAPOR PRESSURES
2-65
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Formula
sec-Butyl chloride (2-Chlorobutane)
tert-Butyl chloride
sec-Butyl chloroacetate
2-tert-Butyl-4-cresol
4-tert-Butyl-2-cresol
iso-Butyl dichloroacetate
2,3-Butylene glycol (2,3-butanediol)
2-Butyl-2-ethylbutane-1,3-diol
2-tert-Butyl-4-ethylphenol
n-Butyl formate
iso-Butyl formate
sec-Butyl formate
sec-Butyl glycolate
iso-Butyl iodide (1-iodo-2-methylpropane)
isobutyrate
isovalerate
levulinate
naphthylketone (1-isovaleronaphthone)
2-sec-Butylphenol
2-tert-Butylphenol
4-iso-Butylphenol
4-sec-Butylphenol
4-tert-Butylphenol
2-(4-tert-Butylphenoxy)ethyl acetate
4-tert-Butylphenyl dichlorophosphate
C4H9Cl
C4H9Cl
C6H11ClO2
C11H16O
C11H16O
C6H10Cl2O2
C4H10O2
C10H22O2
C12H15O
C5H10O2
C5H10O2
C5H10O2
C6H12O3
C4H9I
C8H16O2
C9H18O2
C9H16O3
C15H16O
C10H14O
C10H14O
C10H14O
C10H14O
C10H14O
C14H20O3
C10H13Cl2
O2P
C11H14O
C7H14O2
C12H18O
C12H18O
C12H18O
C12H18O
C4H8O2
C4H8O2
C4H7N
C11H14O
C10H16
C10H16O2
C10H16O
C10H19N
C10H20O
C10H20O2
C6H12O2
C6H12O2
C6H10O2
C6H11N
C8H18O
C8H16O
C8H16O2
C8H15N
C12H9N
CO2
CS2
CO
COSe
COS
CBr4
CCl4
CF4
C10H14O
C10H14O
C10H12O2
C2HCl3O
C2H3Cl3O2
C6Cl4O2
C2H3ClO2
C4H4Cl2O3
C6H6ClN
C6H6ClN
C6H6ClN
C6H5Cl
tert-Butyl phenyl ketone (pivalophenone)
iso-Butyl propionate
4-tert-Butyl-2,5-xylenol
4-tert-Butyl-2,6-xylenol
6-tert-Butyl-2,4-xylenol
6-tert-Butyl-3,4-xylenol
Butyric acid
iso-Butyric acid
Butyronitrile
iso-Valerophenone
Camphene
Campholenic acid
d-Camphor
Camphylamine
Capraldehyde
Capric acid
n-Caproic acid
iso-Caproic acid
iso-Caprolactone
Capronitrile
Capryl alcohol (2-octanol)
Caprylaldehyde
Caprylic acid (octanoic acid)
Caprylonitrile
Carbazole
Carbon dioxide
disulfide
monoxide
oxyselenide (carbonyl selenide)
oxysulfide (carbonyl sulfide)
tetrabromide
tetrachloride
tetrafluoride
Carvacrol
Carvone
Chavibetol
Chloral (trichloroacetaldehyde)
hydrate (trichloroacetaldehyde
hydrate)
Chloranil
Chloroacetic acid
anhydride
2-Chloroaniline
3-Chloroaniline
4-Chloroaniline
Chlorobenzene
2-Chlorobenzotrichloride
(2-α,α,α-tetrachlorotoluene)
C7H4Cl4
1
5
10
20
−60.2
−39.8
−29.2
−17.7
17.0
70.0
74.3
28.6
44.0
94.1
76.3
−26.4
−32.7
−34.4
28.3
−17.0
+4.1
16.0
65.0
136.0
57.4
56.6
72.1
71.4
70.0
118.0
96.0
41.8
98.0
103.7
54.3
68.4
122.6
106.2
−4.7
−11.4
−13.3
53.6
+5.8
28.0
41.2
92.1
167.9
86.0
84.2
100.9
100.5
99.2
150.0
129.6
54.6
112.0
118.0
67.5
80.3
136.8
121.0
+6.1
−0.8
−3.1
66.0
17.0
39.9
53.8
105.9
184.0
100.8
98.1
115.5
114.8
114.0
165.8
146.0
57.8
−2.3
88.2
74.0
70.3
83.9
25.5
14.7
−20.0
58.3
85.7
+20.9
119.8
103.9
100.2
113.6
49.8
39.3
+2.1
87.0
97.6
41.5
45.3
51.9
125.0
71.4
66.2
38.3
9.2
32.8
73.4
92.3
43.0
40
60
Melting
point,
°C
100
200
400
760
31.5
+14.6
124.1
187.8
197.8
139.2
145.6
212.0
200.3
67.9
60.0
56.8
135.5
81.0
106.3
124.8
181.8
269.7
179.7
173.8
192.1
194.3
191.5
250.3
240.0
50.0
32.6
146.0
210.0
221.8
160.0
164.0
233.5
223.8
86.2
79.0
75.2
155.6
100.3
126.3
146.4
205.5
294.0
203.8
196.3
214.7
217.6
214.0
277.6
268.2
68.0
51.0
167.8
232.6
247.0
183.0
182.0
255.0
247.8
106.0
98.2
93.6
177.5
120.4
147.5
168.7
229.9
320.0
228.0
219.5
237.0
242.1
238.0
304.4
299.0
Temperature, °C
68.2
127.2
134.0
81.4
93.4
151.2
137.0
18.0
+11.0
+8.4
79.8
29.8
52.4
67.7
120.2
201.6
116.1
113.0
130.3
130.3
129.5
183.3
164.0
−5.0
−19.0
83.6
143.9
150.8
96.7
107.8
167.8
154.0
31.6
24.1
21.3
94.2
42.8
67.2
82.7
136.2
219.7
133.4
129.2
147.2
147.8
146.0
201.5
184.3
+3.4
−11.4
93.0
153.7
161.7
106.6
116.3
178.0
165.4
39.8
32.4
29.6
104.0
51.8
75.9
92.4
147.0
231.5
143.9
140.0
157.0
157.9
156.0
212.8
197.2
14.2
−1.0
105.5
167.0
176.2
119.8
127.8
191.9
179.0
51.0
43.4
40.2
116.4
63.5
88.0
105.2
160.2
246.7
157.3
153.5
171.2
172.4
170.2
228.0
214.3
125.7
68.6
74.0
78.8
142.0
89.5
83.0
66.4
34.6
57.6
92.0
114.1
67.6
99.0
32.3
135.0
119.0
115.0
127.0
61.5
51.2
13.4
101.4
47.2
139.8
82.3
83.7
92.0
152.2
99.5
94.0
80.3
47.5
70.0
101.2
124.0
80.4
114.3
44.8
151.0
135.0
131.0
143.0
74.0
64.0
25.7
116.8
60.4
153.9
97.5
97.6
106.3
165.0
111.8
107.0
95.7
61.7
83.3
110.2
136.4
94.6
130.4
58.5
169.8
152.2
148.5
159.7
88.0
77.8
38.4
133.8
75.7
170.0
114.0
112.5
122.2
179.9
125.0
120.4
112.3
76.9
98.0
120.0
150.6
110.6
−134.3
−73.8
−222.0
−117.1
−132.4
−124.4
−54.3
−217.2
−102.3
−119.8
−119.5
−44.7
−215.0
−95.0
−113.3
−114.4
−34.3
−212.8
−86.3
−106.0
−50.0
−184.6
70.0
57.4
83.6
−37.8
−9.8
−30.0
−174.1
98.4
86.1
113.3
−16.0
+10.0
−19.6
−169.3
113.2
100.4
127.0
−5.0
19.5
−8.2
−164.3
127.9
116.1
143.2
+7.2
29.2
−108.6
−22.5
−210.0
−76.4
−98.3
96.3
+4.3
−158.8
145.2
133.0
159.8
20.2
39.7
140.8
67.6
180.3
163.6
158.2
170.0
96.5
86.3
47.3
144.6
85.0
180.0
124.0
122.0
132.0
189.8
133.3
129.6
123.2
86.8
107.4
126.0
160.0
121.2
248.2
−104.8
−15.3
−208.1
−70.2
−93.0
106.3
12.3
−155.4
155.3
143.8
170.7
29.1
46.2
154.0
79.5
195.0
176.0
172.0
184.0
108.0
98.0
59.0
158.0
97.9
193.7
138.0
134.6
145.3
200.0
144.0
141.4
137.2
99.8
119.8
133.9
172.2
134.8
265.0
−100.2
−5.1
−205.7
−61.7
−85.9
119.7
23.0
−150.7
169.7
157.3
185.5
40.2
55.0
70.7
43.0
67.2
46.3
63.5
59.3
−13.0
89.3
68.3
94.1
72.3
89.8
87.9
+10.6
97.8
81.0
108.0
84.8
102.0
102.1
22.2
106.4
94.2
122.4
99.2
116.7
117.8
35.3
116.1
109.2
138.2
115.6
133.6
135.0
49.7
122.0
118.3
148.0
125.7
144.1
145.8
58.3
129.5
130.7
159.8
139.5
158.0
159.9
70.7
140.3
149.0
177.8
160.0
179.5
182.3
89.4
151.3
169.0
197.0
183.7
203.5
206.6
110.0
162.6
189.5
217.0
208.8
228.5
230.5
132.2
290
61.2
46
0
−10.4
70.5
−45.2
69.0
101.8
117.9
135.8
155.0
167.8
185.0
208.0
233.0
262.1
28.7
175.0
197.7
220.0
97.0
116.4
136.8
217.5
241.3
265.3
196.0
217.8
239.8
192.3
214.2
236.5
204.5
226.7
249.5
125.5
144.5
163.5
115.8
134.5
154.5
76.7
96.8
117.5
180.1
204.2
228.0
117.5
138.7
160.5
212.7
234.0
256.0
157.9
182.0
209.2
153.0
173.8
195.0
164.8
186.3
208.5
217.1
240.3
268.4
160.8
181.0
202.0
158.3
181.0
207.7
157.8
182.1
207.0
119.7
141.0
163.7
138.0
157.5
178.5
145.4
156.5
168.5
190.3
213.9
237.5
155.2
179.5
204.5
292.5
323.0
354.8
−93.0 −85.7 −78.2
+10.4
28.0
46.5
−201.3 −196.3 −191.3
−49.8 −35.6 −21.9
−75.0 −62.7 −49.9
139.7
163.5
189.5
38.3
57.8
76.7
−143.6 −135.5 −127.7
191.2
213.8
237.0
179.6
203.5
227.5
206.8
229.8
254.0
57.8
77.5
97.7
68.0
82.1
96.2
−131.3
−26.5
22.5
−95.3
−90.7
−80.7
99
−71
−74
−47
50
178.5
31.5
−1.5
−35
−38.6
16
244.8
−57.5
−110.8
−205.0
−138.8
90.1
−22.6
−183.7
+0.5
−57
51.7
(Continued )
2-66
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
2-Chlorobenzotrifluoride
(2-chloro-α,α,α-trifluorotoluene)
2-Chlorobiphenyl
4-Chlorobiphenyl
α-Chlorocrotonic acid
Chlorodifluoromethane
Chlorodimethylphenylsilane
1-Chloro-2-ethoxybenzene
2-(2-Chloroethoxy) ethanol
bis-2-Chloroethyl acetacetal
1-Chloro-2-ethylbenzene
1-Chloro-3-ethylbenzene
1-Chloro-4-ethylbenzene
2-Chloroethyl chloroacetate
2-Chloroethyl 2-chloroisopropyl ether
2-Chloroethyl 2-chloropropyl ether
2-Chloroethyl α-methylbenzyl ether
Chloroform (trichloromethane)
1-Chloronaphthalene
4-Chlorophenethyl alcohol
2-Chlorophenol
3-Chlorophenol
4-Chlorophenol
2-Chloro-3-phenylphenol
2-Chloro-6-phenylphenol
Chloropicrin (trichloronitromethane)
1-Chloropropene
2-Chloropyridine
3-Chlorostyrene
4-Chlorostyrene
1-Chlorotetradecane
2-Chlorotoluene
3-Chlorotoluene
4-Chlorotoluene
Chlorotriethylsilane
1-Chloro-1,2,2-trifluoroethylene
Chlorotrifluoromethane
Chlorotrimethylsilane
trans-Cinnamic acid
Cinnamyl alcohol
Cinnamylaldehyde
Citraconic anhydride
cis-α-Citral
d-Citronellal
Citronellic acid
Citronellol
Citronellyl acetate
Coumarin
o-Cresol (2-cresol; 2-methylphenol)
m-Cresol (3-cresol; 3-methylphenol)
p-Cresol (4-cresol; 4-methylphenol)
cis-Crotonic acid
trans-Crotonic acid
cis-Crotononitrile
trans-Crotononitrile
Cumene
4-Cumidene
Cuminal
Cuminyl alcohol
2-Cyano-2-n-butyl acetate
Cyanogen
bromide
chloride
iodide
Cyclobutane
Cyclobutene
Cyclohexane
Cyclohexaneethanol
Cyclohexanol
Cyclohexanone
2-Cyclohexyl-4,6-dinitrophenol
Cyclopentane
Cyclopropane
Cymene
1
5
10
20
60
100
200
400
760
88.3
197.0
212.5
155.9
−76.4
124.7
141.8
139.5
150.7
110.0
113.6
116.0
140.0
115.8
125.6
164.8
10.4
180.4
188.1
106.0
143.0
150.0
237.0
237.1
53.8
−15.1
104.6
121.2
122.0
215.5
94.7
96.3
96.6
82.3
−66.7
−111.7
+6.0
232.4
177.8
177.7
145.4
160.0
140.1
195.4
159.8
161.0
216.5
127.4
138.0
140.0
116.3
128.0
50.1
62.8
88.1
158.0
160.0
176.2
133.8
−51.8
22.6
−24.9
97.6
−32.8
−41.2
25.5
142.7
103.7
90.4
229.0
−1.3
−70.0
110.8
108.3
219.6
237.8
173.8
−65.8
145.5
162.0
157.2
169.8
130.2
133.8
137.0
159.8
135.7
146.3
186.3
25.9
204.2
210.0
126.4
164.8
172.0
261.3
261.6
71.8
+1.3
125.0
142.2
143.5
240.3
115.0
116.6
117.1
101.6
−55.0
−102.5
21.9
253.3
199.8
199.3
165.8
181.8
160.0
214.5
179.8
178.8
240.0
146.7
157.3
157.3
133.9
146.0
68.0
81.1
107.3
180.0
182.8
197.9
152.2
−42.6
33.8
−14.1
111.5
−18.9
−27.8
42.0
161.7
121.7
110.3
248.7
+13.8
−59.1
131.4
130.0
243.8
264.5
193.2
−53.6
168.6
185.5
176.5
190.5
152.2
156.7
159.8
182.2
156.5
169.8
210.8
42.7
230.8
234.5
149.8
188.7
196.0
289.4
289.5
91.8
18.0
147.7
165.7
166.0
267.5
137.1
139.7
139.8
123.6
−41.7
−92.7
39.4
276.7
224.6
222.4
189.8
205.0
183.8
236.6
201.0
197.8
264.7
168.4
179.0
179.4
152.2
165.5
88.0
101.5
129.2
203.2
206.7
221.7
173.4
−33.0
46.0
−2.3
126.1
−3.4
−12.2
60.8
183.5
141.4
132.5
269.8
31.0
−46.9
153.5
152.2
267.5
292.9
212.0
−40.8
193.5
208.0
196.0
212.6
177.6
181.1
184.3
205.0
180.0
194.1
235.0
61.3
259.3
259.3
174.5
214.0
220.0
317.5
317.0
111.9
37.0
170.2
190.0
191.0
296.0
159.3
162.3
162.3
146.3
−27.9
−81.2
57.9
300.0
250.0
246.0
213.5
228.0
206.5
257.0
221.5
217.0
291.0
190.8
202.8
201.8
171.9
185.0
108.0
122.8
152.4
227.0
232.0
246.6
195.2
−21.0
61.5
+13.1
141.1
+12.9
+2.4
80.7
205.4
161.0
155.6
291.5
49.3
−33.5
177.2
Temperature, °C
Formula
C7H4ClF3
C12H9Cl
C12H9Cl
C4H5ClO2
CHClF2
C8H11ClSi
C8H9ClO
C4H9ClO2
C6H12Cl2O2
C8H9Cl
C8H9Cl
C8H9Cl
C4H6Cl2O2
C5H10Cl2O
C5H10Cl2O
C10H13ClO
CHCl3
C10H7Cl
C8H9ClO
C6H5ClO
C6H5ClO
C6H5ClO
C12H9ClO
C12H9ClO
CCl3NO2
C3H5Cl
C5H4ClN
C8H7Cl
C8H7Cl
C14H29Cl
C7H7Cl
C7H7Cl
C7H7Cl
C6H15ClSi
C2ClF3
CClF3
C3H9ClSi
C9H8O2
C9H10O
C9H8O
C5H4O3
C10H16O
C10H18O
C10H18O2
C10H20O
C12H22O2
C9H6O2
C7H8O
C7H8O
C7H8O
C4H6O2
C4H6O2
C4H5N
C4H5N
C9H12
C9H13N
C10H12O
C10H14O
C7H11NO2
C2N2
CBrN
CClN
CIN
C4H8
C4H6
C6H12
C8H16O
C6H12O
C6H10O
C12H14N2O5
C5H10
C3H6
C10H14
40
0.0
89.3
96.4
70.0
−122.8
29.8
45.8
53.0
56.2
17.2
18.6
19.2
46.0
24.7
29.8
62.3
−58.0
80.6
84.0
12.1
44.2
49.8
118.0
119.8
−25.5
−81.3
13.3
25.3
28.0
98.5
+5.4
+4.8
+5.5
−4.9
−116.0
−149.5
−62.8
127.5
72.6
76.1
47.1
61.7
44.0
99.5
66.4
74.7
106.0
38.2
52.0
53.0
33.5
24.7
109.8
129.8
95.6
−110.2
56.7
72.8
78.3
83.7
43.0
45.2
46.4
72.1
50.1
56.5
91.4
−39.1
104.8
114.3
38.2
72.0
78.2
152.2
153.7
−3.3
−63.4
38.8
51.3
54.5
131.8
30.6
30.3
31.0
+19.8
−102.5
−139.2
−43.6
157.8
102.5
105.8
74.8
90.0
71.4
127.3
93.6
100.2
137.8
64.0
76.0
76.5
57.4
−29.0
−19.5
+2.9
60.0
58.0
74.2
42.0
−95.8
−35.7
−76.7
25.2
−92.0
−99.1
−45.3
50.4
21.0
+1.4
132.8
−68.0
−116.8
17.3
−7.1
+3.5
26.8
88.2
87.3
103.7
68.7
−83.2
−18.3
−61.4
47.2
−76.0
−83.4
−25.4
77.2
44.0
26.4
161.8
−49.6
−104.2
43.9
37.1
134.7
146.0
108.0
−103.7
70.0
86.5
90.7
97.6
56.1
58.1
60.0
86.0
63.0
70.0
106.0
−29.7
118.6
129.0
51.2
86.1
92.2
169.7
170.7
+7.8
−54.1
51.7
65.2
67.5
148.2
43.2
43.2
43.8
32.0
−95.9
−134.1
−34.0
173.0
117.8
120.0
88.9
103.9
84.8
141.4
107.0
113.0
153.4
76.7
87.8
88.6
69.0
80.0
+4.0
15.0
38.3
102.2
102.0
118.0
82.0
−76.8
−10.0
−53.8
57.7
−67.9
−75.4
−15.9
90.0
56.0
38.7
175.9
−40.4
−97.5
57.0
50.6
151.2
164.0
121.2
−96.5
84.7
101.5
104.1
112.2
70.3
73.0
75.5
100.0
77.2
84.8
121.8
−19.0
134.4
145.0
65.9
101.7
108.1
186.7
189.8
20.0
−44.0
65.8
80.0
82.0
166.2
56.9
57.4
57.8
45.5
−88.2
−128.5
−23.2
189.5
133.7
135.7
103.8
119.4
99.8
155.6
121.5
126.0
170.0
90.5
101.4
102.3
82.0
93.0
16.4
27.8
51.5
117.8
117.9
133.8
96.2
−70.1
−1.0
−46.1
68.6
−58.7
−66.6
−5.0
104.0
68.8
52.5
191.2
−30.1
−90.3
71.1
65.9
169.9
183.8
135.6
−88.6
101.2
117.8
118.4
127.8
86.2
89.2
91.8
116.0
92.4
101.5
139.6
−7.1
153.2
162.0
82.0
118.0
125.0
207.4
208.2
33.8
−32.7
81.7
96.5
98.0
187.0
72.0
73.0
73.5
60.2
−79.7
−121.9
−11.4
207.1
151.0
152.2
120.3
135.9
116.1
171.9
137.2
140.5
189.0
105.8
116.0
117.7
96.0
107.8
30.0
41.8
66.1
134.2
135.2
150.3
111.8
−62.7
+8.6
−37.5
80.3
−48.4
−56.4
+6.7
119.8
83.0
67.8
206.7
−18.6
−82.3
87.0
75.4
182.1
196.0
144.4
−83.4
111.5
127.8
127.5
138.0
96.4
99.6
102.0
126.2
102.2
111.8
150.0
+0.5
165.6
173.5
92.0
129.4
136.1
219.6
220.0
42.3
−25.1
91.6
107.2
108.5
199.8
81.8
83.2
83.3
69.5
−74.1
−117.3
−4.0
217.8
162.0
163.7
131.3
146.3
126.2
182.1
147.2
149.7
200.5
115.5
125.8
127.0
104.5
116.7
38.5
50.9
75.4
145.0
146.0
161.7
121.5
−57.9
14.7
−32.1
88.0
−41.8
−50.0
14.7
129.8
91.8
77.5
216.0
−11.3
−77.0
97.2
Melting
point,
°C
−6.0
34
75.5
−160
−80.2
−53.3
−62.6
−63.5
−20
7
32.5
42
+6
−64
−99.0
−15.0
+0.9
+7.3
−157.5
133
33
−7.5
70
30.8
10.9
35.5
15.5
72
−96.0
−34.4
58
−6.5
−50
+6.6
23.9
−45.0
−93.7
−126.6
−68.2
VAPOR PRESSURES
2-67
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
cis-Decalin
trans-Decalin
Decane
Decan-2-one
1-Decene
Decyl alcohol
Decyltrimethylsilane
Dehydroacetic acid
Desoxybenzoin
Diacetamide
Diacetylene (1,3-butadiyne)
Diallyldichlorosilane
Diallyl sulfide
Diisoamyl ether
oxalate
sulfide
Dibenzylamine
Dibenzyl ketone (1,3-diphenyl2-propanone)
1,4-Dibromobenzene
1,2-Dibromobutane
dl-2,3-Dibromobutane
meso-2,3-Dibromobutane
1,2-Dibromodecane
Di(2-bromoethyl) ether
α,β-Dibromomaleic anhydride
1,2-Dibromo-2-methylpropane
1,3-Dibromo-2-methylpropane
1,2-Dibromopentane
1,2-Dibromopropane
1,3-Dibromopropane
2,3-Dibromopropene
2,3-Dibromo-1-propanol
Diisobutylamine
2,6-Ditert-butyl-4-cresol
4,6-Ditert-butyl-2-cresol
4,6-Ditert-butyl-3-cresol
2,6-Ditert-butyl-4-ethylphenol
4,6-Ditert-butyl-3-ethylphenol
Diisobutyl oxalate
2,4-Ditert-butylphenol
Dibutyl phthalate
sulfide
Diisobutyl d-tartrate
Dicarvacryl-mono-(6-chloro-2-xenyl)
phosphate
Dicarvacryl-2-tolyl phosphate
Dichloroacetic acid
1,2-Dichlorobenzene
1,3-Dichlorobenzene
1,4-Dichlorobenzene
1,2-Dichlorobutane
2,3-Dichlorobutane
1,2-Dichloro-1,2-difluoroethylene
Dichlorodifluoromethane
Dichlorodiphenyl silane
Dichlorodiisopropyl ether
Di(2-chloroethoxy) methane
Dichloroethoxymethylsilane
1,2-Dichloro-3-ethylbenzene
1,2-Dichloro-4-ethylbenzene
1,4-Dichloro-2-ethylbenzene
cis-1,2-Dichloroethylene
trans-1,2-Dichloro ethylene
Di(2-chloroethyl) ether
Dichlorofluoromethane
1,5-Dichlorohexamethyltrisiloxane
Dichloromethylphenylsilane
1,1-Dichloro-2-methylpropane
1,2-Dichloro-2-methylpropane
1,3-Dichloro-2-methylpropane
2,4-Dichlorophenol
2,6-Dichlorophenol
1
5
10
20
40
C10H18
C10H18
C10H22
C10H20O
C10H20
C10H22O
C13H30Si
C8H8O4
C14H12O
C4H7NO2
C4H2
C6H10Cl2Si
C6H10S
C10H22O
C12H22O4
C10H22S
C14H15N
C15H14O
22.5
−0.8
16.5
44.2
14.7
69.5
67.4
91.7
123.3
70.0
−82.5
+9.5
−9.5
18.6
85.4
43.0
118.3
125.5
50.1
+30.6
42.3
71.9
40.3
97.3
96.4
122.0
156.2
95.0
−68.0
34.8
+14.4
44.3
116.0
73.0
149.8
159.8
64.2
47.2
55.7
85.8
53.7
111.3
111.0
137.3
173.5
108.0
−61.2
47.4
26.6
57.0
131.4
87.6
165.6
177.6
79.8
65.3
69.8
100.7
67.8
125.8
126.5
153.0
192.0
122.6
−53.8
61.3
39.7
70.7
147.7
102.7
182.2
195.7
97.2
85.7
85.5
117.1
83.3
142.1
144.0
171.0
212.0
138.2
−45.9
76.4
54.2
86.3
165.7
120.0
200.2
216.6
C6H4Br2
C4H8Br2
C4H8Br2
C4H8Br2
C10H20Br2
C4H8Br2O
C4H2Br2O3
C4H8Br2
C4H8Br2
C5H10Br2
C3H6Br2
C3H6Br2
C3H4Br2
C3H6Br2O
C8H19N
C15H24O
C15H24O
C15H24O
C16H26O
C16H26O
C10H18O4
C14H22O
C16H22O4
C8H18S
C12H22O6
C32H34ClO4P
61.0
7.5
+5.0
+1.5
95.7
47.7
50.0
−28.8
14.0
19.8
−7.0
+9.7
−6.0
57.0
−5.1
85.8
86.2
103.7
89.1
111.5
63.2
84.5
148.2
+21.7
117.8
204.2
79.3
33.2
30.0
26.6
123.6
75.3
78.0
−3.0
40.0
45.4
+17.3
35.4
+17.9
84.5
+18.4
116.2
117.3
135.2
121.4
142.6
91.2
115.4
182.1
51.8
151.8
234.5
87.7
46.1
41.6
39.3
137.3
88.5
92.0
+10.5
53.0
58.0
29.4
48.0
30.0
98.2
30.6
131.0
132.4
150.0
137.0
157.4
105.3
130.0
198.2
66.4
169.0
249.3
103.6
60.0
56.4
53.2
151.0
103.6
106.7
25.7
67.5
72.0
42.3
62.1
43.2
113.5
43.7
147.0
149.0
167.0
154.0
174.0
120.3
146.0
216.2
80.5
188.0
264.5
C27H33O4P
C2H2Cl2O2
C6H4Cl2
C6H4Cl2
C6H4Cl2
C4H8Cl2
C4H8Cl2
C2Cl2F2
CCl2F2
C12H10Cl2Si
C6H12Cl2O
C5H10Cl2O2
C8H8Cl2OSi
C8H8Cl2
C8H8Cl2
C8H8Cl2
C2H2Cl2
C2H2Cl2
C4H8Cl2O
CHCl2F
C6H18Cl2
O2Si3
C7H8Cl2Si
C4H8Cl2
C4H8Cl2
C4H8Cl2
C6H4Cl2O
C6H4Cl2O
180.2
44.0
20.0
12.1
209.3
69.8
46.0
39.0
−23.6
−25.2
−82.0
−118.5
109.6
29.6
53.0
−33.8
46.0
47.0
38.5
−58.4
−65.4
23.5
−91.3
26.0
−0.3
−3.0
−65.6
−104.6
142.4
55.2
80.4
−12.1
75.0
77.2
68.0
−39.2
−47.2
49.3
−75.5
52.0
221.8
82.6
59.1
52.0
54.8
+11.5
+8.5
−57.3
−97.8
158.0
68.2
94.0
−1.3
90.0
92.3
83.2
−29.9
−38.0
62.0
−67.5
65.1
35.7
−31.0
−25.8
−3.0
53.0
59.5
63.5
−8.4
−4.2
+20.6
80.0
87.6
77.4
+2.6
+6.7
32.0
92.8
101.0
60
Melting
point,
°C
100
200
400
760
108.0
98.4
95.5
127.8
93.5
152.0
154.3
181.5
224.5
148.0
−41.0
86.3
63.7
96.0
177.0
130.6
212.2
229.4
123.2
114.6
108.6
142.0
106.5
165.8
169.5
197.5
241.3
160.6
−34.0
99.7
75.8
109.6
192.2
145.3
227.3
246.6
145.4
136.2
128.4
163.2
126.7
186.2
191.0
219.5
265.2
180.8
−20.9
119.4
94.8
129.0
215.0
166.4
249.8
272.3
169.9
160.1
150.6
186.7
149.2
208.8
215.5
244.5
293.0
202.0
−6.1
142.0
116.1
150.3
240.0
191.0
274.3
301.7
194.6
186.7
174.1
211.0
172.0
231.0
240.0
269.0
321.0
223.0
+9.7
165.3
138.6
173.4
265.0
216.0
300.0
330.5
120.8
76.0
72.0
68.0
167.4
119.8
123.5
42.3
83.5
87.4
57.2
77.8
57.8
129.8
57.8
164.1
167.4
185.3
172.1
192.3
137.5
164.3
235.8
96.0
208.5
280.5
131.6
86.0
82.0
78.0
177.5
130.0
133.8
53.7
93.7
97.4
66.4
87.8
67.0
140.0
67.0
175.2
179.0
196.1
183.9
204.4
147.8
175.8
247.8
105.8
221.6
290.7
146.5
99.8
95.3
91.7
190.2
144.0
147.7
68.8
107.4
110.1
78.7
101.3
79.5
153.0
79.2
190.0
194.0
211.0
198.0
218.0
161.8
190.0
263.7
118.6
239.5
304.9
168.5
120.2
115.7
111.8
209.6
165.0
168.0
92.1
117.8
130.2
97.8
121.7
98.0
173.8
97.6
212.8
217.5
233.0
220.0
241.7
183.5
212.5
287.0
138.0
264.7
323.8
192.5
143.5
138.0
134.2
229.8
188.0
192.0
119.8
150.6
151.8
118.5
144.1
119.5
196.0
118.0
237.6
243.4
257.1
244.0
264.6
205.8
237.0
313.5
159.0
294.0
342.0
218.6
166.3
160.5
157.3
250.4
212.5
215.0
149.0
174.6
175.0
141.6
167.5
141.2
219.0
139.5
262.5
269.3
282.0
268.6
290.0
229.5
260.8
340.0
182.0
324.0
361.0
237.0
96.3
73.4
66.2
69.2
24.5
21.2
−48.3
−90.1
176.0
82.2
109.5
+11.3
105.9
109.6
99.8
−19.4
−28.0
76.0
−58.6
79.0
251.5
111.8
89.4
82.0
84.8
37.7
35.0
−38.2
−81.6
195.5
97.3
125.5
24.4
123.8
127.5
118.0
−7.9
−17.0
91.5
−48.8
94.8
260.3
121.5
99.5
92.2
95.2
47.8
43.9
−31.8
−76.1
207.5
106.9
135.8
32.6
135.0
139.0
129.0
−0.5
−10.0
101.5
−42.6
105.0
272.5
134.0
112.9
105.0
108.4
60.2
56.0
−23.0
−68.6
223.8
119.7
149.6
44.1
149.8
153.3
144.0
+9.5
−0.2
114.5
−33.9
118.2
290.0
152.3
133.4
125.9
128.3
79.7
74.0
−10.0
−57.0
248.0
139.0
170.0
61.0
172.0
176.0
166.2
24.6
+14.3
134.0
−20.9
138.3
309.8
173.7
155.8
149.0
150.2
100.8
94.2
+5.0
−43.9
275.5
159.8
192.0
80.3
197.0
201.7
191.5
41.0
30.8
155.4
−6.2
160.2
330.0
194.4
179.0
173.0
173.9
123.5
116.0
20.9
−29.8
304.0
182.7
215.0
100.6
222.1
226.6
216.3
59.0
47.8
178.5
+8.9
184.0
92.4
14.6
18.7
44.8
107.7
115.5
109.5
28.2
32.0
58.6
123.4
131.6
120.0
37.0
40.2
67.5
133.5
141.8
134.2
48.2
51.7
78.8
146.0
154.6
155.5
65.8
68.9
96.1
165.2
175.5
180.2
85.4
87.8
115.4
187.5
197.7
205.5
106.0
108.0
135.0
210.0
220.0
Temperature, °C
Formula
−43.3
−30.7
−29.7
+3.5
+7
60
78.5
−34.9
−83
−26
34.5
87.5
−64.5
−34.5
−70.3
−55.5
−34.4
−70
−79.7
73.5
9.7
−17.6
−24.2
53.0
−80.4
−112
−40.8
−76.4
−61.2
−80.5
−50.0
−135
−53.0
45.0
(Continued )
2-68
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
α,α-Dichlorophenylacetonitrile
Dichlorophenylarsine
1,2-Dichloropropane
2,3-Dichlorostyrene
2,4-Dichlorostyrene
2,5-Dichlorostyrene
2,6-Dichlorostyrene
3,4-Dichlorostyrene
3,5-Dichlorostyrene
1,2-Dichlorotetraethylbenzene
1,4-Dichlorotetraethylbenzene
1,2-Dichloro-1,1,2,2-tetrafluoroethane
Dichloro-4-tolylsilane
3,4-Dichloro-α,α,α-trifluorotoluene
Dicyclopentadiene
Diethoxydimethylsilane
Diethoxydiphenylsilane
Diethyl adipate
Diethylamine
N-Diethylaniline
Diethyl arsanilate
1,2-Diethylbenzene
1,3-Diethylbenzene
1,4-Diethylbenzene
Diethyl carbonate
cis-Diethyl citraconate
Diethyl dioxosuccinate
Diethylene glycol
Diethyleneglycol-bis-chloroacetate
Diethylene glycol dimethyl ether
Di(2-methoxyethyl) ether
glycol ethyl ether
Diethyl ether
ethylmalonate
fumarate
glutarate
Diethylhexadecylamine
Diethyl itaconate
ketone (3-pentanone)
malate
maleate
malonate
mesaconate
oxalate
phthalate
sebacate
2,5-Diethylstyrene
Diethyl succinate
isosuccinate
sulfate
sulfide
sulfite
d-Diethyl tartrate
dl-Diethyl tartrate
3,5-Diethyltoluene
Diethylzinc
1-Dihydrocarvone
Dihydrocitronellol
1,4-Dihydroxyanthraquinone
Dimethylacetylene (2-butyne)
Dimethylamine
N,N-Dimethylaniline
Dimethyl arsanilate
Di(α-methylbenzyl) ether
2,2-Dimethylbutane
2,3-Dimethylbutane
Dimethyl citraconate
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
trans-1,3-Dimethylcyclohexane
cis-1,3-Dimethylcyclohexane
cis-1,4-Dimethylcyclohexane
trans-1,4-Dimethylcyclohexane
1
5
10
20
40
C8H5Cl2N
C6H5AsCl2
C3H6Cl2
C8H6Cl2
C8H6Cl2
C8H6Cl2
C8H6Cl2
C8H6Cl2
C8H6Cl2
C14H20Cl2
C14H20Cl2
C2Cl2F4
C7H8Cl2Si
C7H3Cl2F3
C10H8
C6H16O2Si
C16H20O2Si
C10H18O4
C4H11N
C10H15N
C10H16As
NO3
C10H14
C10H14
C10H14
C5H10O3
C9H14O4
C8H10O6
C4H10O3
C8H12Cl2O5
56.0
61.8
−38.5
61.0
53.5
55.5
47.8
57.2
53.5
105.6
91.7
−95.4
46.2
11.0
−19.1
111.5
74.0
84.0
100.0
−17.0
90.1
82.2
83.9
75.7
86.0
82.2
138.7
126.1
−80.0
71.7
38.3
34.1
+2.4
142.8
106.6
49.7
78.0
98.1
116.0
−6.1
104.6
97.4
98.2
90.0
100.4
97.4
155.0
143.8
−72.3
84.2
52.2
47.6
13.3
157.6
123.0
−33.0
91.9
113.8
133.1
+6.0
120.5
111.8
114.0
105.5
116.2
111.8
172.5
162.0
−63.5
97.8
67.3
62.0
25.3
174.3
138.3
−22.6
107.2
130.0
151.0
19.4
137.8
129.2
131.0
122.4
133.7
129.2
192.2
183.2
−53.7
113.2
84.0
77.9
38.0
193.2
154.6
−11.3
123.6
38.0
22.3
20.7
20.7
−10.1
59.8
70.0
91.8
148.3
62.6
48.7
46.8
47.1
+12.3
88.3
98.0
120.0
180.0
74.8
62.0
59.9
60.3
23.8
103.0
112.0
133.8
195.8
88.0
76.4
74.5
74.7
36.0
118.2
126.8
148.0
212.0
C6H14O3
C6H14O3
C4H10O
C9H16O4
C8H12O4
C9H16O4
C20H43N
C9H14O4
C5H10O
C8H14O5
C8H12O4
C7H12O4
C9H14O4
C6H10O4
C12H14O4
C14H26O4
C12H16
C8H14O4
C8H14O4
C4H10O4S
C4H10S
C4H10O3S
C8H14O6
C8H14O6
C11H16
C4H10Zn
C10H16O
C10H22O
C14H8O4
C4H6
C2H7N
C8H11N
C8H12AsNO3
C16H18O
C6H14
C6H14
C7H10O4
C8H16
C8H16
C8H16
C8H16
C8H16
C8H16
C8H16
13.0
45.3
−74.3
50.8
53.2
65.6
139.8
51.3
−12.7
80.7
57.3
40.0
62.8
47.4
108.8
125.3
49.7
54.6
39.8
47.0
−39.6
10.0
102.0
100.0
34.0
−22.4
46.6
68.0
196.7
−73.0
−87.7
29.5
15.0
96.7
−69.3
−63.6
50.8
−24.4
−15.9
−21.1
−19.4
−22.7
−20.0
−24.3
37.6
72.0
−56.9
77.8
81.2
94.7
175.8
80.2
+7.5
110.4
85.6
67.5
91.0
71.8
140.7
156.2
78.4
83.0
66.7
74.0
−18.6
34.2
133.0
131.7
61.5
0.0
75.5
91.7
239.8
−57.9
−72.2
56.3
39.6
128.3
−50.7
−44.5
78.2
−1.4
+7.3
+1.7
+3.4
0.0
+3.2
−1.7
50.0
85.8
−48.1
91.6
95.3
109.7
194.0
95.2
17.2
125.3
100.0
81.3
105.3
83.8
156.0
172.1
92.6
96.6
80.0
87.7
−8.0
46.4
148.0
147.2
75.3
+11.7
90.0
103.0
259.8
−50.5
−64.6
70.0
51.8
144.0
−41.5
−34.9
91.8
+10.3
18.4
13.0
14.9
+11.2
14.5
+10.1
63.0
100.3
−38.5
106.0
110.2
125.4
213.5
111.0
27.9
141.2
115.3
95.9
120.3
96.8
173.6
189.8
108.5
111.7
94.7
102.1
+3.5
59.7
164.2
163.8
90.2
24.2
106.0
115.0
282.0
−42.5
−56.0
84.8
65.0
160.3
−31.1
−24.1
106.5
23.0
31.1
25.6
27.4
23.6
27.1
22.6
60
100
200
400
760
141.0
163.2
28.0
149.0
140.0
142.0
133.3
144.6
140.0
204.8
195.8
−47.5
122.6
95.0
88.0
46.3
205.0
165.8
−4.0
133.8
154.5
178.9
39.4
163.5
153.8
155.8
147.6
158.2
153.8
220.7
212.0
−39.1
135.5
109.2
101.7
57.6
220.0
179.0
+6.0
147.3
176.2
202.8
57.0
185.7
176.0
178.0
169.0
181.5
176.0
245.6
238.5
−26.3
153.5
129.0
121.8
74.2
243.8
198.2
21.0
168.2
199.5
228.8
76.0
210.0
200.0
202.5
193.5
205.7
200.0
272.8
265.8
−12.0
175.2
150.5
144.2
93.2
259.7
219.1
38.0
192.4
223.5
256.5
96.8
235.0
225.0
227.0
217.0
230.0
225.0
302.0
296.5
+3.5
196.3
172.8
166.6
113.5
296.0
240.0
55.5
215.5
102.6
92.5
90.4
91.1
49.5
135.7
143.8
164.3
229.0
111.8
102.6
100.7
101.3
57.9
146.2
153.7
174.0
239.5
123.8
116.2
114.4
115.3
69.7
160.0
167.7
187.5
252.0
141.9
136.7
134.8
136.1
86.5
182.3
188.0
207.0
271.5
161.0
159.0
156.9
159.0
105.8
206.5
210.8
226.5
291.8
181.0
183.5
181.1
183.8
125.8
230.3
233.5
244.8
313.0
77.5
116.7
27.7
122.4
126.7
142.8
235.0
128.2
39.4
157.8
131.8
113.3
137.3
110.6
192.1
207.5
125.8
127.8
111.0
118.0
16.1
74.2
182.3
181.7
107.0
38.0
123.7
127.6
307.4
−33.9
−46.7
101.6
79.7
179.6
−19.5
−12.4
122.6
37.3
45.3
39.7
41.4
37.5
41.1
36.5
86.8
126.8
−21.8
132.4
137.7
153.2
248.5
139.9
46.7
169.0
142.4
123.0
147.9
119.7
204.1
218.4
136.8
138.2
121.4
128.6
24.2
83.8
194.0
193.2
117.7
47.2
134.7
136.7
323.3
−27.8
−40.7
111.9
88.6
191.5
−12.1
−4.9
132.7
45.7
54.4
48.7
50.4
46.4
50.1
45.4
99.5
140.3
−11.5
146.0
151.1
167.8
265.5
154.3
56.2
183.9
156.0
136.2
161.6
130.8
219.5
234.4
151.0
151.1
134.8
142.5
35.0
96.3
208.5
208.0
131.7
59.1
149.7
145.9
344.5
−18.8
−32.6
125.8
101.0
206.8
−2.0
+5.4
145.8
57.9
66.8
61.0
62.5
58.5
62.3
57.6
118.0
159.0
+2.2
166.0
172.2
189.5
292.8
177.5
70.6
205.3
177.8
155.5
183.2
147.9
243.0
255.8
173.2
171.7
155.1
162.5
51.3
115.8
230.4
230.0
152.4
77.0
171.8
160.2
377.8
−5.0
−20.4
146.5
119.8
229.7
+13.4
21.1
165.8
76.2
85.6
79.6
81.0
76.9
80.8
76.0
138.5
180.3
17.9
188.7
195.8
212.8
324.6
203.1
86.3
229.5
201.7
176.8
205.8
166.2
267.5
280.3
198.0
193.8
177.7
185.5
69.7
137.0
254.8
254.3
176.5
97.3
197.0
176.8
413.0
+10.6
−7.1
169.2
140.3
254.8
31.0
39.0
188.0
97.2
107.0
100.9
102.1
97.8
101.9
97.0
159.8
201.9
34.6
211.5
218.5
237.0
355.0
227.9
102.7
253.4
225.0
198.9
229.0
185.7
294.0
305.5
223.0
216.5
201.3
209.5
88.0
159.0
280.0
280.0
200.7
118.0
223.0
193.5
450.0
27.2
+7.4
193.1
160.5
281.0
49.7
58.0
210.5
119.5
129.7
123.4
124.4
120.1
124.3
119.3
Temperature, °C
Formula
Melting
point,
°C
−94
−12.1
32.9
−21
−38.9
−34.4
−31.4
−83.9
−43.2
−43
−116.3
+0.6
−42
−49.8
−40.6
1.3
−20.8
−25.0
−99.5
17
−28
194
−32.5
−96
+2.5
−99.8
−128.2
−34
−50.0
−88.0
−92.0
−76.2
−87.4
−36.9
VAPOR PRESSURES
2-69
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Dimethyl ether
2,2-Dimethylhexane
2,3-Dimethylhexane
2,4-Dimethylhexane
2,5-Dimethylhexane
3,3-Dimethylhexane
3,4-Dimethylhexane
Dimethyl itaconate
1-Dimethyl malate
Dimethyl maleate
malonate
trans-Dimethyl mesaconate
2,7-Dimethyloctane
Dimethyl oxalate
2,2-Dimethylpentane
2,3-Dimethylpentane
2,4-Dimethylpentane
3,3-Dimethylpentane
2,3-Dimethylphenol (2,3-xylenol)
2,4-Dimethylphenol (2,4-xylenol)
2,5-Dimethylphenol (2,5-xylenol)
3,4-Dimethylphenol (3,4-xylenol)
3,5-Dimethylphenol (3,5-xylenol)
Dimethylphenylsilane
Dimethyl phthalate
3,5-Dimethyl-1,2-pyrone
4,6-Dimethylresorcinol
Dimethyl sebacate
2,4-Dimethylstyrene
2,5-Dimethylstyrene
α,α-Dimethylsuccinic anhydride
Dimethyl sulfide
d-Dimethyl tartrate
dl-Dimethyl tartrate
N,N-Dimethyl-2-toluidine
N,N-Dimethyl-4-toluidine
Di(nitrosomethyl) amine
Diosphenol
1,4-Dioxane
Dipentene
Diphenylamine
Diphenyl carbinol (benzhydrol)
chlorophosphate
disulfide
1,2-Diphenylethane (dibenzyl)
Diphenyl ether
1,1-Diphenylethylene
trans-Diphenylethylene
1,1-Diphenylhydrazine
Diphenylmethane
Diphenyl sulfide
Diphenyl-2-tolyl thiophosphate
1,2-Dipropoxyethane
1,2-Diisopropylbenzene
1,3-Diisopropylbenzene
Dipropylene glycol
Dipropyleneglycol monobutyl ether
isopropyl ether
Di-n-propyl ether
Diisopropyl ether
Di-n-propyl ketone (4-heptanone)
Di-n-propyl oxalate
Diisopropyl oxalate
Di-n-propyl succinate
Di-n-propyl d-tartrate
Diisopropyl d-tartrate
Divinyl acetylene (1,5-hexadiene-3-yne)
1,3-Divinylbenzene
Docosane
n-Dodecane
1-Dodecene
n-Dodecyl alcohol
Dodecylamine
Dodecyltrimethylsilane
Elaidic acid
1
5
10
20
40
−101.1
−7.9
−1.1
−5.3
−5.5
−4.4
+0.2
94.0
104.0
73.0
59.8
74.0
30.5
44.0
−28.7
−20.8
−27.4
−25.0
83.8
78.0
78.0
93.8
89.2
30.3
131.8
107.6
76.8
139.8
61.9
55.9
88.1
−58.0
133.2
131.8
54.1
74.3
27.8
95.4
−12.8
40.4
141.7
145.0
160.5
164.0
119.8
97.8
119.6
145.8
159.3
107.4
129.0
179.8
−10.3
67.8
62.3
102.1
92.0
72.8
−22.3
−37.4
44.4
80.2
69.0
107.6
147.7
133.7
−24.4
60.0
195.4
75.8
74.0
120.2
111.8
122.1
206.7
−93.3
+3.1
+9.9
+5.2
+5.3
+6.1
11.3
106.6
118.3
86.4
72.0
87.8
42.3
56.0
−18.7
−10.3
−17.1
−14.4
97.6
91.3
91.3
107.7
102.4
42.6
147.6
122.0
90.7
156.2
75.8
69.0
102.0
−49.2
148.2
147.5
66.2
86.7
40.0
109.0
−1.2
53.8
157.0
162.0
182.0
180.0
136.0
114.0
135.0
161.0
176.1
122.8
145.0
201.6
+5.0
81.8
76.0
116.2
106.0
86.2
−11.8
−27.4
55.0
93.9
81.9
122.2
163.5
148.2
−14.0
73.8
213.0
90.0
87.8
134.7
127.8
137.7
223.5
−85.2
15.0
22.1
17.2
17.2
18.2
23.5
119.7
133.8
101.3
85.0
102.1
55.8
69.4
−7.5
+1.1
−5.9
−2.9
112.0
105.0
105.0
122.0
117.0
56.2
164.0
136.4
105.8
175.8
90.8
84.0
116.3
−39.4
164.3
164.0
80.2
100.0
53.7
124.0
+12.0
68.2
175.2
180.9
203.8
197.0
153.7
130.8
151.8
179.8
194.0
139.8
162.0
215.5
22.3
96.8
91.2
131.3
120.4
100.8
0.0
−16.7
66.2
108.6
95.6
138.0
180.4
164.0
−2.8
88.7
233.5
104.6
102.4
150.0
141.6
153.8
242.3
−76.2
28.2
35.6
30.5
30.4
31.7
37.1
133.7
150.1
117.2
100.0
118.0
71.2
83.6
+5.0
13.9
+6.5
+9.9
129.2
121.5
121.5
138.0
133.3
71.4
182.8
152.7
122.5
196.0
107.7
100.2
132.3
−28.4
182.4
182.4
95.0
116.3
68.2
141.2
25.2
84.3
194.3
200.0
227.9
214.8
173.7
150.0
170.8
199.0
213.5
157.8
182.8
230.6
42.3
114.0
107.9
147.4
136.3
117.0
+13.2
−4.5
78.1
124.6
110.5
154.8
199.7
181.8
+10.0
105.5
254.5
121.7
118.6
167.2
157.4
172.1
260.8
Melting
point,
°C
100
200
400
760
−62.7
48.2
56.0
50.6
50.5
52.5
57.7
153.7
175.1
140.4
121.9
141.5
93.9
104.8
23.9
33.3
25.4
29.3
152.2
143.0
143.0
161.0
156.0
94.2
210.0
177.5
147.3
222.6
132.3
124.7
155.3
−12.0
208.8
209.5
118.1
140.3
90.3
165.6
45.1
108.3
222.8
227.5
265.0
241.3
202.8
178.8
198.6
227.4
242.5
186.3
211.8
252.5
74.2
138.7
132.3
169.9
159.8
140.3
33.0
13.7
96.0
148.1
132.6
180.3
227.0
207.3
29.5
130.0
286.0
146.2
142.3
192.0
182.1
199.5
288.0
−50.9
65.7
73.8
68.1
68.0
70.0
75.6
171.0
196.3
160.0
140.0
161.0
114.0
123.3
40.3
50.1
41.8
46.2
173.0
161.5
161.5
181.5
176.2
114.2
232.7
198.0
167.8
245.0
153.2
145.6
175.8
+2.6
230.5
232.3
138.3
161.6
110.0
186.2
62.3
128.2
247.5
250.0
299.5
262.6
227.8
203.3
222.8
251.7
267.2
210.7
236.8
270.3
103.8
159.8
153.7
189.9
180.0
160.0
50.3
30.0
111.2
168.0
151.2
202.5
250.1
228.2
46.0
151.4
314.2
167.2
162.2
213.0
203.0
222.0
312.4
−37.8
85.6
94.1
88.2
87.9
90.4
96.0
189.8
219.5
182.2
159.8
183.5
136.0
143.3
59.2
69.4
60.6
65.5
196.0
184.2
184.2
203.6
197.8
136.4
257.8
221.0
192.0
269.6
177.5
168.7
197.5
18.7
255.0
257.4
161.5
185.4
131.3
209.5
81.8
150.5
274.1
275.6
337.2
285.8
255.0
230.7
249.8
278.3
294.0
237.5
263.9
290.0
140.0
184.3
177.6
210.5
203.8
183.1
69.5
48.2
127.3
190.3
171.8
226.5
275.6
251.8
64.4
175.2
343.5
191.0
185.5
235.7
225.0
248.0
337.0
−23.7
106.8
115.6
109.4
109.1
112.0
117.7
208.0
242.6
205.0
180.7
206.0
159.7
163.3
79.2
89.8
80.5
86.1
218.0
211.5
211.5
225.2
219.5
159.3
283.7
245.0
215.0
293.5
202.0
193.0
219.5
36.0
280.0
282.0
184.8
209.5
153.0
232.0
101.1
174.6
302.0
301.0
378.0
310.0
284.0
258.5
277.0
306.5
322.2
264.5
292.5
310.0
180.0
209.0
202.0
231.8
227.0
205.6
89.5
67.5
143.7
213.5
193.5
250.8
303.0
275.0
84.0
199.5
376.0
216.2
208.0
259.0
248.0
273.0
362.0
Temperature, °C
Formula
C2H6O
−115.7
−29.7
C8H18
−23.0
C8H18
C8H18
−26.9
−26.7
C8H18
−25.8
C8H18
C8H18
−22.1
69.3
C7H10O4
75.4
C6H10O5
C6H8O4
45.7
35.0
C5H8O4
46.8
C7H10O4
C10H22
+6.3
20.0
C4H6O4
−49.0
C7H16
C7H16
−42.0
−48.0
C7H16
−45.9
C7H16
C8H10O
56.0
51.8
C8H10O
51.8
C8H10O
C8H10O
66.2
62.0
C8H10O
+5.3
C8H12Si
C10H10O4
100.3
78.6
C7H8O2
49.0
C8H10O2
C12H22O4
104.0
34.2
C10H12
29.0
C10H12
C6H8O3
61.4
−75.6
C2H6S
102.1
C6H10O6
C6H10O6
100.4
28.8
C9H13N
50.1
C9H13N
C2H5N3O2
+3.2
66.7
C10H16O2
−35.8
C4H8O2
C10H16
14.0
108.3
C12H11N
110.0
C13H12O
C12H10ClPO3
121.5
131.6
C12H10S2
86.8
C14H14
C12H10O
66.1
87.4
C14H12
113.2
C14H12
C12H12N2
126.0
76.0
C13H12
96.1
C12H10S
C18H17O3PS
159.7
−38.8
C8H18O2
40.0
C12H18
C12H18
34.7
73.8
C6H14O3
64.7
C10H22O3
C9H20O3
46.0
−43.3
C6H14O
−57.0
C6H14O
C7H14O
23.0
53.4
C8H14O4
43.2
C8H14O4
C10H18O4
77.5
115.6
C10H18O6
103.7
C10H18O6
C6H6
−45.1
32.7
C10H10
157.8
C22H46
C12H26
47.8
47.2
C12H24
91.0
C12H26O
C12H27N
82.8
91.2
C15H34Si
171.3
C18H34O2
60
−70.4
36.7
44.2
39.0
38.9
40.4
45.8
142.6
160.4
127.1
109.7
127.8
80.8
92.8
13.0
22.1
14.5
18.1
139.5
131.0
131.0
148.0
143.5
81.3
194.0
163.8
133.2
208.0
118.0
110.7
142.4
−21.4
193.8
193.8
105.2
126.4
77.7
151.3
33.8
94.6
206.9
212.0
244.2
226.2
186.0
162.0
183.4
211.5
225.9
170.2
194.8
240.4
55.8
124.3
118.2
156.5
146.3
126.8
21.6
+3.4
85.8
134.8
120.0
166.0
211.7
192.6
18.1
116.0
268.3
132.1
128.5
177.8
168.0
184.2
273.0
−138.5
−90.7
38
−62
−52.8
−123.7
−135
−119.5
−135.0
75
25.5
74.5
62.5
68
51.5
38
−83.2
61.5
89
−61
10
52.9
68.5
61
51.5
27
124
44
26.5
−105
−122
−60
−32.6
−66.9
44.5
−9.6
−31.5
24
51.5
(Continued )
2-70
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Epichlorohydrin
1,2-Epoxy-2-methylpropane
Erucic acid
Estragole (p-methoxy allyl benzene)
Ethane
Ethoxydimethylphenylsilane
Ethoxytrimethylsilane
Ethoxytriphenylsilane
Ethyl acetate
acetoacetate
Ethylacetylene (1-butyne)
Ethyl acrylate
α-Ethylacrylic acid
α-Ethylacrylonitrile
Ethyl alcohol (ethanol)
Ethylamine
4-Ethylaniline
N-Ethylaniline
2-Ethylanisole
3-Ethylanisole
4-Ethylanisole
Ethylbenzene
Ethyl benzoate
benzoylacetate
bromide
α-bromoisobutyrate
n-butyrate
isobutyrate
Ethylcamphoronic anhydride
Ethyl isocaproate
carbamate
carbanilate
Ethylcetylamine
Ethyl chloride
chloroacetate
chloroglyoxylate
α-chloropropionate
trans-cinnamate
3-Ethylcumene
4-Ethylcumene
Ethyl cyanoacetate
Ethylcyclohexane
Ethylcyclopentane
Ethyl dichloroacetate
N,N-diethyloxamate
N-Ethyldiphenylamine
Ethylene
Ethylene-bis-(chloroacetate)
Ethylene chlorohydrin (2-chloroethanol)
diamine (1,2-ethanediamine)
dibromide (1,2-dibromethane)
dichloride (1,2-dichloroethane)
glycol (1,2-ethanediol)
glycol diethyl ether
(1,2-diethoxyethane)
glycol dimethyl ether
(1,2-dimethoxyethane)
glycol monomethyl ether
(2-methoxyethanol)
oxide
Ethyl α-ethylacetoacetate
fluoride
formate
2-furoate
glycolate
3-Ethylhexane
2-Ethylhexyl acrylate
Ethylidene chloride (1,1-dichloroethane)
fluoride (1,1-difluoroethane)
Ethyl iodide
Ethyl l-leucinate
Ethyl levulinate
Ethyl mercaptan (ethanethiol)
Ethyl methylcarbamate
Ethyl methyl ether
1
5
10
20
−16.5
−69.0
206.7
52.6
−159.5
36.3
−50.9
167.0
−43.4
28.5
−92.5
−29.5
47.0
−29.0
−31.3
−82.3
52.0
38.5
29.7
33.7
33.5
−9.8
44.0
107.6
−74.3
10.6
−18.4
−24.3
118.2
11.0
107.8
133.2
−89.8
+1.0
−5.1
+6.6
87.6
28.3
31.5
67.8
−14.5
−32.2
9.6
76.0
98.3
−168.3
112.0
−4.0
−11.0
−27.0
−44.5
53.0
−33.5
+5.6
−50.0
239.7
80.0
−148.5
63.1
−31.0
198.2
−23.5
54.0
−76.7
−8.7
70.7
−6.4
−12.0
−66.4
80.0
66.4
55.9
60.3
60.2
+13.9
72.0
136.4
−56.4
35.8
+4.0
−2.4
149.8
35.8
65.8
131.8
168.2
−73.9
25.4
+18.0
30.2
108.5
55.5
58.4
93.5
+9.2
−10.8
34.0
106.3
130.2
−158.3
142.4
+19.0
+10.5
+4.7
−24.0
79.7
−10.2
16.6
−40.3
254.5
93.7
−142.9
76.2
−20.7
213.5
−13.5
67.3
−68.7
+2.0
82.0
+5.0
−2.3
−58.3
93.8
80.6
69.0
73.9
73.9
25.9
86.0
150.3
−47.5
48.0
15.3
+8.4
165.0
48.0
77.8
143.7
186.0
−65.8
37.5
29.9
41.9
134.0
68.8
72.0
106.0
20.6
−0.1
46.3
121.7
146.0
−153.2
158.0
30.3
21.5
18.6
−13.6
92.1
+1.6
29.0
−29.5
270.6
108.4
−136.7
91.0
−9.8
230.0
−3.0
81.1
−59.9
13.0
94.4
17.7
+8.0
−48.6
109.0
96.0
83.1
88.5
88.5
38.6
101.4
166.8
−37.8
61.8
27.8
20.6
181.8
61.7
91.0
155.5
205.5
−56.8
50.4
42.0
54.3
150.3
83.6
86.7
119.8
33.4
+11.7
59.5
137.7
162.8
−147.6
173.5
42.5
33.0
32.7
−2.4
105.8
14.7
42.0
−17.3
289.1
124.6
−129.8
107.2
+3.7
247.0
+9.1
96.2
−50.0
26.0
108.1
31.8
19.0
−39.8
125.7
113.2
98.8
104.8
104.7
52.8
118.2
181.8
−26.7
77.0
41.5
33.8
199.8
76.3
105.6
168.8
226.5
−47.0
65.2
56.0
68.2
169.2
99.9
103.3
133.8
47.6
25.0
74.0
154.4
182.0
−141.3
191.0
56.0
45.8
48.0
+10.0
120.0
29.7
50.6
−9.7
300.2
135.2
−125.4
127.5
11.5
258.3
16.6
106.0
−43.4
33.5
116.7
40.6
26.0
−33.4
136.0
123.6
109.0
115.5
115.4
61.8
129.0
191.9
−19.5
86.7
50.1
42.3
211.5
85.8
114.8
177.3
239.8
−40.6
74.0
65.2
77.3
181.2
110.2
113.8
142.1
56.7
33.4
83.6
166.0
193.7
−137.3
201.8
64.1
53.8
57.9
18.1
129.5
39.0
62.0
+1.2
314.4
148.5
−119.3
131.4
22.1
273.5
27.0
118.5
−34.9
44.5
127.5
53.0
34.9
−25.1
149.8
137.3
122.3
129.2
128.4
74.1
143.2
205.0
−10.0
99.8
62.0
53.5
226.6
98.4
126.2
187.9
256.8
−32.0
86.0
76.6
89.3
196.0
124.3
127.2
152.8
69.0
45.0
96.1
180.3
209.8
−131.8
215.0
75.0
62.5
70.4
29.4
141.8
51.8
C4H10O2
−48.0
−26.2
−15.3
−3.0
+10.7
19.7
31.8
50.0
70.8
93.0
C3H8O2
−13.5
+10.2
22.0
34.3
47.8
56.4
68.0
85.3
104.3
124.4
−89.7
40.5
−117.0
−60.5
37.6
14.3
−20.0
50.0
−60.7
−112.5
−54.4
27.8
47.3
−76.7
26.5
−91.0
−73.8
67.3
−103.8
−42.2
63.8
38.8
+2.1
77.7
−41.9
−98.4
−34.3
57.3
74.0
−59.1
51.0
−75.6
−65.7
80.2
−97.7
−33.0
77.1
50.5
12.8
91.8
−32.3
−91.7
−24.3
72.1
87.3
−50.2
63.2
−67.8
−56.6
94.6
−90.0
−22.7
91.5
63.9
25.0
106.3
−21.9
−84.1
−13.1
88.0
101.8
−40.7
76.1
−59.1
−46.9
110.3
−81.8
−11.5
107.5
78.1
38.5
123.7
−10.2
−75.8
−0.9
106.0
117.7
−29.8
91.0
−49.4
−40.7
120.6
−76.4
−4.3
117.5
87.6
47.1
134.0
−2.9
−70.4
+7.2
117.8
127.6
−22.4
100.0
−43.3
−32.1
133.8
−69.3
−5.4
130.4
99.8
58.9
147.9
+7.2
−63.2
18.0
131.8
141.3
−13.0
112.0
−34.8
−19.5
153.2
−58.0
20.0
150.1
117.8
76.7
168.2
22.4
−52.0
34.1
149.8
160.2
+1.5
130.0
−22.0
−4.9
175.6
−45.5
37.1
172.5
138.0
97.0
192.2
39.8
−39.5
52.3
167.3
183.0
17.7
149.8
−7.8
+10.7
198.0
−32.0
54.3
195.0
158.2
118.5
216.0
57.4
−26.5
72.4
184.0
206.2
35.0
170.0
+7.5
C2H4O
C8H14O3
C2H5F
C3H6O2
C7H8O3
C4H8O3
C8H18
C11H20O2
C2H4Cl2
C2H4F2
C2H5I
C8H17NO2
C7H12O3
C2H6S
C4H9NO2
C3H8O
60
100
200
400
760
Temperature, °C
Formula
C3H5ClO
C4H8O
C22H42O2
C10H12O
C2H6
C10H16OSi
C5H14OSi
C20H20OSi
C4H8O2
C6H10O3
C4H6
C5H8O2
C5H8O2
C5H7N
C2H6O
C2H7N
C8H11N
C8H11N
C9H12O
C9H12O
C9H12O
C8H10
C9H10O2
C11H12O3
C2H5Br
C6H11BrO2
C6H12O2
C6H12O2
C11H16O5
C8H16O2
C3H7NO2
C9H11NO2
C18H39N
C2H5Cl
C4H7ClO2
C4H5ClO3
C5H9ClO2
C11H12O2
C11H16
C11H16
C5H7NO2
C8H16
C7H14
C4H6Cl2O2
C8H15NO3
C14H15N
C2H4
C6H8Cl2O4
C2H5ClO
C2H8N2
C2H4Br2
C2H4Cl2
C2H6O2
C6H14O2
40
79.3
98.0
117.9
17.5
36.0
55.5
336.5
358.8
381.5
168.7
192.0
215.0
−110.2 −99.7 −88.6
151.5
175.0
199.5
38.1
56.3
75.7
295.0
319.5
344.0
42.0
59.3
77.1
138.0
158.2
180.8
−21.6
−6.9
+8.7
61.5
80.0
99.5
144.0
160.7
179.2
71.6
92.2
114.0
48.4
63.5
78.4
−12.3
+2.0
16.6
170.6
194.2
217.4
156.9
180.8
204.0
142.1
164.2
187.1
149.7
172.8
196.5
149.2
172.3
196.5
92.7
113.8
136.2
164.8
188.4
213.4
223.8
244.7
265.0
+4.5
21.0
38.4
119.7
141.2
163.6
79.8
100.0
121.0
71.0
90.0
110.0
248.5
272.8
298.0
117.8
139.2
160.4
144.2
164.0
184.0
203.8
220.0
237.0
283.3
313.0
342.0
−18.6
−3.9 +12.3
103.8
123.8
144.2
94.5
114.7
135.0
107.2
126.2
146.5
219.3
245.0
271.0
145.4
168.2
193.0
148.3
171.8
195.8
169.8
187.8
206.0
87.8
109.1
131.8
62.4
82.3
103.4
115.2
135.9
156.5
202.8
226.5
252.0
233.0
258.8
286.0
−123.4 −113.9 −103.7
237.3
259.5
283.5
91.8
110.0
128.8
81.0
99.0
117.2
89.8
110.1
131.5
45.7
64.0
82.4
158.5
178.5
197.3
71.8
94.1
119.5
Melting
point,
°C
−25.6
33.5
−183.2
−82.4
−45
−130
−71.2
−112
−80.6
−4
−63.5
−94.9
−34.6
−117.8
−93.3
−88.2
49
52.5
−139
−26
12
−111.3
−138.6
−169
−69
8.5
10
−35.3
−15.6
−111.3
−79
34
−96.7
−117
−105
−121
VAPOR PRESSURES
2-71
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
1-Ethylnaphthalene
Ethyl α-naphthyl ketone
(1-propionaphthone)
Ethyl 3-nitrobenzoate
3-Ethylpentane
4-Ethylphenetole
2-Ethylphenol
3-Ethylphenol
4-Ethylphenol
Ethyl phenyl ether (phenetole)
Ethyl propionate
Ethyl propyl ether
Ethyl salicylate
3-Ethylstyrene
4-Ethylstyrene
Ethylisothiocyanate
2-Ethyltoluene
3-Ethyltoluene
4-Ethyltoluene
Ethyl trichloroacetate
Ethyltrimethylsilane
Ethyltrimethyltin
Ethyl isovalerate
2-Ethyl-1,4-xylene
4-Ethyl-1,3-xylene
5-Ethyl-1,3-xylene
Eugenol
iso-Eugenol
Eugenyl acetate
Fencholic acid
d-Fenchone
dl-Fenchyl alcohol
Fluorene
Fluorobenzene
2-Fluorotoluene
3-Fluorotoluene
4-Fluorotoluene
Formaldehyde
Formamide
Formic acid
trans-Fumaryl chloride
Furfural (2-furaldehyde)
Furfuryl alcohol
Geraniol
Geranyl acetate
Geranyl n-butyrate
Geranyl isobutyrate
Geranyl formate
Glutaric acid
Glutaric anhydride
Glutaronitrile
Glutaryl chloride
Glycerol
Glycerol dichlorohydrin
(1,3-dichloro-2-propanol)
Glycol diacetate
Glycolide (1,4-dioxane-2,6-dione)
Guaicol (2-methoxyphenol)
Heneicosane
Heptacosane
Heptadecane
Heptaldehyde (enanthaldehyde)
n-Heptane
Heptanoic acid (enanthic acid)
1-Heptanol
Heptanoyl chloride (enanthyl chloride)
2-Heptene
Heptylbenzene
Heptyl cyanide (enanthonitrile)
Hexachlorobenzene
Hexachloroethane
Hexacosane
Hexadecane
1-Hexadecene
n-Hexadecyl alcohol (cetyl alcohol)
1
100
200
400
760
Melting
point,
°C
164.1
180.0
204.6
230.8
258.1
−27
206.9
192.6
17.5
119.8
117.9
130.0
131.3
86.6
27.2
−12.0
136.7
99.2
97.3
50.8
76.4
73.3
73.6
85.5
−9.0
30.0
55.2
96.0
97.2
92.6
155.8
167.0
183.0
171.8
99.5
110.8
185.2
+11.5
34.7
37.0
37.8
−70.6
137.5
24.0
79.5
82.1
95.7
141.8
150.0
170.1
164.0
136.2
226.3
185.5
176.4
128.3
198.0
93.0
218.2
205.0
25.7
129.8
127.9
139.8
141.7
95.4
35.1
−4.0
147.6
109.6
107.6
59.8
86.0
82.9
83.2
94.4
−1.2
38.4
64.0
106.2
107.4
103.0
167.3
178.2
194.0
181.5
109.8
120.2
197.8
19.6
43.7
45.8
46.5
−65.0
147.0
32.4
89.0
91.5
104.0
151.5
160.3
180.2
174.0
147.2
235.5
196.2
189.5
139.1
208.0
102.0
233.5
220.3
36.9
143.5
141.8
152.0
154.2
108.4
45.2
+6.8
161.5
123.2
121.5
71.9
99.0
95.9
96.3
107.4
+9.2
50.0
75.9
120.0
121.2
116.5
182.2
194.0
209.7
194.0
123.6
132.3
214.7
30.4
55.3
57.5
58.1
−57.3
157.5
43.8
101.0
103.4
115.9
165.3
175.2
193.8
187.7
160.7
247.0
212.5
205.5
151.8
220.1
114.8
255.5
244.6
53.8
163.2
161.6
171.8
175.0
127.9
61.7
23.3
183.7
144.0
142.0
90.0
119.0
115.5
116.1
125.8
25.0
67.3
93.8
140.2
141.8
137.4
204.7
217.2
232.5
215.0
144.0
150.0
240.3
47.2
73.0
75.4
76.0
−46.0
175.5
61.4
120.0
121.8
133.1
185.6
196.3
214.0
207.6
182.6
265.0
236.5
230.0
172.4
240.0
133.3
280.2
270.6
73.0
185.7
184.5
193.3
197.4
149.8
79.8
41.6
207.0
167.2
165.0
110.1
141.4
137.8
136.4
146.0
42.8
87.6
114.0
163.1
164.4
159.6
228.3
242.3
257.4
237.8
166.8
173.2
268.6
65.7
92.8
95.4
96.1
−33.0
193.5
80.3
140.0
141.8
151.8
207.8
219.8
235.0
228.5
205.8
283.5
261.0
257.3
195.3
263.0
153.5
306.0
298.0
93.5
208.0
207.5
214.0
219.0
172.0
99.1
61.7
231.5
191.5
189.0
131.0
165.1
161.3
162.0
167.0
62.0
108.8
134.3
186.9
188.4
183.7
253.5
267.5
282.0
264.1
191.0
201.0
295.0
84.7
114.0
116.0
117.0
−19.5
210.5
100.6
160.0
161.8
170.0
230.0
243.3
257.4
251.0
230.0
303.0
287.0
286.2
217.0
290.0
174.3
106.1
148.6
121.6
243.4
305.7
195.8
66.3
22.3
139.5
99.8
86.4
21.5
144.0
92.6
206.0
102.3
295.2
181.3
178.8
219.8
115.8
158.2
131.0
255.3
318.3
207.3
74.0
30.6
148.5
108.0
93.5
30.0
154.8
103.0
219.0
112.0
307.8
193.2
190.8
234.3
128.0
173.2
144.0
272.0
333.5
223.0
84.0
41.8
160.0
119.5
102.7
41.3
170.2
116.8
235.5
124.2
323.2
208.5
205.3
251.7
147.8
194.0
162.7
296.5
359.4
247.8
102.0
58.7
179.5
136.6
116.3
58.6
193.3
137.7
258.5
143.1
348.4
231.7
226.8
280.2
168.3
217.0
184.1
323.8
385.0
274.5
125.5
78.0
199.6
155.6
130.7
78.1
217.8
160.0
283.5
163.8
374.6
258.3
250.0
312.7
190.5
240.0
205.0
350.5
410.6
303.0
155.0
98.4
221.5
175.8
145.0
98.5
244.0
184.6
309.4
185.6
399.8
287.5
274.0
344.0
5
10
20
70.0
101.4
116.8
133.8
152.0
C13H12O
C9H9NO4
C7H16
C10H14O
C8H10O
C8H10O
C8H10O
C8H10O
C5H10O2
C5H12O
C9H10O3
C10H12
C10H12
C3H5NS
C9H12
C9H12
C9H12
C4H5Cl3O2
C5H14Si
C5H14Sn
C7H14O2
C10H14
C10H14
C10H14
C10H12O2
C10H12O2
C12H14O3
C10H16O2
C10H16O
C10H18O
C13H10
C6H5F
C7H7F
C7H7F
C7H7F
CH2O
CH3NO
CH2O2
C4H2Cl2O2
C5H4O2
C5H6O2
C10H18O
C12H20O2
C14H24O2
C14H24O2
C11H18O2
C5H8O4
C5H6O3
C5H6N2
C5H6Cl2O2
C3H8O3
C3H6Cl2O
124.0
108.1
−37.8
48.5
46.2
60.0
59.3
18.1
−28.0
−64.3
61.2
28.3
26.0
−13.2
9.4
7.2
7.6
20.7
−60.6
−30.0
−6.1
25.7
26.3
22.1
78.4
86.3
101.6
101.7
28.0
45.8
−43.4
−24.2
−22.4
−21.8
155.5
140.2
−17.0
75.7
73.4
86.8
86.5
43.7
−7.2
−45.0
90.0
55.0
52.7
+10.6
34.8
32.3
32.7
45.5
−41.4
−7.6
+17.0
52.0
53.0
48.8
108.1
117.0
132.3
128.7
54.7
70.3
129.3
−22.8
−2.2
−0.3
+0.3
70.5
−20.0
+15.0
18.5
31.8
69.2
73.5
96.8
90.9
61.8
155.5
100.8
91.3
56.1
125.5
28.0
96.3
−5.0
38.5
42.6
56.0
96.8
102.7
125.2
119.6
90.3
183.8
133.3
123.7
84.0
153.8
52.2
171.0
155.0
−6.8
89.5
87.0
100.2
100.2
56.4
+3.4
−35.0
104.2
68.3
66.3
22.8
47.6
44.7
44.9
57.7
−31.8
+3.8
28.7
65.6
66.4
62.1
123.0
132.4
148.0
142.3
68.3
82.1
146.0
−12.4
+8.9
+11.0
11.8
−88.0
109.5
+2.1
51.8
54.8
68.0
110.0
117.9
139.0
133.0
104.3
196.0
149.5
140.0
97.8
167.2
64.7
188.1
173.6
+4.7
103.8
101.5
114.5
115.0
70.3
14.3
−24.0
119.3
82.8
80.8
36.1
61.2
58.2
58.5
70.6
−21.0
16.1
41.3
79.8
80.6
76.5
138.7
149.0
164.2
155.8
83.0
95.6
164.2
−1.2
21.4
23.4
24.0
−79.6
122.5
10.3
65.0
67.8
81.0
125.6
133.0
153.8
147.9
119.8
210.5
166.0
156.5
112.3
182.2
78.0
C6H10O4
C4H4O4
C7H8O2
C21H44
C27H56
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H13ClO
C7H14
C13H20
C7H13N
C6Cl6
C2Cl6
C26H54
C16H34
C16H32
C16H34O
38.3
64.1
103.0
79.1
188.0
248.6
145.2
32.7
−12.7
101.3
64.3
54.6
−14.1
94.6
47.8
149.3
49.8
240.0
135.2
131.7
158.3
77.1
116.6
92.0
205.4
266.8
160.0
43.0
−2.1
113.2
74.7
64.6
−3.5
110.0
61.6
166.4
73.5
257.4
149.8
146.2
177.8
90.8
132.0
106.0
223.2
284.6
177.7
54.0
+9.5
125.6
85.8
75.0
+8.3
126.0
76.3
185.7
87.6
275.8
164.7
162.0
197.8
60
Temperature, °C
Formula
C12H12
40
52.4
152.6
211.7
115.0
12.0
−34.0
78.0
42.4
34.2
−35.8
64.0
21.0
114.4
32.7
204.0
105.3
101.6
122.7
47
−118.6
−45
−4
46.5
−30.2
−72.6
1.3
−5.9
−95.5
−99.3
−10
295
19
5
35
113
−42.1
−80
−110.8
−92
8.2
97.5
17.9
−31
97
28.3
40.4
59.5
22.5
−42
−90.6
−10
34.6
230
186.6
56.6
18.5
4
49.3
(Continued )
2-72
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
n-Hexadecylamine (cetylamine)
Hexaethylbenzene
n-Hexane
1-Hexanol
2-Hexanol
3-Hexanol
1-Hexene
n-Hexyl levulinate
n-Hexyl phenyl ketone (enanthophenone)
Hydrocinnamic acid
Hydrogen cyanide (hydrocyanic acid)
Hydroquinone
4-Hydroxybenzaldehyde
α-Hydroxyisobutyric acid
α-Hydroxybutyronitrile
4-Hydroxy-3-methyl-2-butanone
4-Hydroxy-4-methyl-2-pentanone
3-Hydroxypropionitrile
Indene
Iodobenzene
Iodononane
2-Iodotoluene
α-Ionone
Isoprene
Lauraldehyde
Lauric acid
Levulinaldehyde
Levulinic acid
d-Limonene
Linalyl acetate
Maleic anhydride
Menthane
1-Menthol
Menthyl acetate
benzoate
formate
Mesityl oxide
Methacrylic acid
Methacrylonitrile
Methane
Methanethiol
Methoxyacetic acid
N-Methylacetanilide
Methyl acetate
acetylene (propyne)
acrylate
alcohol (methanol)
Methylamine
N-Methylaniline
Methyl anthranilate
benzoate
2-Methylbenzothiazole
α-Methylbenzyl alcohol
Methyl bromide
2-Methyl-1-butene
2-Methyl-2-butene
Methyl isobutyl carbinol (2-methyl4-pentanol)
n-butyl ketone (2-hexanone)
isobutyl ketone (4-methyl-2-pentanone)
n-butyrate
isobutyrate
caprate
caproate
caprylate
chloride
chloroacetate
cinnamate
α-Methylcinnamic acid
Methylcyclohexane
Methylcyclopentane
Methylcyclopropane
Methyl n-decyl ketone (n-dodecan-2-one)
dichloroacetate
N-Methyldiphenylamine
1
5
10
20
123.6
157.8
134.3
−34.5
47.2
34.8
25.7
−38.0
120.0
130.3
133.5
−55.3
153.3
153.2
98.5
65.8
69.3
46.7
87.8
44.3
50.6
96.2
65.9
108.8
−62.3
108.4
150.6
54.9
128.1
40.4
82.5
63.4
35.7
83.2
85.8
154.2
75.8
+14.1
48.5
−23.3
−199.0
−75.3
79.3
103.8
−38.6
−97.5
−23.6
−25.3
−81.3
62.8
109.0
64.4
97.5
75.2
−80.6
−72.8
−57.0
+22.1
176.0
150.3
−25.0
58.2
45.0
36.7
−28.1
134.7
145.5
148.7
−47.7
163.5
169.7
110.5
77.8
81.0
58.8
102.0
58.5
64.0
109.0
79.8
123.0
−53.3
123.7
166.0
68.0
141.8
53.8
96.0
78.7
48.3
96.0
100.0
170.0
90.0
26.0
60.0
−12.5
−195.5
−67.5
92.0
118.6
−29.3
−90.5
−13.5
−16.2
−73.8
76.2
124.2
77.3
111.2
88.0
−72.8
−64.3
−47.9
33.3
195.7
168.0
−14.1
70.3
55.9
49.0
−17.2
150.2
161.0
165.0
−39.7
174.6
186.8
123.8
90.7
94.0
72.0
117.9
73.9
78.3
123.0
95.6
139.0
−43.5
140.2
183.6
82.7
154.1
68.2
111.4
95.0
62.7
110.3
115.4
186.3
105.8
37.9
72.7
−0.6
−191.8
−58.8
106.5
135.1
−19.1
−82.9
−2.7
−6.0
−65.9
90.5
141.5
91.8
125.5
102.1
−64.0
−54.8
−37.9
45.4
C6H12O
C6H12O
C5H10O2
C5H10O2
C11H22O2
C7H14O2
C9H18O2
CH3Cl
C3H5ClO2
C10H10O2
C10H10O2
C7H14
C6H12
C4H8
C12H24O
C3H4Cl2O2
C13H13N
60
100
215.7
187.7
−2.3
83.7
67.9
62.2
−5.0
167.8
178.9
183.3
−30.9
192.0
206.0
138.0
104.8
108.2
86.7
134.1
90.7
94.4
138.1
112.4
155.6
−32.6
157.8
201.4
98.3
169.5
84.3
127.7
111.8
78.3
126.1
132.1
204.3
123.0
51.7
86.4
+12.8
−187.7
−49.2
122.0
152.2
−7.9
−74.3
+9.2
+5.0
−56.9
106.0
159.7
107.8
141.2
117.8
−54.2
−44.1
−26.7
58.2
228.8
199.7
+5.4
92.0
76.0
70.7
+2.8
179.0
189.8
194.0
−25.1
203.0
217.5
146.4
113.9
117.4
96.0
144.7
100.8
105.0
147.7
123.8
166.3
−25.4
168.7
212.7
108.4
178.0
94.6
138.1
122.0
88.6
136.1
143.2
215.8
133.8
60.4
95.3
21.5
−185.1
−43.1
131.8
164.2
−0.5
−68.8
17.3
12.1
−51.3
115.8
172.0
117.4
150.4
127.4
−48.0
−37.3
−19.4
67.0
245.8
216.0
15.8
102.8
87.3
81.8
13.0
193.6
204.2
209.0
−17.8
216.5
233.5
157.7
125.0
129.0
108.2
157.7
114.7
118.3
159.8
138.1
181.2
−16.0
184.5
227.5
121.8
190.2
108.3
151.8
135.8
102.1
149.4
156.7
230.4
148.0
72.1
106.6
32.8
−181.4
−34.8
144.5
179.8
+9.4
−61.3
28.0
21.2
−43.7
129.8
187.8
130.8
163.9
140.3
−39.4
−28.0
−9.9
78.0
28.8
+19.7
−5.5
−13.0
93.5
30.0
61.7
−99.5
19.0
108.1
155.0
−14.0
−33.8
−80.6
106.0
26.7
134.0
38.8
30.0
+5.0
−2.9
108.0
42.0
74.9
−92.4
30.0
123.0
169.8
−3.2
−23.7
−72.8
120.4
38.1
149.7
50.0
40.8
16.7
+8.4
123.0
55.4
89.0
−84.8
41.5
140.0
185.2
+8.7
−12.8
−64.0
136.0
50.7
165.8
62.0
52.8
29.6
21.0
139.0
70.0
105.3
−76.0
54.5
157.9
201.8
22.0
−0.6
−54.2
152.4
64.7
184.0
69.8
60.4
37.4
28.9
148.6
79.7
115.3
−70.4
63.0
170.0
212.0
30.5
+7.2
−48.0
163.8
73.6
195.4
79.8
70.4
48.0
39.6
161.5
91.4
128.0
−63.0
73.5
185.8
224.8
42.1
17.9
−39.3
177.5
85.4
210.1
200
400
760
Temperature, °C
Formula
C16H35N
C18H30
C6H14
C6H14O
C6H14O
C6H14O
C6H12
C11H20O3
C13H18O
C9H10O2
CHN
C6H6O2
C7H6O2
C4H8O3
C5H9NO
C5H10O2
C6H12O2
C3H5NO
C9H8
C6H5I
C9H19I
C7H7I
C13H20O
C5H8
C12H24O
C12H24O2
C5H8O2
C5H8O3
C10H16
C12H20O2
C4H2O3
C10H20
C10H20O
C12H22O2
C17H24O2
C11H20O2
C6H10O
C4H6O2
C4H5N
CH4
CH4S
C3H6O3
C9H11NO
C3H6O2
C3H4
C4H6O2
CH4O
CH5N
C7H9N
C8H9NO2
C8H8O2
C8H7NS
C8H10O
CH3Br
C5H10
C5H10
C6H14O
40
−53.9
24.4
14.6
+2.5
−57.5
90.0
100.0
102.2
−71.0
132.4
121.2
73.5
41.0
44.6
22.0
58.7
16.4
24.1
70.0
37.2
79.5
−79.8
77.7
121.0
28.1
102.0
14.0
55.4
44.0
+9.7
56.0
57.4
123.2
47.3
−8.7
25.5
−44.5
−205.9
−90.7
52.5
−57.2
−111.0
−43.7
−44.0
−95.8
36.0
77.6
39.0
70.0
49.0
−96.3
−89.1
−75.4
−0.3
+7.7
−1.4
−26.8
−34.1
63.7
+5.0
34.2
−2.9
77.4
125.7
−35.9
−53.7
−96.0
77.1
3.2
103.5
272.2
300.4
330.0
241.7
268.5
298.3
31.6
49.6
68.7
119.6
138.0
157.0
103.7
121.8
139.9
98.3
117.0
135.5
29.0
46.8
66.0
215.7
241.0
266.8
225.0
248.3
271.3
230.8
255.0
279.8
−5.3 +10.2
25.9
238.0
262.5
286.2
256.8
282.6
310.0
175.2
193.8
212.0
142.0
159.8
178.8
146.5
165.5
185.0
126.8
147.5
167.9
178.0
200.0
221.0
135.6
157.8
181.6
139.8
163.9
188.6
179.0
199.3
219.5
160.0
185.7
211.0
202.5
225.2
250.0
−1.2 +15.4
32.6
207.8
231.8
257.0
249.8
273.8
299.2
142.0
164.0
187.0
208.3
227.4
245.8
128.5
151.4
175.0
173.3
196.2
220.0
155.9
179.5
202.0
122.7
146.0
169.5
168.3
190.2
212.0
178.8
202.8
227.0
253.2
277.1
301.0
169.8
194.2
219.0
90.0
109.8
130.0
123.9
142.5
161.0
50.0
70.3
90.3
−175.5 −168.8 −161.5
−22.1
−7.9
+6.8
163.5
184.2
204.0
202.3
227.4
253.0
24.0
40.0
57.8
−49.8 −37.2 −23.3
43.9
61.8
80.2
34.8
49.9
64.7
−32.4 −19.7
−6.3
149.3
172.0
195.5
212.4
238.5
266.5
151.4
174.7
199.5
183.2
204.5
225.5
159.0
180.7
204.0
−26.5 −11.9
+3.6
−13.8
+2.5
20.2
+4.9
21.6
38.5
94.9
113.5
131.7
94.3
85.6
64.3
55.7
181.6
109.8
148.1
−51.2
90.5
209.6
245.0
59.6
34.0
−26.0
199.0
103.2
232.8
111.0
102.0
83.1
73.6
202.9
129.8
170.0
−38.0
109.5
235.0
266.8
79.6
52.3
−11.3
222.5
122.6
257.0
127.5
119.0
102.3
92.6
224.0
150
193.0
−24.0
130.3
263.0
288.0
100.9
71.8
+4.5
246.5
143.0
282.0
Melting
point,
°C
130
−95.3
−51.6
−98.5
48.5
−13.2
170.3
115.5
79
−47
−2
−28.5
−146.7
44.5
48
33.5
−96.9
58
42.5
54.5
−59
15
−182.5
−121
102
−98.7
−102.7
−97.8
−93.5
−57
24
−12.5
15.4
−93
−135
−133
−56.9
−84.7
−84.7
−18
−40
−97.7
−31.9
33.4
−126.4
−142.4
−7.6
VAPOR PRESSURES
2-73
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Methyl n-dodecyl ketone (2-tetradecanone)
Methylene bromide (dibromomethane)
chloride (dichloromethane)
Methyl ethyl ketone (2-butanone)
2-Methyl-3-ethylpentane
3-Methyl-3-ethylpentane
Methyl fluoride
formate
α-Methylglutaric anhydride
Methyl glycolate
2-Methylheptadecane
2-Methylheptane
3-Methylheptane
4-Methylheptane
2-Methyl-2-heptene
6-Methyl-3-hepten-2-ol
6-Methyl-5-hepten-2-ol
2-Methylhexane
3-Methylhexane
Methyl iodide
laurate
levulinate
methacrylate
myristate
α-naphthyl ketone (1-acetonaphthone)
β-naphthyl ketone (2-acetonaphthone)
n-nonyl ketone (undecan-2-one)
palmitate
n-pentadecyl ketone (2-heptdecanone)
2-Methylpentane
3-Methylpentane
2-Methyl-1-pentanol
2-Methyl-2-pentanol
Methyl n-pentyl ketone (2-heptanone)
phenyl ether (anisole)
2-Methylpropene
Methyl propionate
4-Methylpropiophenone
2-Methylpropionyl bromide
Methyl propyl ether
n-propyl ketone (2-pentanone)
isopropyl ketone (3-Methyl-2-butanone)
2-Methylquinoline
Methyl salicylate
α-Methyl styrene
4-Methyl styrene
Methyl n-tetradecyl ketone
(2-hexadecanone)
thiocyanate
isothiocyanate
undecyl ketone (2-tridecanone)
isovalerate
Monovinylacetylene (butenyne)
Myrcene
Myristaldehyde
Myristic acid (tetradecanoic acid)
Naphthalene
1-Naphthoic acid
2-Naphthoic acid
1-Naphthol
2-Naphthol
1-Naphthylamine
2-Naphthylamine
Nicotine
2-Nitroaniline
3-Nitroaniline
4-Nitroaniline
2-Nitrobenzaldehyde
3-Nitrobenzaldehyde
Nitrobenzene
Nitroethane
Nitroglycerin
Nitromethane
2-Nitrophenol
2-Nitrophenyl acetate
1
5
10
20
99.3
−35.1
−70.0
−48.3
−24.0
−23.9
−147.3
−74.2
93.8
+9.6
119.8
−21.0
−19.8
−20.4
−16.1
41.6
41.9
−40.4
−39.0
130.0
−13.2
−52.1
−28.0
−1.8
−1.4
−137.0
−57.0
125.4
33.7
152.0
+1.3
+2.6
+1.5
+6.7
65.0
66.0
−19.5
−18.1
−55.0
117.9
66.4
−10.0
145.7
146.3
152.3
95.5
166.8
161.6
−41.7
−39.8
38.0
+16.8
43.6
30.0
−96.5
−21.5
89.3
38.4
−54.3
+8.0
−1.0
104.0
81.6
34.0
42.0
145.5
−2.4
−43.3
−17.7
+9.5
+9.9
−131.6
−48.6
141.8
45.3
168.7
12.3
13.3
12.4
17.8
76.7
77.8
−9.1
−7.8
−45.8
133.2
79.7
+1.0
160.8
161.5
168.5
108.9
184.3
178.0
−32.1
−30.1
49.6
27.6
55.5
42.2
−81.9
−11.8
103.8
50.6
−45.4
17.9
+8.3
119.0
95.3
47.1
55.1
161.3
+9.7
−33.4
−6.5
21.7
22.3
−125.9
−39.2
157.7
58.1
186.0
24.4
25.4
24.5
30.4
89.3
90.4
+2.3
+3.6
−35.6
149.0
93.7
11.0
177.8
178.4
185.7
123.1
202.0
196.4
−21.4
−19.4
61.6
38.8
67.7
55.8
−73.4
−1.0
120.2
64.1
−35.4
28.5
18.3
134.0
110.0
61.8
69.2
179.8
23.3
−22.3
+6.0
35.2
36.2
−119.1
−28.7
177.5
72.3
204.8
37.9
38.9
38.0
44.0
102.7
104.0
14.9
16.4
−24.2
166.0
109.5
25.5
195.8
196.8
203.8
139.0
C16H32O
C2H3NS
C2H3NS
C13H26O
C6H12O2
C4H4
C10H16
C14H28O
C14H28O2
C10H8
C11H8O2
C11H8O2
C10H8O
C10H8O
C10H9N
C10H9N
C10H14N2
C6H6N2O2
C6H6N2O2
C6H6N2O2
C7H5NO3
C7H5NO3
C6H5NO2
C2H5NO2
C3H5N3O9
CH3NO2
C6H5NO3
C8H7NO4
151.5
+9.8
−8.3
117.0
+2.9
−77.7
40.0
132.0
174.1
74.2
184.0
189.7
125.5
128.6
137.7
141.6
91.8
135.7
151.5
177.6
117.7
127.4
71.6
+1.5
167
−7.9
76.8
128.0
167.3
21.6
+5.4
131.8
14.0
−70.0
53.2
148.3
190.8
85.8
196.8
202.8
142.0
145.5
153.8
157.6
107.2
150.4
167.8
194.4
133.4
142.8
84.9
12.5
188
+2.8
90.4
142.0
184.6
34.5
20.4
147.8
26.4
−61.3
67.0
166.2
207.6
101.7
211.2
216.9
158.0
161.8
171.6
175.8
123.7
167.7
185.5
213.2
150.0
159.0
99.3
24.8
210
14.1
105.8
155.8
60
100
200
400
760
191.4
31.6
−15.7
14.0
43.9
45.0
−115.0
−21.9
189.9
81.8
216.3
46.6
47.6
46.6
52.8
111.5
112.8
23.0
24.5
−16.9
176.8
119.3
34.5
207.5
208.6
214.7
148.6
206.0
42.3
−6.3
25.0
55.7
57.1
−109.0
−12.9
205.0
93.7
231.5
58.3
59.4
58.3
64.6
122.6
123.8
34.1
35.6
−7.0
190.8
133.0
47.0
222.6
223.8
229.8
161.0
228.2
58.5
+8.0
41.6
73.6
75.3
−99.9
+0.8
229.1
111.8
254.5
76.0
77.1
76.1
82.3
139.5
140.0
50.8
52.4
+8.0
253.3
79.0
24.1
60.0
94.0
96.2
−89.5
16.0
255.5
131.7
279.8
96.2
97.4
96.3
102.2
156.6
156.6
69.8
71.6
25.3
278.0
98.6
40.7
79.6
115.6
118.3
−78.2
32.0
282.5
151.5
306.5
117.6
118.9
117.7
122.5
175.5
174.3
90.0
91.9
42.4
153.4
63.0
245.3
246.7
251.6
181.2
175.8
82.0
269.8
270.5
275.8
202.3
197.7
101.0
295.8
295.5
301.0
224.0
214.3
−9.7
−7.3
74.7
51.3
81.2
70.7
−63.8
+11.0
138.0
79.4
−24.3
39.8
29.6
150.8
126.2
77.8
85.0
226.7
−1.9
+0.1
83.4
58.8
89.8
80.1
−57.7
18.7
149.3
88.8
−17.4
47.3
36.2
161.7
136.7
88.3
95.0
242.0
+8.1
10.5
94.2
69.2
100.0
93.0
−49.3
29.0
164.2
101.6
−8.1
56.8
45.5
176.2
150.0
102.2
108.6
265.8
24.1
26.5
111.3
85.0
116.1
112.3
−36.7
44.2
187.4
120.5
+6.0
71.0
59.0
197.8
172.6
121.8
128.7
291.7
41.6
44.2
129.8
102.6
133.2
133.8
−22.2
61.8
212.7
141.7
22.5
86.8
73.8
211.7
197.5
143.0
151.2
319.5
60.3
63.3
147.9
121.2
150.2
155.5
−6.9
79.8
238.5
163.0
39.1
103.3
88.9
246.5
223.2
165.4
175.0
203.7
49.0
38.2
165.7
39.8
−51.7
82.6
186.0
223.5
119.3
225.0
231.5
177.8
181.7
191.5
195.7
142.1
186.0
204.2
234.2
168.8
177.7
115.4
38.0
235
27.5
122.1
172.8
215.0
58.1
47.5
176.6
48.2
−45.3
92.6
198.3
237.2
130.2
234.5
241.3
190.0
193.7
203.8
208.1
154.7
197.8
216.5
245.9
180.7
189.5
125.8
46.5
251
35.5
132.6
181.7
230.5
70.4
59.3
191.5
59.8
−37.1
106.0
214.5
250.5
145.5
245.8
252.7
206.0
209.8
220.0
224.3
169.5
213.0
232.1
261.8
196.2
204.3
139.9
57.8
254.4
89.8
77.5
214.0
77.3
−24.1
126.0
240.4
272.3
167.7
263.5
270.3
229.6
234.0
244.9
249.7
193.8
236.3
255.3
284.5
220.0
227.4
161.2
74.8
279.8
110.8
97.8
238.3
96.7
−10.1
148.3
267.9
294.6
193.2
281.4
289.5
255.8
260.6
272.2
277.4
219.8
260.0
280.2
310.2
246.8
252.1
185.8
94.0
307.0
132.9
119.0
262.5
116.7
+5.3
171.5
297.8
318.0
217.9
300.0
308.5
282.5
288.0
300.8
306.1
247.3
284.5
305.7
336.0
273.5
278.3
210.6
114.0
46.6
146.4
194.1
63.5
167.6
213.0
82.0
191.0
233.5
101.2
214.5
253.0
Temperature, °C
Formula
C14H28O
CH2Br2
CH2Cl2
C4H8O
C8H18
C8H18
CH3F
C2H4O2
C6H8O3
C3H6O3
C18H38
C8H18
C8H18
C8H18
C8H16
C8H16O
C8H16O
C7H16
C7H16
CH3I
C13H26O2
C6H10O3
C5H8O2
C15H30O2
C12H10O
C12H10O
C11H22O
C17H34O2
C17H34O
C6H14
C6H14
C6H14O
C6H14O
C7H14O
C7H8O
C4H8
C4H8O2
C10H12O
C4H7BrO
C4H10O
C5H10O
C5H10O
C10H9N
C8H8O3
C9H10
C9H10
40
87.8
39.8
−30.5
115.0
115.6
120.2
68.2
134.3
129.6
−60.9
−59.0
15.4
−4.5
19.3
+5.4
−105.1
−42.0
59.6
13.5
−72.2
−12.0
−19.9
75.3
54.0
7.4
16.0
109.8
−14.0
−34.7
86.8
−19.2
−93.2
14.5
99.0
142.0
52.6
156.0
160.8
94.0
104.3
108.0
61.8
104.0
119.3
142.4
85.8
96.2
44.4
−21.0
127
−29.0
49.3
100.0
Melting
point,
°C
−52.8
−96.7
−85.9
−114.5
−90
−99.8
−109.5
−120.8
−121.1
−118.2
−64.4
5
18.5
55.5
15
30
−154
−118
−103
−37.3
−140.3
−87.5
−77.8
−92
−1
−8.3
−23.2
−51
35.5
28.5
23.5
57.5
80.2
160.5
184
96
122.5
50
111.5
71.5
114
146.5
40.9
58
+5.7
−90
11
−29
45
(Continued )
2-74
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
1-Nitropropane
2-Nitropropane
2-Nitrotoluene
3-Nitrotoluene
4-Nitrotoluene
4-Nitro-1,3-xylene (4-nitro-m-xylene)
Nonacosane
Nonadecane
n-Nonane
1-Nonanol
2-Nonanone
Octacosane
Octadecane
n-Octane
n-Octanol (1-octanol)
2-Octanone
n-Octyl acrylate
iodide (1-Iodooctane)
Oleic acid
Palmitaldehyde
Palmitic acid
Palmitonitrile
Pelargonic acid
Pentachlorobenzene
Pentachloroethane
Pentachloroethylbenzene
Pentachlorophenol
Pentacosane
Pentadecane
1,3-Pentadiene
1,4-Pentadiene
Pentaethylbenzene
Pentaethylchlorobenzene
n-Pentane
iso-Pentane (2-methylbutane)
neo-Pentane (2,2-dimethylpropane)
2,3,4-Pentanetriol
1-Pentene
α-Phellandrene
Phenanthrene
Phenethyl alcohol (phenyl cellosolve)
2-Phenetidine
Phenol
2-Phenoxyethanol
2-Phenoxyethyl acetate
Phenyl acetate
Phenylacetic acid
Phenylacetonitrile
Phenylacetyl chloride
Phenyl benzoate
4-Phenyl-3-buten-2-one
Phenyl isocyanate
isocyanide
Phenylcyclohexane
Phenyl dichlorophosphate
m-Phenylene diamine
(1,3-phenylenediamine)
Phenylglyoxal
Phenylhydrazine
N-Phenyliminodiethanol
1-Phenyl-1,3-pentanedione
2-Phenylphenol
4-Phenylphenol
3-Phenyl-1-propanol
Phenyl isothiocyanate
Phorone
iso-Phorone
Phosgene (carbonyl chloride)
Phthalic anhydride
Phthalide
Phthaloyl chloride
2-Picoline
Pimelic acid
α-Pinene
β-Pinene
1
5
10
20
−9.6
−18.8
50.0
50.2
53.7
65.6
234.2
133.2
+1.4
59.5
32.1
226.5
119.6
−14.0
54.0
23.6
58.5
45.8
176.5
121.6
153.6
134.3
108.2
98.6
+1.0
96.2
+13.5
+4.1
79.1
81.0
85.0
95.0
269.8
166.3
25.8
86.1
59.0
260.3
152.1
+8.3
76.5
48.4
87.7
74.8
208.5
154.6
188.1
168.3
126.0
129.7
27.2
130.0
25.3
15.8
93.8
96.0
100.5
109.8
286.4
183.5
38.0
99.7
72.3
277.4
169.6
19.2
88.3
60.9
102.0
90.0
223.0
171.8
205.8
185.8
137.4
144.3
39.8
148.0
194.2
91.6
−71.8
−83.5
86.0
90.0
−76.6
−82.9
−102.0
155.0
−80.4
20.0
118.2
58.2
67.0
40.1
78.0
82.6
38.2
97.0
60.0
48.0
106.8
81.7
10.6
12.0
67.5
66.7
230.0
121.0
−53.8
−66.2
120.0
123.8
−62.5
−65.8
−85.4
189.3
−63.3
45.7
154.3
85.9
94.7
62.5
106.6
113.5
64.8
127.0
89.0
75.3
141.5
112.2
36.0
37.0
96.5
95.9
248.2
135.4
−45.0
−57.1
135.8
140.7
−50.1
−57.0
−76.7
204.5
−54.5
58.0
173.0
100.0
108.6
73.8
121.2
128.0
78.0
141.3
103.5
89.0
157.8
127.4
48.5
49.7
111.3
110.0
37.9
28.2
109.6
112.8
117.7
125.8
303.6
200.8
51.2
113.8
87.2
295.4
187.5
31.5
101.0
74.3
117.8
105.9
240.0
190.0
223.8
204.2
149.8
160.0
53.9
166.0
192.2
266.1
150.2
−34.8
−47.7
152.4
158.1
−40.2
−47.3
−67.2
220.5
−46.0
72.1
193.7
114.8
123.7
86.0
136.0
144.5
92.3
156.0
119.4
103.6
177.0
143.8
62.5
63.4
126.4
125.9
51.8
41.8
126.3
130.7
136.0
143.3
323.2
220.0
66.0
129.0
103.4
314.2
207.4
45.1
115.2
89.8
135.6
123.8
257.2
210.0
244.4
223.8
163.7
178.5
69.9
186.2
211.2
285.6
167.7
−23.4
−37.0
171.9
178.2
−29.2
−36.5
−56.1
239.6
−34.1
87.8
215.8
130.5
139.9
100.1
152.2
162.3
108.1
173.6
136.3
119.8
197.6
161.3
77.7
78.3
144.0
143.4
C6H8N2
C8H6O2
C6H8N2
C10H15NO2
C11H12O2
C12H10O
C12H10O
C9H12O
C7H5NS
C9H14O
C9H14O
CCl2O
C8H4O3
C8H6O2
C8H4Cl2O2
C6H7N
C7H12O4
C10H16
C10H16
99.8
71.8
145.0
98.0
100.0
131.2
75.0
101.6
179.2
128.5
131.6
74.7
47.2
42.0
38.0
−92.9
96.5
95.5
86.3
−11.1
163.4
−1.0
+4.2
102.4
75.6
68.3
66.7
−77.0
121.3
127.7
118.3
+12.6
196.2
+24.6
30.0
147.0
87.8
115.8
195.8
144.0
146.2
176.2
116.0
89.8
81.5
81.2
−69.3
134.0
144.0
134.2
24.4
212.0
37.3
42.3
163.8
100.7
131.5
213.4
159.9
163.3
193.8
131.2
115.5
95.6
96.8
−60.3
151.7
161.3
151.0
37.4
229.3
51.4
58.1
182.5
115.5
148.2
233.0
178.0
180.3
213.0
147.4
122.5
111.3
114.5
−50.3
172.0
181.0
170.0
51.2
247.0
66.8
71.5
60
100
200
400
760
60.5
50.3
137.6
142.5
147.9
153.8
334.8
232.8
75.5
139.0
113.8
326.8
219.7
53.8
123.8
99.0
145.6
135.4
269.8
222.6
256.0
236.6
172.3
190.1
80.0
199.0
223.4
298.4
178.4
−16.5
−30.0
184.2
191.0
−22.2
−29.6
−49.0
249.8
−27.1
97.6
229.9
141.2
149.8
108.4
163.2
174.0
118.1
184.5
147.7
129.8
210.8
172.6
87.7
88.0
154.2
153.6
72.3
62.0
151.5
156.9
163.0
168.5
350.0
248.0
88.1
151.3
127.4
341.8
236.0
65.7
135.2
111.7
159.1
150.0
286.0
239.5
271.5
251.5
184.4
205.5
93.5
216.0
239.6
314.0
194.0
−6.7
−20.6
200.0
208.0
−12.6
−20.2
−39.1
263.5
−17.7
110.6
249.0
154.0
163.5
121.4
176.5
189.2
131.6
198.2
161.8
143.5
227.8
187.8
100.6
101.0
169.3
168.0
90.2
80.0
173.7
180.3
186.7
191.7
373.2
271.8
107.5
170.5
148.2
364.8
260.6
83.6
152.0
130.4
180.2
173.3
309.8
264.1
298.7
277.1
203.1
227.0
114.0
241.8
261.8
339.0
216.1
+8.0
−6.7
224.1
230.3
+1.9
−5.9
−23.7
284.5
−3.4
130.6
277.1
175.0
184.0
139.0
197.6
211.3
151.2
219.5
184.2
163.8
254.0
211.0
120.8
120.8
191.3
189.8
110.6
99.8
197.7
206.8
212.5
217.5
397.2
299.8
128.2
192.1
171.2
388.9
288.0
104.0
173.8
151.0
204.0
199.3
334.7
292.3
326.0
304.5
227.5
251.6
137.2
269.3
285.0
365.4
242.8
24.7
+8.3
250.2
257.2
18.5
+10.5
−7.1
307.0
+12.8
152.0
308.0
197.5
207.0
160.0
221.0
235.0
173.5
243.0
208.5
186.0
283.5
235.4
142.7
142.3
214.6
213.0
131.6
120.3
222.3
231.9
238.3
244.0
421.8
330.0
150.8
213.5
195.0
412.5
317.0
125.6
195.2
172.9
227.0
225.5
360.0
321.0
353.8
332.0
253.5
276.0
160.5
299.0
309.3
390.3
270.5
42.1
26.1
277.0
285.0
36.1
27.8
+9.5
327.2
30.1
175.0
340.2
219.5
228.0
181.9
245.3
259.7
195.9
265.5
233.5
210.0
314.0
261.0
165.6
165.0
240.0
239.5
194.0
124.2
158.7
245.3
189.8
192.2
225.3
156.8
133.3
121.4
125.6
−44.0
185.3
193.5
182.2
59.9
258.2
76.8
81.2
209.9
136.2
173.5
260.6
204.5
205.9
240.9
170.3
147.7
134.0
140.6
−35.6
202.3
210.0
197.8
71.4
272.0
90.1
94.0
233.0
153.8
195.4
284.5
226.7
227.9
263.2
191.2
169.6
153.5
163.3
−22.3
228.0
234.5
222.0
89.0
294.5
110.2
114.1
259.0
173.5
218.2
311.3
251.2
251.8
285.5
212.8
194.0
175.3
188.7
−7.6
256.8
261.8
248.3
108.4
318.5
132.3
136.1
285.5
193.5
243.5
337.8
276.5
275.0
308.0
235.0
218.5
197.2
215.2
+8.3
284.5
290.0
275.8
128.8
342.1
155.0
158.3
Temperature, °C
Formula
C3H7NO2
C3H7NO2
C7H7NO2
C7H7NO2
C7H7NO2
C8H9NO2
C29H60
C19H40
C9H20
C9H20O
C9H18O
C28H58
C18H38
C8H18
C8H18O
C8H16O
C11H20O2
C8H17I
C18H34O2
C16H32O
C16H32O2
C16H31N
C9H18O2
C6HCl5
C2HCl5
C8H5Cl5
C6HCl5O
C25H52
C15H32
C5H8
C5H8
C16H26
C16H25Cl
C5H12
C5H12
C5H12
C5H12O3
C5H10
C10H16
C14H10
C8H10O2
C8H11NO
C6H6O
C8H10O2
C10H12O3
C8H8O2
C8H8O2
C8H7N
C8H7ClO
C13H10O2
C10H10O
C7H5NO
C7H5N
C12H16
C6H5Cl2O2P
40
Melting
point,
°C
−108
−93
−4.1
15.5
51.9
+2
63.8
32
−53.7
−5
−19
61.6
28
−56.8
−15.4
−16
−45.9
14
34
64.0
31
12.5
85.5
−22
188.5
53.3
10
−129.7
−159.7
−16.6
99.5
40.6
11.6
−6.7
76.5
−23.8
70.5
41.5
+7.5
62.8
73
19.5
56.5
164.5
−21.0
28
−104
130.8
73
88.5
−70
103
−55
VAPOR PRESSURES
TABLE 2-10
2-75
Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Piperidine
Piperonal
Propane
Propenylbenzene
Propionamide
Propionic acid
anhydride
Propionitrile
Propiophenone
n-Propyl acetate
iso-Propyl acetate
n-Propyl alcohol (1-propanol)
iso-Propyl alcohol (2-propanol)
n-Propylamine
Propylbenzene
Propyl benzoate
n-Propyl bromide (1-bromopropane)
iso-Propyl bromide (2-bromopropane)
n-Propyl n-butyrate
isobutyrate
iso-Propyl isobutyrate
Propyl carbamate
n-Propyl chloride (1-chloropropane)
iso-Propyl chloride (2-chloropropane)
iso-Propyl chloroacetate
Propyl chloroglyoxylate
Propylene
Propylene glycol (1,2-Propanediol)
Propylene oxide
n-Propyl formate
iso-Propyl formate
4,4′-iso-Propylidenebisphenol
n-Propyl iodide (1-iodopropane)
iso-Propyl iodide (2-iodopropane)
n-Propyl levulinate
iso-Propyl levulinate
Propyl mercaptan (1-propanethiol)
2-iso-Propylnaphthalene
iso-Propyl β-naphthyl ketone
(2-isobutyronaphthone)
2-iso-Propylphenol
3-iso-Propylphenol
4-iso-Propylphenol
Propyl propionate
4-iso-Propylstyrene
Propyl isovalerate
Pulegone
Pyridine
Pyrocatechol
Pyrocaltechol diacetate
(1,2-phenylene diacetate)
Pyrogallol
Pyrotartaric anhydride
Pyruvic acid
Quinoline
iso-Quinoline
Resorcinol
Safrole
Salicylaldehyde
Salicylic acid
Sebacic acid
Selenophene
Skatole
Stearaldehyde
Stearic acid
Stearyl alcohol (1-octadecanol)
Styrene
Styrene dibromide [(1,2-dibromoethyl)
benzene]
Suberic acid
Succinic anhydride
Succinimide
Succinyl chloride
α-Terpineol
Terpenoline
1
5
10
20
87.0
−128.9
17.5
65.0
4.6
20.6
−35.0
50.0
−26.7
−38.3
−15.0
−26.1
−64.4
6.3
54.6
−53.0
−61.8
−1.6
−6.2
−16.3
52.4
−68.3
−78.8
+3.8
9.7
−131.9
45.5
−75.0
−43.0
−52.0
193.0
−36.0
−43.3
59.7
48.0
−56.0
76.0
−7.0
117.4
−115.4
43.8
91.0
28.0
45.3
−13.6
77.9
−5.4
−17.4
+5.0
−7.0
−46.3
31.3
83.8
−33.4
−42.5
+22.1
+16.8
+5.8
77.6
−50.0
−61.1
28.1
32.3
−120.7
70.8
−57.8
−22.7
−32.7
224.2
−13.5
−22.1
86.3
74.5
−36.3
107.9
+3.9
132.0
−108.5
57.0
105.0
39.7
57.7
−3.0
92.2
+5.0
−7.2
14.7
+2.4
−37.2
43.4
98.0
−23.3
−32.8
34.0
28.3
17.0
90.0
−41.0
−52.0
40.2
43.5
−112.1
83.2
−49.0
−12.6
−22.7
240.8
−2.4
−11.7
99.9
88.0
−26.3
123.4
15.8
148.0
−100.9
71.5
119.0
52.0
70.4
+8.8
107.6
16.0
+4.2
25.3
12.7
−27.1
56.8
114.3
−12.4
−22.0
47.0
40.6
29.0
103.2
−31.0
−42.0
53.9
55.6
−104.7
96.4
−39.3
−1.7
−12.1
255.5
+10.0
0.0
114.0
102.4
−15.4
140.3
29.2
165.7
−92.4
87.7
134.8
65.8
85.6
22.0
124.3
28.8
17.0
36.4
23.8
−16.0
71.6
131.8
−0.3
−10.1
61.5
54.3
42.4
117.7
−19.5
−31.0
68.7
68.8
−96.5
111.2
−28.4
+10.8
−0.2
273.0
23.6
+13.2
130.1
118.1
−3.2
159.0
60
Melting
point,
°C
100
200
400
760
37.7
177.0
−87.0
97.8
144.3
74.1
94.5
30.1
135.0
37.0
25.1
43.5
30.5
−9.0
81.1
143.3
+7.5
−2.5
70.3
63.0
51.4
126.5
−12.1
−23.5
78.0
77.2
−91.3
119.9
−21.3
18.8
+7.5
282.9
32.1
21.6
140.6
127.8
+4.6
171.4
49.0
191.7
−79.6
111.7
156.0
85.8
107.2
41.4
149.3
47.8
35.7
52.8
39.5
+0.5
94.0
157.4
18.0
+8.0
82.6
73.9
62.3
138.3
−2.5
−13.7
90.3
88.0
−84.1
132.0
−12.0
29.5
17.8
297.0
43.8
32.8
154.0
141.8
15.3
187.6
66.2
214.3
−68.4
132.0
174.2
102.5
127.8
58.2
170.2
64.0
51.7
66.8
53.0
15.0
113.5
180.1
34.0
23.8
101.0
91.8
80.2
155.8
+12.2
+1.3
108.8
104.7
−73.3
149.7
+2.1
45.3
33.6
317.5
61.8
50.0
175.6
161.6
31.5
211.8
85.7
238.5
−55.6
154.7
194.0
122.0
146.0
77.7
194.2
82.0
69.8
82.0
67.8
31.5
135.7
205.2
52.0
41.5
121.7
112.0
100.0
175.8
29.4
18.1
128.0
123.0
−60.9
168.1
17.8
62.6
50.5
339.0
81.8
69.5
198.0
185.2
49.2
238.5
106.0
263.0
−42.1
179.0
213.0
141.1
167.0
97.1
218.0
101.8
89.0
97.8
82.5
48.5
159.2
231.0
71.0
60.0
142.7
133.9
120.5
195.0
46.4
36.5
148.6
150.0
−47.7
188.2
34.5
81.3
68.3
360.5
102.5
89.5
221.2
208.2
67.4
266.0
Temperature, °C
Formula
C5H11N
C8H6O3
C 3 H8
C9H10
C3H7NO
C3H6O2
C6H10O3
C3H5N
C9H10O
C5H10O2
C5H10O2
C3H8O
C3H8O
C3H9N
C9H12
C10H12O2
C3H7Br
C3H7Br
C7H14O2
C7H14O2
C7H14O2
C4H9NO2
C3H7Cl
C3H7Cl
C5H9ClO2
C5H7ClO3
C3H6
C3H8O2
C3H6O
C4H8O2
C4H8O2
C15H16O2
C3H7I
C3H7I
C8H14O3
C8H14O3
C3H8S
C13H14
40
C14H14O
C9H12O
C9H12O
C9H12O
C6H12O2
C11H14
C8H16O2
C10H16O
C5H5N
C6H6O2
133.2
56.6
62.0
67.0
−14.2
34.7
+8.0
58.3
−18.9
165.4
83.8
90.3
94.7
+8.0
62.3
32.8
82.5
+2.5
104.0
181.0
97.0
104.1
108.0
19.4
76.0
45.1
94.0
13.2
118.3
197.7
111.7
119.8
123.4
31.6
91.2
58.0
106.8
24.8
134.0
215.6
127.5
136.2
139.8
45.0
108.0
72.8
121.7
38.0
150.6
227.0
137.7
146.6
149.7
53.8
118.4
82.3
130.2
46.8
161.7
242.3
150.3
160.2
163.3
65.2
132.8
95.0
143.1
57.8
176.0
264.0
170.1
182.0
184.0
82.7
153.9
113.9
162.5
75.0
197.7
288.2
192.6
205.0
206.1
102.0
178.0
135.0
189.8
95.6
221.5
313.0
214.5
228.0
228.2
122.4
202.5
155.9
221.0
115.4
245.5
C10H10O4
C6H6O3
C5H6O3
C3H4O3
C9H7N
C9H7N
C6H6O2
C10H10O2
C7H6O2
C7H6O3
C10H18O4
C4H4Se
C9H9N
C18H36O
C18H36O2
C18H36O
C8H8
98.0
69.7
21.4
59.7
63.5
108.4
63.8
33.0
113.7
183.0
−39.0
95.0
140.0
173.7
150.3
−7.0
129.8
151.7
99.7
45.8
89.6
92.7
138.0
93.0
60.1
136.0
215.7
−16.0
124.2
174.6
209.0
185.6
+18.0
145.7
167.7
114.2
57.9
103.8
107.8
152.1
107.6
73.8
146.2
232.0
−4.0
139.6
192.1
225.0
202.0
30.8
161.8
185.3
130.0
70.8
119.8
123.7
168.0
123.0
88.7
156.8
250.0
+9.1
154.3
210.6
243.4
220.0
44.6
179.8
204.2
147.8
85.3
136.7
141.6
185.3
140.1
105.2
172.2
268.2
24.1
171.9
230.8
263.3
240.4
59.8
191.6
216.3
158.6
94.1
148.1
152.0
195.8
150.3
115.7
182.0
279.8
33.8
183.6
244.2
275.5
252.7
69.5
206.5
232.0
173.8
106.5
163.2
167.6
209.8
165.1
129.4
193.4
294.5
47.0
197.4
260.0
291.0
269.4
82.0
228.7
255.3
196.1
124.7
186.2
190.0
230.8
186.2
150.0
210.0
313.2
66.7
218.8
285.0
316.5
293.5
101.3
253.3
281.5
221.0
144.7
212.3
214.5
253.4
210.0
173.7
230.5
332.8
89.8
242.5
313.8
343.0
320.3
122.5
278.0
309.0
247.4
165.0
237.7
240.5
276.5
233.0
196.5
256.0
352.3
114.3
266.2
342.5
370.0
349.5
145.2
C8H8Br2
C8H14O4
C4H4O3
C4H5NO2
C4H4Cl2O2
C10H18O
C10H16
86.0
172.8
92.0
115.0
39.0
52.8
32.3
115.6
205.5
115.0
143.2
65.0
80.4
58.0
129.8
219.5
128.2
157.0
78.0
94.3
70.6
145.2
238.2
145.3
174.0
91.8
109.8
84.8
161.8
254.6
163.0
192.0
107.5
126.0
100.0
172.2
265.4
174.0
203.0
117.2
136.3
109.8
186.3
279.8
189.0
217.4
130.0
150.1
122.7
207.8
300.5
212.0
240.0
149.3
171.2
142.0
230.0
322.8
237.0
263.5
170.0
194.3
163.5
254.0
345.5
261.0
287.5
192.5
217.5
185.0
−9
37
−187.1
−30.1
79
−22
−45
−91.9
21
−92.5
−127
−85.8
−83
−99.5
−51.6
−109.9
−89.0
−95.2
−122.8
−117
−185
−112.1
−92.9
−98.8
−90
−112
15.5
26
61
−76
−42
105
133
13.6
−15
24.6
110.7
11.2
−7
159
134.5
95
63.5
69.3
58.5
−30.6
142
119.6
125.5
17
35
(Continued )
2-76
PHYSICAL AnD CHEMICAL DATA
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Formula
1,1,1,2-Tetrabromoethane
1,1,2,2-Tetrabromoethane
Tetraisobutylene
Tetracosane
1,2,3,4-Tetrachlorobenzene
1,2,3,5-Tetrachlorobenzene
1,2,4,5-Tetrachlorobenzene
1,1,2,2-Tetrachloro-1,2-difluoroethane
1,1,1,2-Tetrachloroethane
1,1,2,2-Tetrachloroethane
1,2,3,5-Tetrachloro-4-ethylbenzene
Tetrachloroethylene
2,3,4,6-Tetrachlorophenol
3,4,5,6-Tetrachloro-1,2-xylene
Tetradecane
Tetradecylamine
Tetradecyltrimethylsilane
Tetraethoxysilane
1,2,3,4-Tetraethylbenzene
Tetraethylene glycol
Tetraethylene glycol chlorohydrin
Tetraethyllead
Tetraethylsilane
Tetralin
1,2,3,4-Tetramethylbenzene
1,2,3,5-Tetramethylbenzene
1,2,4,5-Tetramethylbenzene
2,2,3,3-Tetramethylbutane
Tetramethylene dibromide
(1,4-dibromobutane)
Tetramethyllead
Tetramethyltin
Tetrapropylene glycol monoisopropyl ether
Thioacetic acid (mercaptoacetic acid)
Thiodiglycol (2,2′-thiodiethanol)
Thiophene
Thiophenol (benzenethiol)
α-Thujone
Thymol
Tiglaldehyde
Tiglic acid
Tiglonitrile
Toluene
Toluene-2,4-diamine
2-Toluic nitrile (2-tolunitrile)
4-Toluic nitrile (4-tolunitrile)
2-Toluidine
3-Toluidine
4-Toluidine
2-Tolyl isocyanide
4-Tolylhydrazine
Tribromoacetaldehyde
1,1,2-Tribromobutane
1,2,2-Tribromobutane
2,2,3-Tribromobutane
1,1,2-Tribromoethane
1,2,3-Tribromopropane
Triisobutylamine
Triisobutylene
2,4,6-Tritertbutylphenol
Trichloroacetic acid
Trichloroacetic anhydride
Trichloroacetyl bromide
2,4,6-Trichloroaniline
1,2,3-Trichlorobenzene
1,2,4-Trichlorobenzene
1,3,5-Trichlorobenzene
1,2,3-Trichlorobutane
1,1,1-Trichloroethane
1,1,2-Trichloroethane
Trichloroethylene
Trichlorofluoromethane
2,4,5-Trichlorophenol
2,4,6-Trichlorophenol
C2H2Br4
C2H2Br4
C16H32
C24H50
C6H2Cl4
C6H2Cl4
C6H2Cl4
C2Cl4F2
C2H2Cl4
C2H2Cl4
C8H6Cl4
C2Cl4
C6H2Cl4O
C8H6Cl4
C14H30
C14H31N
C17H38Si
C8H20O4Si
C14H22
C8H18O5
C8H17ClO4
C8H20Pb
C8H20Si
C10H12
C10H14
C10H14
C10H14
C8H18
C4H8Br2
C4H12Pb
C4H12Sn
C15H32O5
C2H4O2S
C4H10O2S
C4H4S
C6H6S
C10H16O
C10H14O
C5H8O
C5H8O2
C5H7N
C7H8
C7H10N2
C8H7N
C8H7N
C7H9N
C7H9N
C7H9N
C8H7N
C7H10N2
C2HBr3O
C4H7Br3
C4H7Br3
C4H7Br3
C2H3Br3
C3H5Br3
C12H27N
C12H24
C18H30O
C2HCl3O2
C4Cl6O3
C2BrCl3O
C6H4Cl3N
C6H3Cl3
C6H3Cl3
C6H3Cl3
C4H7Cl3
C2H3Cl3
C2H3Cl3
C2HCl3
CCl3F
C6H3Cl3O
C6H3Cl3O
1
5
10
20
58.0
65.0
63.8
183.8
68.5
58.2
83.3
95.5
93.7
219.6
99.6
89.0
95.7
110.0
108.5
237.6
114.7
104.1
108.5
126.0
124.5
255.3
131.2
121.6
−37.5
−16.3
−3.8
77.0
−20.6
100.0
94.4
76.4
102.6
120.0
16.0
65.7
153.9
110.1
38.4
−1.0
38.0
42.6
40.6
45.0
−17.4
−16.0
+7.4
+20.7
110.0
+2.4
130.3
125.0
106.0
135.8
150.7
40.3
96.2
183.7
141.8
63.6
+23.9
65.3
68.7
65.8
65.0
+3.2
−5.0
19.3
33.0
126.0
13.8
145.3
140.3
120.7
152.0
166.2
52.6
111.6
197.1
156.1
74.8
36.3
79.0
81.8
77.8
74.6
13.5
32.0
−29.0
−51.3
116.6
60.0
42.0
−40.7
18.6
38.3
64.3
−25.0
52.0
−25.5
−26.7
106.5
36.7
42.5
44.0
41.0
42.0
25.2
82.4
18.5
45.0
41.0
38.2
32.6
47.5
32.3
18.0
95.2
51.0
56.2
−7.4
134.0
40.0
38.4
58.8
−6.8
−31.0
147.8
87.7
96.0
−20.8
43.7
65.7
92.8
−1.6
77.8
−2.4
−4.4
137.2
64.0
71.3
69.3
68.0
68.2
51.0
110.0
45.0
73.5
69.0
66.0
58.0
75.8
57.4
44.0
126.1
76.0
85.3
+16.7
157.8
70.0
67.3
63.8
27.2
−32.0
−2.0
−22.8
−67.6
102.1
105.9
72.4
+4.4
−20.6
163.0
101.5
128.0
−10.9
56.0
79.3
107.4
+10.0
90.2
+9.2
+6.4
151.7
77.9
85.8
81.4
82.0
81.8
64.0
123.8
58.0
87.8
83.2
79.8
70.6
90.0
69.8
56.5
142.0
88.2
99.6
29.3
170.0
85.6
81.7
78.0
40.0
−21.9
+8.3
−12.4
−59.0
117.3
120.2
40
60
100
200
400
760
Temperature, °C
+0.5
−52.0
−24.0
−43.8
−84.3
72.0
76.5
Melting
point,
°C
+6.7
32.1
46.2
143.7
26.3
161.0
156.0
135.6
170.0
183.5
65.8
127.7
212.3
172.6
88.0
50.0
93.8
95.8
91.0
88.0
24.6
123.2
144.0
142.2
276.3
149.2
140.0
146.0
19.8
46.7
60.8
162.1
40.1
179.1
174.2
152.7
189.0
201.5
81.1
145.8
228.0
190.0
102.4
65.3
110.4
111.5
105.8
104.2
36.8
132.0
155.1
152.6
288.4
160.0
152.0
157.7
28.1
56.0
70.0
175.0
49.2
190.0
185.8
164.0
200.2
213.3
90.7
156.7
237.8
200.5
111.7
74.8
121.3
121.8
115.4
114.8
44.5
144.0
170.0
167.5
305.2
175.7
168.0
173.5
38.6
68.0
83.2
191.6
61.3
205.2
200.5
178.5
215.7
227.8
103.6
172.4
250.0
214.7
123.8
88.0
135.3
135.7
128.3
128.1
54.8
161.5
192.5
190.0
330.5
198.0
193.7
196.0
55.0
87.2
102.2
215.3
79.8
227.2
223.0
201.8
239.8
250.0
123.5
196.0
268.4
236.5
142.0
108.0
157.2
155.7
149.9
149.5
70.2
181.0
217.5
214.6
358.0
225.5
220.0
220.5
73.1
108.2
124.0
243.0
100.0
250.4
248.3
226.8
264.6
275.0
146.2
221.4
288.0
258.2
161.8
130.2
181.8
180.0
173.7
172.1
87.4
200.0
243.5
240.0
386.4
254.0
246.0
245.0
92.0
130.5
145.9
270.0
120.8
275.0
273.5
252.5
291.2
300.0
168.5
248.0
307.8
281.5
183.0
153.0
207.2
204.4
197.9
195.9
106.3
87.6
16.6
−9.3
179.8
115.8
165.0
0.0
69.7
93.7
122.6
23.2
103.8
22.1
18.4
167.9
93.0
101.7
95.1
96.7
95.8
78.2
138.6
72.1
103.2
98.6
94.6
84.2
105.8
83.0
70.0
158.0
101.8
114.3
42.1
182.6
101.8
97.2
93.7
55.0
−10.8
21.6
−1.0
−49.7
134.0
135.8
104.0
30.3
+3.5
197.7
131.8
210.0
+12.5
84.2
110.0
139.8
37.0
119.0
36.7
31.8
185.7
110.0
109.5
110.0
113.5
111.5
94.0
154.1
87.8
120.2
116.0
111.8
100.0
122.8
97.8
86.7
177.4
116.3
131.2
57.2
195.8
119.8
114.8
110.8
71.5
+1.6
35.2
+11.9
−39.0
151.5
152.2
115.1
39.2
11.7
209.0
142.0
240.5
20.1
93.9
120.2
149.8
45.8
127.8
46.0
40.3
196.2
120.8
130.0
119.8
123.8
121.5
104.0
165.0
97.5
131.6
127.0
122.2
110.0
134.0
107.3
96.7
188.0
125.9
141.8
66.7
204.5
131.5
125.7
121.8
82.0
9.5
44.0
20.0
−32.3
162.5
163.5
128.7
50.8
22.8
223.3
154.0
285
30.5
106.6
134.0
164.1
57.7
140.5
58.2
51.9
211.5
135.0
145.2
133.0
136.7
133.7
117.7
178.0
110.2
146.0
141.8
136.3
123.5
148.0
119.7
110.0
203.0
137.8
155.2
79.5
214.6
146.0
140.0
136.0
96.2
20.0
55.7
31.4
−23.0
178.0
177.8
149.8
68.8
39.8
245.0
173.8
89.0
58.5
268.3
197.5
110.0
78.0
292.7
−20
−27.5
46.5
125.8
154.2
185.5
75.4
158.0
77.8
69.5
232.8
156.0
167.3
153.0
157.6
154.0
137.8
198.0
130.0
167.8
163.5
157.8
143.5
170.0
138.0
130.2
226.2
155.4
176.2
98.4
229.8
168.2
162.0
157.7
118.0
36.2
73.3
48.0
−9.1
201.5
199.0
64.7
146.7
177.8
209.2
95.5
179.2
99.7
89.5
256.0
180.0
193.0
176.2
180.6
176.9
159.9
219.5
151.6
192.0
188.0
182.2
165.4
195.0
157.8
153.0
250.6
175.2
199.8
120.2
246.4
193.5
187.7
183.0
143.0
54.6
93.0
67.0
+6.8
226.5
222.5
84.4
168.0
201.0
231.8
116.4
198.5
122.0
110.6
280.0
205.2
217.6
199.7
203.3
200.4
183.5
242.0
174.0
216.2
213.8
206.5
188.4
220.0
179.0
179.0
276.3
195.6
223.0
143.0
262.0
218.5
213.0
208.4
169.0
74.1
113.9
86.7
23.7
251.8
246.0
−38.3
51.1
46.5
54.5
139
26.5
−68.7
−36
−19.0
69.5
5.5
11.6
−136
−31.0
−6.2
−24.0
79.5
−102.2
−16.5
51.5
64.5
−95.0
99
−13
29.5
−16.3
−31.5
44.5
65.5
−26
16.5
−22
57
78
52.5
17
63.5
−30.6
−36.7
−73
62
68.5
VAPOR PRESSURES
2-77
TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued )
Pressure, mmHg
Compound
Name
Tri-2-chlorophenylthiophosphate
1,1,1-Trichloropropane
1,2,3-Trichloropropane
1,1,2-Trichloro-1,2,2-trifluoroethane
Tricosane
Tridecane
Tridecanoic acid
Triethoxymethylsilane
Triethoxyphenylsilane
1,2,4-Triethylbenzene
1,3,4-Triethylbenzene
Triethylborine
Triethyl camphoronate
citrate
Triethyleneglycol
Triethylheptylsilane
Triethyloctylsilane
Triethyl orthoformate
phosphate
Triethylthallium
Trifluorophenylsilane
Trimethallyl phosphate
2,3,5-Trimethylacetophenone
Trimethylamine
2,4,5-Trimethylaniline
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
1,3,5-Trimethylbenzene
2,2,3-Trimethylbutane
Trimethyl citrate
Trimethyleneglycol (1,3-propanediol)
1,2,4-Trimethyl-5-ethylbenzene
1,3,5-Trimethyl-2-ethylbenzene
2,2,3-Trimethylpentane
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
2,3,4-Trimethylpentane
2,2,4-Trimethyl-3-pentanone
Trimethyl phosphate
2,4,5-Trimethylstyrene
2,4,6-Trimethylstyrene
Trimethylsuccinic anhydride
Triphenylmethane
Triphenylphosphate
Tripropyleneglycol
Tripropyleneglycol monobutyl ether
Tripropyleneglycol monoisopropyl ether
Tritolyl phosphate
Undecane
Undecanoic acid
10-Undecenoic acid
Undecan-2-ol
n-Valeric acid
iso-Valeric acid
γ-Valerolactone
Valeronitrile
Vanillin
Vinyl acetate
2-Vinylanisole
3-Vinylanisole
4-Vinylanisole
Vinyl chloride (1-chloroethylene)
cyanide (acrylonitrile)
fluoride (1-fluoroethylene)
Vinylidene chloride (1,1-dichloroethene)
4-Vinylphenetole
2-Xenyl dichlorophosphate
2,4-Xyaldehyde
2-Xylene (2-xylene)
3-Xylene (3-xylene)
4-Xylene (4-xylene)
2,4-Xylidine
2,6-Xylidine
1
5
10
20
188.2
217.2
231.2
246.7
261.7
−28.8
+9.0
−68.0
170.0
59.4
137.8
−1.5
71.0
46.0
47.9
−7.0
33.7
−49.4
206.3
98.3
166.3
+22.8
98.8
74.2
76.0
107.0
114.0
70.0
73.7
+5.5
39.6
+9.3
−31.0
93.7
79.0
−97.1
68.4
16.8
13.6
9.6
150.2
138.7
144.0
99.8
104.8
29.2
67.8
37.6
−9.7
131.0
108.0
−81.7
95.9
42.9
38.3
34.7
106.2
59.4
43.7
38.8
−29.0
−36.5
−25.8
−26.3
14.7
26.0
48.1
37.5
53.5
169.7
193.5
96.0
101.5
82.4
154.6
32.7
101.4
114.0
71.1
42.2
34.5
37.5
−6.0
107.0
−48.0
41.9
43.4
45.2
−105.6
−51.0
−149.3
−77.2
64.0
138.2
59.0
−3.8
−6.9
−8.1
52.6
44.0
146.2
87.2
71.2
67.0
−7.1
−15.0
−3.9
−4.1
36.0
53.7
77.0
65.7
82.6
188.4
230.4
125.7
131.6
112.4
184.2
59.7
133.1
142.8
99.0
67.7
59.6
65.8
+18.1
138.4
−28.0
68.0
69.9
72.0
−90.8
−30.7
−138.0
−60.0
91.7
171.1
85.9
+20.2
+16.8
+15.5
79.8
72.6
+4.2
46.0
−40.3
223.0
104.0
181.0
34.6
112.6
88.5
90.2
−148.0
166.0
144.0
158.1
114.6
120.6
40.5
82.1
51.7
+0.8
149.8
122.3
−73.8
109.0
55.9
50.7
47.4
−18.8
160.4
100.6
84.6
80.5
+3.9
−4.3
+6.9
+7.1
46.4
67.8
91.6
79.7
97.4
197.0
249.8
140.5
147.0
127.3
198.0
73.9
149.0
156.3
112.8
79.8
71.3
79.8
30.0
154.0
−18.0
81.0
83.0
85.7
−83.7
−20.3
−132.2
−51.2
105.6
187.0
99.0
32.1
28.3
27.3
93.0
87.0
16.2
59.3
−30.0
242.0
120.2
195.8
47.2
127.2
104.0
105.8
−140.6
183.6
171.1
174.0
130.3
137.7
53.4
97.8
67.7
12.3
169.8
137.5
−65.0
123.7
69.9
64.5
61.0
−7.5
177.2
115.5
99.7
96.0
16.0
+7.5
19.2
19.3
57.6
83.0
107.1
94.8
113.8
206.8
269.7
155.8
161.8
143.7
213.2
85.6
166.0
172.0
127.5
93.1
84.0
95.2
43.3
170.5
−7.0
94.7
97.2
100.0
−75.7
−9.0
−125.4
−41.7
120.3
205.0
114.0
45.1
41.1
40.1
107.6
102.7
29.9
74.0
−18.5
261.3
137.7
212.4
61.7
143.5
121.7
122.6
−131.4
201.8
190.4
191.3
148.0
155.7
67.5
115.7
85.4
25.4
192.0
154.2
−55.2
139.8
85.4
79.8
76.1
+5.2
194.2
131.0
106.0
113.2
29.5
20.7
33.0
32.9
69.8
100.0
124.2
111.8
131.0
215.5
290.3
173.7
179.8
161.4
229.7
104.4
185.6
188.7
143.7
107.8
98.0
101.9
57.8
188.7
+5.3
110.0
112.5
116.0
−66.8
+3.8
−118.0
−31.1
136.3
223.8
129.7
59.5
55.3
54.4
123.8
120.2
60
100
200
400
760
271.5
283.8
302.8
322.0
341.3
38.3
83.6
−11.2
273.8
148.2
222.0
70.4
153.2
132.2
133.4
−125.2
213.5
202.5
201.5
158.2
168.0
76.0
126.3
95.7
33.2
207.0
165.7
−48.8
149.5
95.3
89.5
85.8
13.3
205.5
141.1
126.3
123.8
38.1
29.1
41.8
41.6
77.3
110.0
135.5
122.3
142.2
221.2
305.2
184.6
190.2
173.2
239.8
115.2
197.2
199.5
153.7
116.6
107.3
122.4
66.9
199.8
13.0
119.8
122.3
126.1
−61.1
11.8
−113.0
−24.0
146.4
236.0
139.8
68.8
64.4
63.5
133.7
131.5
50.0
96.1
−1.7
289.8
162.5
236.0
82.7
167.5
146.8
147.7
−116.0
228.6
217.8
214.6
174.0
184.3
88.0
141.6
112.1
44.2
225.7
179.7
−40.3
162.0
108.8
102.8
98.9
24.4
219.6
153.4
140.3
137.9
49.9
40.7
53.8
53.4
87.6
124.0
149.8
136.8
156.5
228.4
322.5
199.0
204.4
187.8
252.2
128.1
212.5
213.5
167.2
128.3
118.9
136.5
78.6
214.5
23.3
132.3
135.3
139.7
−53.2
22.8
−106.2
−15.0
159.8
251.5
152.2
81.3
76.8
75.9
146.8
146.0
67.7
115.6
+13.5
313.5
185.0
255.2
101.0
188.0
168.3
168.3
−101.0
250.8
242.2
235.2
196.0
208.0
106.0
163.7
136.0
60.1
255.0
201.3
−27.0
182.3
129.0
122.7
118.6
41.2
241.3
172.8
160.3
158.4
67.8
58.1
72.0
71.3
102.2
145.0
171.8
157.8
179.8
239.7
349.8
220.2
224.4
209.7
271.8
149.3
237.8
232.8
187.7
146.0
136.2
157.7
97.7
237.3
38.4
151.0
154.0
159.0
−41.3
38.7
−95.4
−1.0
180.0
275.3
172.3
100.2
95.5
94.6
166.4
168.0
87.5
137.0
30.2
339.8
209.4
276.5
121.8
210.5
193.7
193.2
−81.0
276.0
267.5
256.6
221.0
235.0
125.7
187.0
163.5
78.7
288.5
224.3
−12.5
203.7
152.0
145.4
141.0
60.4
264.2
193.8
184.5
183.5
88.2
78.0
92.7
91.8
118.4
167.8
196.1
182.3
205.5
249.8
379.2
244.3
247.0
232.8
292.7
171.9
262.8
254.0
209.8
165.0
155.2
182.3
118.7
260.0
55.5
172.1
175.8
182.0
−28.0
58.3
−84.0
+14.8
202.8
301.5
194.1
121.7
116.7
115.9
188.3
193.7
108.2
158.0
47.6
366.5
234.0
299.0
143.5
233.5
218.0
217.5
−56.2
301.0
294.0
278.3
247.0
262.0
146.0
211.0
192.1
98.3
324.0
247.5
+2.9
234.5
176.1
169.2
164.7
80.9
287.0
214.2
208.1
208.0
109.8
99.2
114.8
113.5
135.0
192.7
221.2
207.0
231.0
259.2
413.5
267.2
269.5
256.6
313.0
195.8
290.0
275.0
232.0
184.4
175.1
207.5
140.8
285.0
72.5
194.0
197.5
204.5
−13.8
78.5
−72.2
31.7
225.0
328.5
215.5
144.4
139.1
138.3
211.5
217.9
Temperature, °C
Formula
C18H12Cl3O3
PS
C3H5Cl3
C3H5Cl3
C2Cl3F3
C23H48
C13H28
C13H26O2
C7H18O3Si
C12H20O3Si
C12H18
C12H18
C6H15B
C15H26O6
C12H20O7
C6H14O4
C13H30Si
C14H32Si
C7H16O3
C6H15O4P
C6H15Tl
C6H5F3Si
C12H21PO4
C11H14O
C3H9N
C9H13N
C9H12
C9H12
C9H12
C7H16
C9H14O7
C3H8O2
C11H16
C11H16
C8H18
C8H18
C8H18
C8H18
C8H16O
C3H9O4P
C11H14
C11H14
C7H10O3
C19H16
C18H15O4P
C9H20O4
C13H28O4
C12H26O4
C21H21O4P
C11H24
C11H22O2
C11H20O2
C11H24O
C5H10O2
C5H10O2
C5H8O2
C5H9N
C8H8O3
C4H6O2
C9H10O
C9H10O
C9H10O
C2H3Cl
C3H3N
C2H3F
C2H2Cl2
C10H12O
C12H9Cl2PO
C9H10O
C8H10
C8H10
C8H10
C8H11N
C8H11N
40
Melting
point,
°C
−77.7
−14.7
−35
47.7
−6.2
41
135
−63.0
−117.1
67
−25.5
−44.1
−44.8
−25.0
78.5
−112.3
−107.3
−101.5
−109.2
93.4
49.4
−25.6
29.5
24.5
−34.5
−37.6
81.5
−153.7
−82
−160.5
−122.5
75
−25.2
−47.9
+13.3
2-78
PHYSICAL AnD CHEMICAL DATA
VAPOR PRESSURES OF SOLUTIOnS
TABLE 2-11 Partial Pressures of Water over Aqueous Solutions of HCl*
log10 pmm = A − B/T, (T in K), which, however, agrees only approximately with the table. The table is more nearly correct.
Partial pressure of H2O, mmHg, °C
% HCl
A
B
0°
5°
10°
15°
20°
25°
30°
35°
40°
45°
50°
60°
6
10
14
18
20
8.99156
8.99864
8.97075
8.98014
8.97877
2282
2295
2300
2323
2334
4.18
3.84
3.39
2.87
2.62
6.04
5.52
4.91
4.21
3.83
8.45
7.70
6.95
5.92
5.40
11.7
10.7
9.65
8.26
7.50
15.9
14.6
13.1
11.3
10.3
21.8
20.0
18.0
15.4
14.1
29.1
26.8
24.1
20.6
19.0
39.4
35.5
31.9
27.5
25.1
50.6
47.0
42.1
36.4
33.3
66.2
61.5
55.3
47.9
43.6
86.0
80.0
72.0
62.5
57.0
139
130
116
102
93.5
22
24
26
28
30
9.02708
8.96022
9.01511
8.97611
9.00117
2363
2356
2390
2395
2422
2.33
2.05
1.76
1.50
1.26
3.40
3.04
2.60
2.24
1.90
4.82
4.31
3.71
3.21
2.73
6.75
6.03
5.21
4.54
3.88
9.30
8.30
7.21
6.32
5.41
12.6
11.4
9.95
8.75
7.52
17.1
15.4
13.5
11.8
10.2
22.8
20.4
18.0
15.8
13.7
30.2
27.1
24.0
21.1
18.4
39.8
35.7
31.7
27.9
24.3
52.0
46.7
41.5
36.5
32.0
32
34
36
38
40
42
9.03317
9.07143
9.11815
9.20783
9.33923
9.44953
2453
2487
2526
2579
2647
2709
1.04
0.85
0.68
0.53
0.41
0.31
1.57
1.29
1.03
0.81
0.63
0.48
2.27
1.87
1.50
1.20
0.94
0.72
3.25
2.70
2.19
1.75
1.37
1.06
4.55
3.81
3.10
2.51
2.00
1.56
6.37
5.35
4.41
3.60
2.88
2.30
11.7
9.95
8.33
6.92
5.68
4.60
15.7
13.5
11.4
9.52
7.85
6.45
21.0
18.1
15.4
13.0
10.7
8.90
27.7
24.0
20.4
17.4
14.5
12.1
8.70
7.32
6.08
5.03
4.09
3.28
70°
80°
90°
100° 110°
220
204
185
162
150
333
310
273
248
230
492
463
425
374
345
715
677
625
550
510
960
892
783
729
85.6
77.0
69.0
60.7
53.5
138
124
112
99.0
87.5
211
194
173
154
136
317
290
261
234
207
467
426
387
349
310
670
611
555
499
444
46.5
40.5
34.8
29.6
25.0
21.2
76.5
66.5
57.0
49.1
42.1
35.8
120
104
90.0
77.5
67.3
57.2
184
161
140
120
105
89.2
275
243
212
182
158
135
396
355
311
266
230
195
∗Uncertainty, ca. 2 percent for solutions of 15 to 30 percent HCl between 0 and 100°; for solutions of > 30 percent HCl the accuracy is ca. 5 percent at the lower
temperatures and ca. 15 percent at the higher temperatures. Below 15 percent HCl, the uncertainty is ca. 5 percent at the lower temperatures and higher strengths to
ca. 15 to 20 percent at the lower strengths and perhaps 15 to 20 percent at the higher temperatures and lower strengths.
International Critical Tables, vol. 3, p. 301.
FIG. 2-1 Vapor pressures of H3PO4 aqueous: partial pressure of H2O vapor. (Courtesy of Victor Chemical Works, Stauffer Chemical Company; measurements by W. H.
Woodstock.)
VAPOR PRESSURES OF SOLUTIOnS
2-79
TABLE 2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions*
Weight percent, H2SO4
°C
0
10
20
30
40
50
60
70
80
90
10.0
20.0
.582E−02
.117E−01
.223E−01
.404E−01
.703E−01
.117
.189
.296
.449
.664
.534E−02
.107E−01
.205E−01
.373E−01
.649E−01
.109
.175
.275
.417
.617
30.0
.448E−02
.909E−02
.174E−01
.319E−01
.558E−01
.939E−01
.152
.239
.365
.542
40.0
.326E−02
.670E−02
.130E−01
.241E−01
.427E−01
.725E−01
.119
.188
.290
.434
50.0
60.0
70.0
75.0
80.0
85.0
.193E−02
.405E−02
.802E−02
.151E−01
.272E−01
.470E−01
.782E−01
.126
.196
.298
.836E−03
.180E−02
.367E−02
.710E−02
.131E−01
.232E−01
.395E−01
.651E−01
.104
.161
.207E−03
.467E−03
.995E−03
.201E−02
.387E−02
.715E−02
.127E−01
.217E−01
.360E−01
.578E−01
.747E−04
.175E−03
.388E−03
.811E−03
.162E−02
.309E−02
.565E−02
.997E−02
.170E−01
.281E−01
.197E−04
.490E−04
.115E−04
.253E−03
.531E−03
.106E−02
.204E−02
.376E−02
.668E−02
.115E−01
.343E−05
.952E−05
.245E−04
.589E−04
.133E−03
.286E−03
.584E−03
.114E−02
.213E−02
.383E−02
.905E−01
.138
.206
.301
.481
.605
.837
1.138
1.525
2.017
.452E−01
.708E−01
.108
.162
.236
.339
.478
.662
.902
1.212
.192E−01
.312E−01
.493E−01
.760E−01
.115
.170
.246
.350
.489
.673
.666E−02
.112E−01
.183E−01
.291E−01
.451E−01
.682E−01
.101
.147
.208
.291
100
110
120
130
140
150
160
170
180
190
.957
1.349
1.863
2.524
3.361
4.404
5.685
7.236
9.093
11.289
.891
1.258
1.740
2.361
3.149
4.132
5.342
6.810
8.571
10.658
.786
1.113
1.544
2.101
2.810
3.697
4.793
6.127
7.731
9.640
.634
.904
1.264
1.732
2.333
3.090
4.031
5.185
6.584
8.259
.441
.638
.903
1.253
1.708
2.289
3.021
3.930
5.045
6.397
.244
.360
.519
.734
1.020
1.392
1.870
2.475
3.233
4.169
200
210
220
230
240
250
260
270
280
290
13.861
16.841
20.264
24.160
28.561
33.494
38.984
45.055
51.726
59.015
13.107
15.951
19.225
22.960
27.188
31.939
37.240
43.116
49.590
56.681
11.887
14.505
17.529
20.992
24.927
29.364
34.334
39.865
45.984
52.715
10.245
12.576
15.287
18.414
21.992
26.056
30.642
35.784
41.514
47.865
8.020
9.948
12.217
14.864
17.929
21.452
25.472
30.030
35.168
40.926
5.312
6.696
8.354
10.322
12.641
15.351
18.496
22.121
26.274
31.003
2.632
3.395
4.331
5.466
6.831
8.458
10.382
12.640
15.269
18.311
1.606
2.101
2.714
3.467
4.381
5.480
6.788
8.333
10.142
12.242
.913
1.220
1.609
2.096
2.699
3.435
4.326
5.395
6.663
8.155
.401
.542
.724
.952
1.237
1.587
2.012
2.525
3.136
3.857
300
310
320
330
340
350
66.934
75.495
84.705
94.567
105.083
116.251
64.407
72.781
81.816
91.518
101.894
112.946
60.081
68.100
76.792
86.172
96.252
107.043
54.868
62.553
70.947
80.077
89.969
100.646
47.346
54.470
62.337
70.988
80.463
90.802
36.360
42.395
49.164
56.721
65.123
74.426
21.808
25.804
30.343
35.473
41.240
47.692
14.665
17.438
20.591
24.153
28.154
32.622
9.897
11.912
14.227
16.867
19.855
23.217
4.701
5.680
6.806
8.093
9.551
11.193
Weight percent, H2SO4
°C
90.0
92.0
94.0
96.0
97.0
99.0
99.5
100.0
0
10
20
30
40
50
60
70
80
90
.518E−06
.159E−05
.448E−05
.117E−04
.285E−04
.652E−04
.141E−03
.290E−03
.569E−03
.107E−02
.242E−06
.762E−06
.220E−05
.587E−05
.146E−04
.341E−04
.754E−04
.158E−03
.316E−03
.606E−03
.107E−06
.344E−06
.101E−05
.275E−05
.696E−05
.166E−04
.372E−04
.795E−04
.162E−03
.315E−03
.401E−07
.130E−06
.390E−06
.108E−05
.278E−05
.672E−05
.154E−04
.334E−04
.691E−04
.137E−03
.218E−07
.713E−07
.215E−06
.598E−06
.155E−05
.379E−05
.875E−05
.192E−04
.400E−04
.801E−04
.980E−08
.323E−07
.978E−07
.275E−06
.720E−06
.177E−05
.413E−05
.912E−05
.192E−04
.388E−04
.569E−08
.188E−07
.572E−07
.161E−06
.424E−06
.105E−05
.245E−05
.544E−05
.115E−04
.234E−04
.268E−08
.888E−08
.271E−07
.766E−07
.202E−06
.503E−06
.118E−05
.263E−05
.559E−05
.114E−04
.775E−09
.258E−08
.789E−08
.224E−07
.595E−07
.149E−06
.350E−06
.784E−06
.168E−05
.343E−05
.196E−09
.655E−09
.201E−08
.575E−08
.153E−07
.384E−07
.910E−07
.205E−06
.439E−06
.903E−06
100
110
120
130
140
150
160
170
180
190
.194E−02
.338E−02
.571E−02
.938E−02
.150E−01
.233E−01
.354E−01
.526E−01
.766E−01
.110
.112E−02
.198E−02
.341E−02
.569E−02
.923E−02
.146E−01
.225E−01
.340E−01
.502E−01
.729E−01
.590E−03
.107E−02
.186E−02
.315E−02
.519E−02
.832E−02
.130E−01
.199E−01
.298E−01
.438E−01
.261E−03
.479E−03
.851E−03
.146E−02
.245E−02
.399E−02
.633E−02
.983E−02
.149E−01
.222E−01
.154E−03
.285E−03
.511E−03
.886E−03
.149E−02
.245E−02
.393E−02
.614E−02
.941E−02
.141E−01
.752E−04
.141E−03
.254E−03
.445E−03
.757E−03
.125E−02
.202E−02
.319E−02
.492E−02
.744E−02
.455E−04
.855E−04
.155E−03
.278E−03
.467E−03
.776E−03
.126E−02
.199E−02
.309E−02
.469E−02
.223E−04
.420E−04
.766E−04
.135E−03
.232E−03
.387E−03
.629E−03
.999E−03
.155E−02
.236E−02
.674E−05
.128E−04
.233E−04
.414E−04
.711E−04
.119E−03
.194E−03
.309E−03
.482E−03
.735E−03
.178E−05
.339E−05
.623E−05
.111E−04
.191E−04
.321E−04
.526E−04
.840E−04
.131E−03
.201E−03
.631E−01
.894E−01
.125
.171
.232
.310
.409
.534
.689
.880
.325E−01
.467E−01
.660E−01
.918E−01
.126
.170
.227
.300
.391
.505
.208E−01
.300E−01
.427E−01
.598E−01
.825E−01
.112
.151
.200
.263
.341
.110E−01
.161E−01
.230E−01
.325E−01
.451E−01
.618E−01
.835E−01
.111
.147
.192
.698E−02
.102E−01
.147E−01
.208E−01
.290E−01
.398E−01
.540E−01
.723E−01
.957E−01
.125
.352E−02
.516E−02
.743E−02
.105E−01
.147E−01
.202E−01
.274E−01
.366E−01
.485E−01
.634E−01
.110E−02
.161E−02
.232E−02
.329E−02
.460E−02
.633E−02
.858E−02
.115E−01
.152E−01
.199E−01
.300E−03
.442E−03
.638E−03
.906E−03
.127E−02
.174E−02
.237E−02
.317E−02
.420E−02
.548E−02
.248
.316
.400
.502
.624
.770
.162
.208
.264
.331
.413
.511
.820E−01
.105
.133
.167
.208
.256
.257E−01
.328E−01
.415E−01
.520E−01
.646E−01
.795E−01
.708E−02
.905E−02
.114E−01
.143E−01
.178E−01
.218E−01
200
210
220
230
240
250
260
270
280
290
.154
.213
.290
.389
.514
.673
.870
1.112
1.407
1.763
.104
.146
.201
.273
.366
.485
.635
.822
1.052
1.335
300
310
320
330
340
350
2.190
2.696
3.292
3.990
4.801
5.738
1.676
2.088
2.578
3.159
3.843
4.641
1.112
1.394
1.732
2.133
2.608
3.164
.646
.817
1.025
1.274
1.571
1.922
.437
.556
.701
.875
1.083
1.331
98.0
98.5
∗Vermeulen, Dong, Robinson, Nguyen, and Gmitro, AIChE meeting, Anaheim, Calif., 1982; and private communication from Prof. Theodore Vermeulen, Chemical
Engineering Dept., University of California, Berkeley.
2-80
PHYSICAL AnD CHEMICAL DATA
TABLE 2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg
g SO2 /
100 g H2O
Temperature, °C
0
10
0.01
0.05
0.10
0.15
0.20
0.02
0.38
1.15
2.10
3.17
0.04
0.66
1.91
3.44
5.13
0.25
0.30
0.40
0.50
1.00
4.34
5.57
8.17
10.9
25.8
6.93
8.84
12.8
17.0
39.5
2.00
3.00
4.00
5.00
6.00
8.00
10.00
15.00
20.00
20
0.07
1.07
3.03
5.37
7.93
10.6
13.5
19.4
25.6
58.4
30
40
50
60
90
120
0.12
1.68
4.62
8.07
11.8
0.19
2.53
6.80
11.7
17.0
0.29
3.69
9.71
16.5
23.8
0.43
5.24
13.5
22.7
32.6
1.21
12.9
31.7
52.2
73.7
2.82
27.0
63.9
104
145
15.7
19.8
28.3
37.1
83.7
58.6
93.2
129
165
202
88.5
139
192
245
299
129
202
277
353
430
183
285
389
496
602
275
351
542
735
407
517
796
585
741
818
22.5
28.2
40.1
52.3
117
31.4
39.2
55.3
72.0
159
42.8
53.3
74.7
96.8
212
95.8
118
164
211
454
253
393
535
679
824
342
530
720
453
700
955
186
229
316
404
856
Condensed from Rabe, A. E. and Harris, J. F., J. Chem. Eng. Data, 8 (3), 333–336, 1963. Copyright © American Chemical Society and reproduced by permission of the copyright owner.
TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3*
mmHg
Percentages are weight % HNO3 in solution.
20%
°C
HNO3
25%
H2O
HNO3
30%
H2O
HNO3
35%
H2O
0
5
10
15
20
4.1
5.7
8.0
10.9
15.2
3.8
5.4
7.6
10.3
14.2
3.6
5.0
7.1
9.7
13.2
25
30
35
40
45
20.6
27.6
36.5
47.5
62
19.2
25.7
33.8
44
57.5
17.8
23.8
31.1
41
53
0.09
0.11
.17
HNO3
40%
H2O
HNO3
3.3
4.6
6.5
8.9
12.0
0.09
.13
.20
.28
16.2
21.7
28.3
37.7
48
0.12
.17
.25
.36
.52
45%
H2O
50%
HNO3
H2O
HNO3
H2O
3.0
4.2
5.8
8.0
10.8
0.10
.15
2.6
3.6
5.0
6.9
9.4
0.12
.18
.27
2.1
3.0
4.2
5.8
7.9
14.6
19.5
25.5
33.5
43
.23
.33
.48
.68
.96
12.7
16.9
22.3
29.3
38.0
.39
.56
.80
1.13
1.57
10.7
14.4
19.0
25.0
32.5
49.5
62.5
80
100
126
2.18
2.95
4.05
5.46
7.25
42.5
54
70
88
110
50
55
60
65
70
0.09
.13
.19
.27
80
100
128
162
200
.13
.18
.28
.40
.54
75
94
121
151
187
.25
.35
.51
.71
1.00
69
87
113
140
174
.42
.59
.85
1.18
1.63
63
79
102
127
159
.75
1.04
1.48
2.05
2.80
56
71
90
114
143
1.35
1.83
2.54
3.47
4.65
75
80
85
90
95
.38
.53
.74
1.01
1.37
250
307
378
458
555
.77
1.05
1.44
1.95
2.62
234
287
352
426
517
1.38
1.87
2.53
3.38
4.53
217
267
325
393
478
2.26
3.07
4.15
5.50
7.32
198
243
297
359
436
3.80
5.10
6.83
9.0
11.7
178
218
268
325
394
6.20
8.15
10.7
13.7
17.8
158
195
240
292
355
9.6
12.5
16.3
20.9
26.8
138
170
211
258
315
6.05
7.90
580
690
530
631
755
15.5
20.0
25.7
32.5
480
573
688
810
23.0
29.2
37.0
46
430
520
625
740
34.2
43.0
54.5
67
84
383
463
560
665
785
100
1.87
675
3.50
628
105
2.50
800
4.65
745
110
115
120
∗International Critical Tables, vol. 3, pp. 304–305.
9.7
12.7
16.5
(Continued )
VAPOR PRESSURES OF SOLUTIOnS
2-81
TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3 (Continued )
mmHg
Percentages are weight % HNO3 in solution.
55%
°C
60%
65%
70%
80%
HNO3
H2O
HNO3
H2O
HNO3
H2O
HNO3
H2O
0
5
10
15
20
0.14
.21
.31
.45
1.8
2.5
3.5
4.9
6.7
0.19
.28
.41
.59
.84
1.5
2.1
3.0
4.1
5.6
0.41
.60
.86
1.21
1.68
1.3
1.8
2.6
3.5
4.9
0.79
1.12
1.58
2.18
3.00
1.1
1.6
2.2
3.0
4.1
25
30
35
40
45
.66
.93
1.30
1.82
2.50
9.1
12.2
16.1
21.3
28.0
1.21
1.66
2.28
3.10
4.20
7.7
10.3
13.6
18.1
23.7
2.32
3.17
4.26
5.70
7.55
6.6
8.8
11.6
15.5
20.0
4.10
5.50
7.30
9.65
12.6
5.5
7.4
9.8
12.8
16.7
50
55
60
65
70
3.41
4.54
6.15
8.18
10.7
36.3
46
60
76
95
5.68
7.45
9.9
13.0
16.8
31
39
51
64
81
10.0
12.8
16.8
21.7
27.5
26.0
33.0
43.0
54.5
68
16.5
21.0
27.1
34.5
43.3
21.8
27.3
35.3
44.5
56
75
80
85
90
95
13.9
18.0
23.0
29.4
37.3
120
148
182
223
272
21.8
27.5
34.8
43.7
55.0
102
126
156
192
233
35.0
43.5
54.5
67.5
83.5
100
105
110
115
120
125
47
58.5
73
90
110
331
400
485
575
685
69.5
84.5
103
126
156
187
285
345
417
495
590
700
103
124
152
181
218
260
HNO3
90%
100%
H 2O
HNO3
H 2O
2
3
4
6
8
1.2
1.7
2.4
5.5
8
11
15
20
10.5
14
18.5
24.5
32
3.2
4
5.5
7
9.5
27
36
47
62
80
1
1.3
1.8
2.4
3
57
77
102
133
170
11
15
22
30
42
41
52
67
85
106
12
15
20
25
31
103
127
157
192
232
4
5
6.5
8
10
215
262
320
385
460
540
625
720
820
86
106
131
160
195
54.5
67.5
83
103
125
70
86
107
130
158
130
158
192
230
278
38
48
60
73
89
282
338
405
480
570
13
16
20
24
29
238
288
345
410
490
580
152
183
221
262
312
372
192
231
278
330
393
469
330
392
465
545
640
108
129
155
185
219
675
790
35
42
TABLE 2-15 Total Vapor Pressures of Aqueous Solutions
of CH3COOH*
Percentages of weight % acetic acid in the solution
mmHg
°C
25%
50%
75%
20
25
30
35
40
16.3
22.1
29.6
39.4
51.7
15.7
21.4
28.8
38.3
50.2
15.3
20.8
27.8
36.6
48.1
45
50
55
60
65
67.0
87.2
110
141
178
65.0
85.0
107
138
172
62.0
80.1
102
130
162
70
75
80
85
90
223
277
342
419
510
216
269
331
407
497
203
251
310
376
458
95
100
618
743
602
725
550
666
∗International Critical Tables, vol. 3, p. 306.
HNO3
2-82
TABLE 2-16 Partial Pressure of H2O over Aqueous Solutions of nH3 (psia)
Liquid mole percent NH3
(liquid weight percent NH3)
0
5
10
15
(0)
(4.74)
(9.5)
(14.29)
32
40
50
60
70
0.089
0.122
0.178
0.256
0.363
0.083
0.115
0.168
0.242
0.343
0.077
0.106
0.156
0.225
0.320
0.071
0.097
0.143
0.207
0.294
80
90
100
110
120
0.507
0.699
0.951
1.277
1.695
0.479
0.661
0.899
1.209
1.607
0.448
0.618
0.843
1.135
1.510
130
140
150
160
170
2.226
2.893
3.723
4.747
6.000
2.112
2.748
3.540
4.519
5.717
180
190
200
210
220
7.520
9.350
11.538
14.136
17.201
230
240
250
20.796
24.986
29.844
t, °F
20
25
30
35
40
45
80
85
90
(23.94)
(28.81)
(33.71)
(38.64)
(43.59)
(48.57)
(53.58)
(58.62)
(63.69)
(68.79)
(73.91)
(79.07)
(84.26)
(89.47)
(94.72)
0.063
0.087
0.129
0.186
0.266
0.055
0.077
0.113
0.164
0.235
0.047
0.065
0.097
0.142
0.204
0.039
0.054
0.081
0.119
0.172
0.031
0.044
0.066
0.098
0.143
0.025
0.035
0.053
0.079
0.116
0.019
0.027
0.041
0.062
0.093
0.014
0.021
0.032
0.049
0.073
0.011
0.016
0.025
0.038
0.058
0.008
0.012
0.019
0.030
0.045
0.006
0.009
0.014
0.023
0.036
0.004
0.007
0.011
0.018
0.028
0.003
0.005
0.008
0.014
0.022
0.002
0.004
0.006
0.010
0.016
0.002
0.002
0.004
0.007
0.011
0.001
0.001
0.002
0.004
0.006
0.413
0.571
0.780
1.052
1.402
0.374
0.518
0.710
0.960
1.283
0.332
0.462
0.634
0.861
1.154
0.289
0.403
0.556
0.758
1.021
0.245
0.345
0.479
0.656
0.889
0.205
0.290
0.405
0.559
0.763
0.168
0.240
0.338
0.470
0.647
0.136
0.196
0.279
0.392
0.544
0.109
0.159
0.228
0.324
0.455
0.087
0.128
0.186
0.268
0.380
0.069
0.103
0.152
0.220
0.316
0.055
0.083
0.123
0.181
0.263
0.043
0.066
0.100
0.148
0.217
0.034
0.052
0.079
0.119
0.176
0.025
0.040
0.061
0.092
0.137
0.018
0.028
0.043
0.065
0.099
0.010
0.015
0.024
0.036
0.056
1.988
2.591
3.343
4.273
5.416
1.850
2.415
3.122
4.000
5.079
1.696
2.221
2.879
3.698
4.709
1.532
2.012
2.618
3.374
4.312
1.361
1.796
2.347
3.039
3.902
1.192
1.582
2.078
2.706
3.493
1.030
1.376
1.821
2.387
3.101
0.881
1.186
1.582
2.090
2.736
0.747
1.016
1.367
1.821
2.405
0.632
0.867
1.177
1.584
2.110
0.532
0.738
1.013
1.376
1.851
0.448
0.628
0.870
1.194
1.622
0.376
0.532
0.746
1.033
1.418
0.313
0.448
0.634
0.887
1.229
0.257
0.371
0.529
0.748
1.047
0.202
0.295
0.425
0.607
0.858
0.147
0.216
0.314
0.453
0.647
0.083
0.124
0.183
0.267
0.386
7.174
8.931
11.035
13.538
16.496
6.807
8.488
10.504
12.910
15.758
6.397
7.994
9.916
12.213
14.941
5.947
7.452
9.270
11.449
14.047
5.465
6.873
8.580
10.635
13.095
4.968
6.275
7.869
9.796
12.115
4.472
5.680
7.160
8.962
11.141
3.995
5.107
6.479
8.160
10.205
3.551
4.573
5.842
7.410
9.331
3.148
4.086
5.262
6.725
8.534
2.787
3.650
4.740
6.110
7.817
2.468
3.262
4.275
5.559
7.175
2.184
2.914
3.856
5.061
6.592
1.928
2.598
3.470
4.598
6.045
1.688
2.297
3.098
4.146
5.504
1.451
1.994
2.718
3.675
4.932
1.201
1.669
2.300
3.147
4.277
0.917
1.290
1.802
2.502
3.455
0.555
0.793
1.129
1.600
2.262
19.971
24.029
28.744
19.111
23.037
27.607
18.162
21.943
26.358
17.124
20.748
24.996
16.020
19.479
23.549
14.886
18.179
22.070
13.760
16.889
20.608
12.679
15.654
19.212
11.672
14.506
17.917
10.754
13.463
16.748
9.930
12.530
15.708
9.192
11.696
14.783
8.522
10.938
13.946
7.889
10.221
13.153
7.255
9.496
12.346
6.573
8.703
11.452
5.777
7.759
10.369
4.751
6.508
8.891
3.196
4.520
6.413
(19.1)
50
55
60
65
70
75
95
The values in Table 2-16 were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, Version 7.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002). The primary source for the properties of aqueous ammonia
mixtures is R. Tillner-Roth and D. G. Friend, “A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia},” J. Phys. Chem. Ref. Data 27:63–96 (1998).
VAPOR PRESSURES OF SOLUTIOnS
TABLE 2-17 Partial Pressures of H2O over Aqueous Solutions of
Sodium Carbonate*
TABLE 2-18 Partial Pressures of H2O and CH3OH over Aqueous
Solutions of Methyl Alcohol*
mmHg
%Na2CO3
t, °C
0
5
10
0
10
20
30
40
50
60
70
80
90
100
4.5
9.2
17.5
31.8
55.3
92.5
149.5
239.8
355.5
526.0
760.0
4.5
9.0
17.2
31.2
54.2
90.7
146.5
235
348
516
746
8.8
16.8
30.4
53.0
88.7
143.5
230.5
342
506
731
15
20
16.3
29.6
57.6
86.5
139.9
225
334
494
715
25
28.8
50.2
84.1
136.1
219
325
482
697
27.8
48.4
81.2
131.6
211.5
315
467
676
2-83
30
39.9°C
Mole
fraction
CH3OH
PH2O,
mmHg
PCH3OH ,
mmHg
0
14.99
17.85
21.07
27.31
31.06
40.1
47.0
55.8
68.9
86.0
100.0
54.7
39.2
38.5
37.2
35.8
34.9
32.8
31.5
27.3
20.7
10.1
0
0
66.1
75.5
85.2
100.6
108.8
127.7
141.6
158.4
186.6
225.2
260.7
26.4
46.1
77.5
125.7
202.5
301
447
648
∗International Critical Tables, vol. 3, p. 372.
59.4°C
Mole
fraction
CH3OH
PH2O,
mmHg
PCH3OH ,
mmHg
0
22.17
27.40
33.24
39.80
47.08
55.5
69.2
78.5
85.9
100.0
145.4
106.9
102.2
96.6
91.7
84.8
76.9
57.8
43.8
30.1
0
0
210.1
240.2
272.1
301.9
335.6
373.7
439.4
486.6
526.9
609.3
∗International Critical Tables, vol. 3, p. 290.
TABLE 2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium Hydroxide*
mmHg
Conc.
g NaOH/
100 g H2O
Temperature, °C
0
20
40
0
4.6
17.5
55.3
5
4.4
16.9
53.2
10
4.2
16.0
50.6
20
3.6
13.9
44.2
30
2.9
11.3
36.6
40
2.2
8.7
28.7
50
6.3
20.7
60
4.4
15.5
70
3.0
10.9
80
2.0
7.6
90
1.3
5.2
100
0.9
3.6
120
1.7
140
160
180
200
250
300
350
400
500
700
1000
2000
4000
8000
∗International Critical Tables, vol. 3, p. 370.
60
80
100
120
160
200
250
300
350
149.5
143.5
137.0
120.5
101.0
81.0
62.5
47.0
34.5
24.5
17.5
12.5
6.3
3.0
1.5
355.5
341.5
325.5
288.5
246.0
202.0
160.5
124.0
94.0
70.5
53.0
38.5
20.5
11.0
6.0
3.5
2.0
0.5
0.1
760.0
730.0
697.0
621.0
537.0
450.0
368.0
294.0
231.0
179.0
138.0
105.0
61.0
35.5
20.5
12.0
7.0
2.0
0.5
1,489
1,430
1,365
1,225
1,070
920
770
635
515
415
330
262
164
102
63
40
25
8
2.7
0.9
4,633
4,450
4,260
3,860
3,460
3,090
2,690
2,340
2,030
1,740
1,490
1,300
915
765
470
340
245
110
50
23
11
11,647
11,200
10,750
9,800
8,950
8,150
7,400
6,750
6,100
5,500
5,000
4,500
3,650
2,980
2,430
1,980
1,620
985
610
380
240
100
29,771
28,600
27,500
25,300
23,300
21,500
19,900
18,400
17,100
15,800
14,700
13,650
11,800
10,300
8,960
7,830
6,870
5,000
3,690
2,750
2,080
1,210
440
64,200
61,800
59,300
54,700
50,800
47,200
44,100
41,200
38,700
36,300
34,200
32,200
28,800
25,900
23,300
21,200
19,200
15,400
12,500
10,300
8,600
6,100
3,300
1,470
150
123,600
118,900
114,100
105,400
98,000
91,600
85,800
80,700
76,000
71,900
68,100
64,600
58,600
53,400
49,000
45,100
41,800
35,000
29,800
25,700
22,400
17,500
11,500
6,800
1,760
120
7
2-84
PHYSICAL AnD CHEMICAL DATA
WATER VAPOR COnTEnT In GASES
The accompanying figure is useful in determining the water vapor content
of air at high pressure in contact with liquid water.
FIG. 2-2 Water content in air at pressures over atmospheric. (Landsbaum, E.M., W.S. Dodds, and L.F. Stutzman. Reprinted from vol. 47, January 1955 issue of Ind. Eng. Chem. [p. 192].
Copyright 1955 by the American Chemical Society and reproduced by permission of the copyright owner.) For other water-in-air data, see Table 2-111, Fig. 2-3 and Section 12 figures
and tables.
SOLUBILITIES
Unit Conversions For this subsection, the following unit conversions
are applicable: °F = 9⁄5°C + 32. To convert cubic centimeters to cubic feet,
multiply by 3.532 × 10−5. To convert millimeters of mercury to pounds-force
per square inch, multiply by 0.01934. To convert grams per liter to pounds
per cubic foot, multiply by 6.243 × 10−2.
Introduction The database containing solubilities was originally published in the International Union for Pure and Applied Chemistry (IUPAC)National Institute of Standards and Technology (NIST) Solubility Data
Series. It is available at no cost online at http://srdata.nist.gov/solubility.
The H in the following tables is the proportionality constant in
Henry’s law, p = Hx, where x is the mole fraction of the solute in the aqueous
liquid phase; p is the partial pressure in atm of the solute in the gas phase;
and H is a proportionality constant, generally referred to as Henry’s constant.
Values of H often have considerable uncertainty and are strong functions of
temperature. To convert values of H at 25°C from atm to atm/(mol/m3),
divide by the molar density of water at 25°C, which is 55,342 mol/m3. Henry’s
law is valid only for dilute solutions.
Additional values of Henry’s constant can be found in “Environmental Simulation Program,” OLI Systems, Inc., Morris Plains, N.J.; “Estimated Henry’s Law
Constant,” EPA Online Tools for Site Assessment Calculation (http://www.epa
.gov/athens/learn2model/part-two/onsite/esthenry.htm); Rolf Sander, “Compilation of Henry’s Law Constants for Inorganic and Organic Species of
Potential Importance in Environmental Chemistry,” Air Chemistry Department, Max-Planck Institute of Chemistry, Mainz, Germany; Rolf Sander,
“Modeling Atmospheric Chemistry: Interactions between Gas-Phase Species
and Liquid Cloud/Aerosol Particles,” Surv. Geophys. 20: 1–31, 1999 (http://
www.henrys-law.org).
TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures*
This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3
of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution.
Substance
Formula
Solid
phase
AlCl3
Al2(SO4)3
(NH4)2Al2(SO4)4
6H2O
18H2O
24H2O
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Aluminum chloride
sulfate
Ammonium aluminum
sulfate
bicarbonate
bromide
chloride
chloroplatinate
chromate
chromium sulfate
dichromate
dihydrogen phosphite
hydrogen phosphate
iodide
magnesium phosphate
manganese phosphate
nitrate
oxalate
perchlorate†
persulfate
sulfate
thiocyanate
vanadate (meta)
Antimonious fluoride
sulfide
Arsenic oxide
Arsenious sulfide
NH4HCO3
NH4Br
NH4Cl
(NH4)2PtCl6
(NH4)2CrO4
(NH4)2Cr2(SO4)4
(NH4)2Cr2O7
NH4H2PO3
(NH4)2HPO4
NH4I
NH4MgPO4
NH4MnPO4
NH4NO3
(NH4)2C2O4
NH4ClO4†
(NH4)2S2O8
(NH4)2SO4
NH4CNS
NH4VO3
SbF3
Sb2S3
As2O5
As2S3
27
28
29
Barium acetate
acetate
carbonate
Ba(C2H3O2)2
Ba(C2H3O2)2
BaCO3
3H2O
1H2O
30
31
32
33
34
35
36
37
38
chlorate
chloride
chromate
hydroxide
iodide
iodide
nitrate
nitrite
oxalate
Ba(ClO3)2
BaCl2
BaCrO4
Ba(OH)2
BaI2
BaI2
Ba(NO3)2
Ba(NO2)2
BaC2O4
1H2O
2H2O
1
2
3
39
40
41
42
43
44
45
46
47
48
49
50
51
perchlorate
sulfate
Beryllium sulfate
sulfate
sulfate
Boric acid
Boron oxide
Bromine
Cadmium chloride
chloride
chloride
cyanide
hydroxide
Ba(ClO4)2
BaSO4
BeSO4
BeSO4
BeSO4
H3BO3
B2O3
Br2
CdCl2
CdCl2
CdCl2
Cd(CN)2
Cd(OH)2
52
53
54
sulfate
Calcium acetate
acetate
CdSO4
Ca(C2H3O2)2
Ca(C2H3O2)2
0°C
10°C
31.2
2.1
33.5
4.99
11.9
60.6
29.4
15.8
68
33.3
0.7
171
1H2O
154.2
0.023
118.3
2.2
11.56
58.2
70.6
119.8
163.2
3.1
73.0
144
384.7
8H2O
6H2O
2H2O
1H2O
3H2O
6H2O
4H2O
2H2O
4H2O
2½H2O
1H2O
2H2O
1H2O
30°C
40°C
50°C
60°C
70°C
80°C
90°C
100°C
40.4
10.94
46.1
14.88
52.2
20.10
59.2
26.70
66.1
73.0
80.8
89.0
109.796°
21
75.5
37.2
27
83.2
41.4
91.1
45.8
99.2
50.4
107.8
55.2
116.8
60.2
126
65.6
135.6
71.3
145.6
77.3
1.25
190.5
0.036
0
297.0
8.0
30.58
199.6
0.030
208.9
0.040
0
421.0
218.7
0.016
0.005
499.0
228.8
0.019
0.007
580.0
10.7825°
24II2O
6H2O
7H2O
20°C
69.8615°
36.4
7.74
59.5
5.17 × 10−5
at 18°
59
62.1
63
0.00168°
20.34
31.6
0.0002
1.67
170.2
5.0
26.95
33.3
0.00028
2.48
185.7
7.0
0.00168°
205.8
1.15 × 10−4
2.66
1.1
4.22
97.59
90.01
76.48
37.4
2.0 × 10−4
19014.5°
13115
172.3
0.052
0
192
4.4
20.85
75.4
170
0.48
444.7
0.00017518°
65.8
71
0.002218°
33.80
35.7
0.00037
3.89
203.1
9.2
67.5
0.002218°
289.1
2.4 × 10−4
3.57
1.5
3.4
125.1
5.04
2.2
3.20
135.1
134.5
1.715°
76.00
36.0
76.60
34.7
40.4
47.17
26031°
181.4
241.8
5.9
78.0
207.7
0.84
563.6
81.0
69.5
71.2
1.32
75
0.0024
at 24.2°
41.70
38.2
0.00046
5.59
219.6
11.6
0.0024
at 24.2°
2.85 × 10−4
52
43.78
6.60
3.13
48.19
95.3
103.3
75.1
76.7
77
74
74
49.61
40.7
43.6
66.81
46.4
49.4
8.22
13.12
20.94
358.7
426.3
46.74
135.3
75
84.84
52.4
261.0
27.0
205.8
495.2
62
14.81
6.2
136.5
104.9
58.8
101.4
247.3
20.3
60.67
11.54
57.01
3.05
73.0
17.1
871.0
88.0
1.78
231.9
14.2
740.0
39.05
79
8.72
4.0
132.1
344.0
10.3
250.3
16.73
271.7
34.2
300
562.3
84.76
23.75
9.5
83
98
30.38
140.4
100
110
40.25
15.7
147.0
−4
2.6 × 10
at 25°
33.8
78.54
33.2
83.68
32.7
33.5
63.13
60.77
31.1
29.7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
2-85
(Continued )
2-86
TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures* (Continued )
This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100
cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution.
Substance
Formula
1
2
3
4
5
6
7
8
9
10
11
Calcium bicarbonate
chloride
chloride
fluoride
hydroxide
nitrate
nitrate
nitrate
nitrite
nitrite
oxalate
Ca(HCO3)2
CaCl2
CaCl2
CaF2
Ca(OH)2
Ca(NO3)2
Ca(NO3)2
Ca(NO3)2
Ca(NO2)2
Ca(NO2)2
CaC2O4
12
13
14
15
16
17
18
19
20
21
22
23
24
sulfate
Carbon dioxide, 760 mm ‡
monoxide, 760 mm ‡
Cesium chloride
nitrate
sulfate
Chlorine, 760 mm ‡
Chromic anhydride
Cuprio chloride
nitrate
nitrate
sulfate
sulfide
CaSO4
CO2
CO
CsCl
CsNO3
Cs2SO4
Cl2
CrO3
CuCl2
Cu(NO3)2
Cu(NO3)2
CuSO4
CuS
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
Cuprous chloride
Ferric chloride
Ferrous chloride
chloride
nitrate
sulfate
sulfate
Hydrobromic acid, 760 mm
Hydrochloric acid, 760 mm
Iodine
Lead acetate
bromide
carbonate
chloride
chromate
fluoride
nitrate
sulfate
Magnesium bromide
chloride
hydroxide
nitrate
sulfate
sulfate
sulfate
Manganous sulfate
sulfate
sulfate
sulfate
Mercurous chloride
Molybdic oxide
Nickel chloride
nitrate
nitrate
sulfate
sulfate
Nitric oxide, 760 mm
Nitrous oxide
CuCl
FeCl3
FeCl2
FeCl2
Fe(NO3)2
FeSO4
FeSO4
HBr
HCl
I2
Pb(C2H3O2)2
PbBr2
PbCO3
PbCl2
PbCrO4
PbF2
Pb(NO3)2
PbSO4
MgBr2
MgCl2
Mg(OH)2
Mg(NO3)2
MgSO4
MgSO4
MgSO4
MnSO4
MnSO4
MnSO4
MnSO4
HgCl
MoO3
NiCl2
Ni(NO3)2
Ni(NO3)2
NiSO4
NiSO4
NO
N2O
Solid
phase
6H2O
2H2O
4H2O
3H2O
0°C
16.15
59.5
65.0
0.185
102.0
0.176
115.3
4H2O
2H2O
62.07
2H2O
0.1759
0.3346
0.0044
161.4
9.33
167.1
1.46
164.9
70.7
81.8
2H2O
6H2O
3H2O
5H2O
4H2O
6H2O
7H2O
1H2O
3H2O
10°C
6.7 × 10−4
at 13°
0.1928
0.2318
0.0035
174.7
14.9
173.1
0.980
73.76
95.28
17.4
74.4
81.9
64.5
221.2
82.3
20.51
210.3
0.6728
6H2O
6H2O
6H2O
7H2O
6H2O
1H2O
7H2O
5H2O
4H2O
1H2O
2H2O
6H2O
6H2O
3H2O
7H2O
6H2O
66.55
40.8
53.23
0.060
48.3
0.0035
94.5
53.5
30.9
42.2
60.01
59.5
0.00014
53.9
79.58
59.5
27.22
32
0.00984
0.001618°
0.165
129.3
6.8 × 10−4
at 25°
0.1688
0.0028
186.5
23.0
178.7
0.716
77.0
125.1
20.7
3.3 × 10−5
at 18°
1.5225°
91.8
83.8
26.5
198
0.029
0.4554
38.8
0.0028
91.0
52.8
16.60
74.5
30°C
102
0.001726°
0.153
152.6
40°C
50°C
17.05
0.00757
0.1705
0.85
0.00011
0.99
7 × 10−6
0.064
56.5
0.0041
96.5
54.5
0.000918°
9.5 × 10−4
at 50°
0.2090
0.1257
0.0024
197.3
33.9
184.1
0.562
0.141
195.9
237.5
70°C
17.50
0.128
0.116
80.34
25
159.8
28.5
33.3
73.0
77.3
315.1
82.5
32.9
40.2
48.6
90°C
0.106
147.0
0.094
0.2047
0.0576
0.0015
229.7
83.8
199.9
0.324
151.9
0.085
0.077
244.8
0.0010
250.0
134.0
210.3
0.219
91.2
99.2
178.8
40
207.8
55
88.7
525.8
100
165.6
50.9
159
363.6
0.1966
0.0013
239.5
107.0
205.0
0.274
100°C
18.40
152.7
358.7
132.6
0.0761
0.0018
218.5
64.4
194.9
0.386
182.1
87.44
80°C
17.95
141.7
281.5
14 × 10−4
at 95°
0.2097
0.0973
0.0021
208.0
47.2
189.9
0.451
174.0
83.8
43.6
0.0006
260.1
163.0
214.9
0.125
217.5
0.1619
0
0
270.5
197.0
220.3
0
206.8
107.9
75.4
535.7
105.3
37.3
105.8
67.3
0.04
55.0425°
1.15
63.3
0.056
171.5
59.6
0.078
1.53
1.94
2.36
3.34
4.75
1.20
1.45
1.70
1.98
2.62
3.34
0.068
66
0.0049
99.2
35.5
44.5
40.8
45.3
62.9
64.5
67.76
66.44
0.0002
0.138
64.2
96.31
0.264
68.9
75
0.0056
101.6
57.5
84.74
45.6
68.8
0.0007
0.476
73.3
122.2
42.46
0.00618
0.1211
60°C
136.8
76.68
14.3
71.02
15.65
20°C
0.00517
0.00440
56.1
85
95
104.1
107.5
61.0
115
130
38.8
113.7
66.0
120.2
73.0
137.0
50.4
53.5
59.5
64.2
62.9
69.0
74.0
68.3
72.6
58.17
55.0
52.0
48.0
42.5
34.0
0.687
78.3
1.206
82.2
2.055
85.2
163.1
50.15
0.00376
54.80
0.00324
2.106
169.1
59.44
0.00267
87.6
235.1
63.17
0.00199
0.00114
76.7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
Potassium acetate
acetate
alum
bicarbonate
bisulfate
bitartrate
carbonate
chlorate
chloride
chromate
dichromate
ferricyanide
hydroxide
hydroxide
nitrate
nitrite
perchlorate
permanganate
persulfate†
sulfate
thiocyanate
Silver cyanide
nitrate
sulfate
Sodium acetate
acetate
bicarbonate
carbonate
carbonate
chlorate
chloride
chromate
chromate
chromate
dichromate
dichromate
dihydrogen phosphate
dihydrogen phosphate
dihydrogen phosphate
hydrogen arsenate
hydrogen phosphate
hydrogen phosphate
hydrogen phosphate
hydrogen phosphate
hydroxide
hydroxide
hydroxide
hydroxide
nitrate
nitrite
oxalate
phosphate, tripyrophosphate
sulfate
sulfate
sulfate
sulfide
sulfide
sulfide
sulfite
sulfite
tetraborate
tetraborate
vanadate (meta)
KC2H3O2
KC2H3O2
K2SO4⋅Al2(SO4)3
KHCO3
KHSO4
KHC4H4O6
K2CO3
KClO3
KCl
K2CrO4
K2Cr2O7
K3Fe(CN)6
KOH
KOH
KNO3
KNO2
KClO4
KMnO4
K2S2O8†
K2SO4
KCNS
AgCN
AgNO3
Ag2SO4
NaC2H3O2
NaC2H3O2
NaHCO3
Na2CO3
Na2CO3
NaClO8
NaCl
Na2CrO4
Na2CrO4
Na2CrO4
Na2Cr2O7
Na2Cr2O7
NaH2PO4
NaH2PO4
NaH2PO4
Na2HAsO4
Na2HPO4
Na2HPO4
Na2HPO4
Na2HPO4
NaOH
NaOH
NaOH
NaOH
NaNO3
NaNO2
Na2C2O4
Na3PO4
Na4P2O7
Na2SO4
Na2SO4
Na2SO4
Na2S
Na2S
Na2S
Na2SO3
Na2SO3
Na2B4O7
Na2B4O7
NaVO8
1½H2O
½H2O
24H2O
2H2O
2H2O
1H2O
†
3H2O
10H2O
1H2O
10H2O
4H2O
216.7
233.9
255.6
3.0
22.4
36.3
0.32
105.5
3.3
27.6
58.2
5
31
97
4.0
27.7
5.9
33.2
51.4
0.53
110.5
7.4
34.0
61.7
12
43
112
13.3
278.8
0.75
2.83
1.62
7.35
177.0
20.9
122
0.573
36.3
119
6.9
7
170
0.695
40.8
121
8.15
12.5
31.6
298.4
1.80
6.4
4.49
11.11
217.5
2.2 × 10−5
222
0.796
46.5
123.5
9.6
21.5
79
35.65
31.70
89
35.72
50.17
101
35.89
88.7
2H2O
163.0
2H2O
1H2O
57.9
12H2O
12H2O
7H2O
2H2O
4H2O
3½H2O
1H2O
12H2O
10H2O
10H2O
7H2O
9H2O
5½H2O
6H2O
7H2O
10H2O
5H2O
2H2O
0.40
108
5
31.0
60.0
7
36
103
7.3
1.67
42
1.05
4.4
2.60
9.22
0.90
113.7
10.5
37.0
63.4
20
50
126
45.8
2.6
9.0
7.19
12.97
11.70
45.4
67.3
1.32
116.9
14
40.0
65.2
26
60
63.9
334.9
4.4
12.56
9.89
14.76
4.1
3.95
9.0
30
15.42
18.8
22.5
20
26.9
36
20
9.95
40.8
3.9
202
16.50
18.17
19.75
21.4
22.8
1.22
669
1.30
114.6
96
91.6
169
54.0
73.9
70
18
158.6
80.2
1.36
146
153
172
37.46
45.8
189
37.93
123.0
316.7
124.8
376.2
179.3
65
190.3
207.3
85
225.3
82.9
88.1
92.4
102.9
244.8
88
84.5
3.7
11
6.23
19.4
44
138
147.5
14.8
104
119
48.3
70.4
52
4.6
139.8
38.5
51.1
72.1
61
396.3
109.0
11.8
95.96
51.8
133.1
380.1
71.0
9
22.2
88.7
47
364.8
40.0
6.5
16.89
46.4
155
37.04
37
20.8
15.325°
110.0
140
36.69
26.5
7.7
2.7
140
85.5
48.5
126
36.37
15.5
3.6
1.6
2.46
126.8
24.5
45.5
68.6
43
66
525
1.15
139
139.5
16.4
138.2
1.5
3.16
5.0
19.5
1.83
121.2
19.3
42.6
66.8
34
455
1.08
83
134
14.45
106.5
109
350
24.75
60.0
376
0.979
65.5
129.5
12.7
85.2
51.5
337.3
17.00
300
0.888
54.5
126
11.1
38.8
50.5
113
36.09
69.9
80
78.0
1.3
8.39
39.1
323.3
177.8
73
72.1
13.9
283.8
129
145
174
104
98.4
114
104.1
124
161
38.47
121.6
6.95
155.7
57
56.7
75.6
80
82.6104
178
246
412.8
21.8
24.1
952
1.41
170
45.5
230
38.99
125.9
426.3
102.2
31
13.50
43
17.45
55
21.83
81
30.04
347
180
163.2
6.33
108
40.26
48.8
28.5
46.7
45.3
43.7
42.5
39.82
36.4
42.69
39.1
28
28.2
10.5
28.8
20.3
30.2
68.4
148
132.6
45.73
43.31
51.40
49.14
313
246.6
59.23
57.28
28.3
24.4
31.5
41
52.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
2-87
∗By N. A. Lange; abridged from “Table of Solubilities of Inorganic Compounds in Water at Various Temperatures” in Lange’s Handbook of Chemistry, 10th ed., McGraw-Hill, New York, 1961 (except for NaCl, which is from CRC
Handbook of Chemistry and Physics, 86th ed., CRC Press, 2005). For tables of the solubility of gases in water at various temperatures, Atack (Handbook of Chemical Data, Reinhold, New York, 1957) gives values at closer
temperature intervals, usually 1 or 5°C, than are tabulated here. For materials marked by ‡, additional data are given in tables subsequent to this one. For the solubility of various hydrocarbons in water at high pressures
see J. Chem. Eng. Data, 4, 212 (1959).
2-88
TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures (Continued )
This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3
of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution.
Substance
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Sodium vanadate (meta)
Stannous chloride
sulfate
Strontium acetate
acetate
chloride
chloride
nitrate
nitrate
nitrate
sulfate
Sulfur dioxide, 760 mm†
Thallium sulfate
Thorium sulfate
sulfate
sulfate
sulfate
Zinc chlorate
chlorate
nitrate
nitrate
sulfate
sulfate
sulfate
Formula
NaVO3
SnCl2
SnSO4
Sr(C2H3O2)2
Sr(C2H3O2)2
SrCl2
SrCl2
Sr(NO3)2
Sr(NO3)2
Sr(NO3)2
SrSO4
SO2
Tl2SO4
Th(SO4)2
Th(SO4)2
Th(SO4)2
Th(SO4)2
ZnClO3
ZnClO3
Zn(NO3)2
Zn(NO3)2
ZnSO4
ZnSO4
ZnSO4
Solid
phase
0°C
10°C
20°C
30°C
21.10 °
269.815°
19
25
83.9
4H2O
½H2O
6H2O
2H2O
1H2O
4H2O
9H2O
8H2O
6H2O
4H2O
6H2O
4H2O
6H2O
3H2O
7H2O
6H2O
1H2O
36.9
43.5
43.61
42.95
47.7
41.6
52.9
52.7
40.1
64.0
70.5
0.0113
22.83
2.70
0.74
1.0
1.50
0.0114
11.29
4.87
1.38
1.62
1.90
145.0
16.21
3.70
0.98
1.25
152.5
94.78
41.9
47
200.3
118.3
54.4
40°C
50°C
26.23
60°C
70°C
80°C
36.9
38.8 °
36.24
36.10
85.9
90.5
93.8
96
98
10.92
12.74
14.61
16.53
18.45
6.64
1.63
1.09
86.6
83.7
80.8
32.97
90°C
100°C
75
18
39.5
58.7
88.6
0.0114
7.81
6.16
1.995
2.45
209.2
65.3
37.35
72.4
81.8
83.8
97.2
90.1
2.998
5.41
4.5
9.21
5.22
4.04
2.54
223.2
36.4
130.4
100.8
139
100
273.1
206.9
70.1
76.8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
SOLUBILITIES
2-89
TABLE 2-21 Solubility as a Function of Temperature and Henry’s Constant at 25çC for Gases in Water
Name
Acetylene
Carbon dioxide
Carbon monoxide
Ethane
Ethylene
Helium
Hydrogen
Methane
Nitrogen
Oxygen
Formula
A
−156.51
−159.854
−171.764
−250.812
−153.027
−105.9768
−125.939
−338.217
−181.587
−171.2542
C2H2
CO2
CO
C2H6
C2H4
He
H2
CH4
N2
O2
C
D
T range, K
H at 25°C, atm
21.403
21.6694
23.3376
34.7413
20.5248
14.0094
16.8893
51.9144
24.7981
23.24323
0
−1.10261E-03
0
0
0
0
0
−0.0425831
0
0
274–343
273–353
273–353
275–323
287–346
273–348
273–345
273–523
273–350
273–333
1,330
1,635
58,000
29,400
11,726
142,900
70,800
39,200
84,600
43,400
B
8,160.2
8,741.68
8,296.9
12,695.6
7,965.2
4,259.62
5,528.45
13,282.1
8,632.13
8,391.24
The constants can be used to calculate solubility by the equation ln x = A + B/T + C ln T + DT, where T is in K and x is the mole fraction of the solute dissolved in water
when the solute partial pressure is 1 atm. With the assumption that Henry’s law is valid up to 1 atm, H = 1/x. Values of the constants are from P. G. T. Fogg and W. Gerrard,
Solubility of Gases in Liquids, Wiley, 1991, New York, and Solubility Data Series, vol. 1, Helium and Neon, IUPAC, Pergamon Press, Oxford, 1979. For higher-temperature
behavior and an up-to-date reference list, see R. Fernandez-Prini, J. L. Alvarez, and A. H. Harvey, J. Phys. Chem. Ref. Data 32(2):903, 2003. To find H at temperatures other
than 25°C, first find the solubility and then take the reciprocal.
TABLE 2-22 Henry’s Constant H for Various Compounds in Water at 25çC
Group
Paraffin hydrocarbons
Olefins
Aromatics
Aldehydes
Ketones
Esters
Chlorine containing
Alcohols
Miscellaneous
Compound
Methane
Ethane
Propane
Butane
Pentane
Octane
Nonane
Ethylene
Propylene
Benzene
Toluene
o-Xylene
Cumene
Phenol
Acetaldehyde
Propionaldehyde
Methylethyl ketone
Methyl formate
Ethyl formate
Methyl acetate
Butyl acetate
Chloromethane
Chloroethane
Chlorobenzene
Methanol
Ethanol
1-Propanol
1-Butanol
Acrylonitrile
Dimethyl sulfide
Dimethyl disulfide
Methyl mercaptan
Ethyl mercaptan
Pyridine
Formula
CH4
C2H6
C3H8
C4H10
C5H12
C8H18
C9H20
C2H4
C3H6
C6H6
C7H8
C8H10
C9H12
C6H6O
C2H4O
C3H6O
C4H8O
C2H4O2
C3H6O2
C3H6O2
C6H12O2
CH3Cl
C2H5Cl
C6H5Cl
CH4O
C2H6O
C3H8O
C4H10O
C3H3N
C2H6S
C2H6S2
CH4S
C2H6S
C5H5N
CAS
74-82-8
74-84-0
74-98-6
106-97-8
109-66-0
111-65-9
111-84-2
74-85-1
115-07-1
71-43-2
108-88-3
95-47-6
98-82-8
108-95-2
75-07-0
123-38-6
78-93-3
107-31-3
109-94-4
79-20-9
123-86-4
74-87-3
75-00-3
108-90-7
67-56-1
64-17-5
71-23-8
71-36-3
107-13-1
75-18-3
624-92-0
74-93-1
75-08-1
110-86-1
H, atm†
36,600
26,700
37,800
51,100
70,000
2,74,000
3,29,000
11,700
11,700
299
354
272
724
0.0394
5.56
4.36
2.59
13.6
13.6
5.04
13.6
556
681
204
0.272
0.272
0.507
0.482
5.54
121
68.1
177
161
0.817
Rating∗
4
3
3
3
3
3
3
3
4
10
10
10
9
7
3
4
5
3
3
3
3
?
10
10
4
4
3
3
3
3
3
3
3
3
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE,
and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR
Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York (2016).
∗The ratings reflect DIPPR ESP’s effort to provide a critical evaluation and quality assessment of each data
point with 15 being the highest score possible. The rating is not directly correlated with the estimated experimental uncertainty.
†
Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if
used for calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of singlepoint values over the ambient temperature range (4°C < T < 50°C) are presented in Sec. 22, under “Air Pollution
Control” > “Biological APC Technologies” > “Estimating Henry’s law constants”. Estimation procedures for the
larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H. Harvey, “Avoid Common Pitfalls When Using
Henry’s Law,” Chem. Eng. Prog., 103(9), 2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping
for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31,
pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the databank of 404 compounds of
environmental interest and other useful property data.)
2-90
PHYSICAL AnD CHEMICAL DATA
TABLE 2-23 Henry’s Constant H for Various Compounds in Water
at 25çC from Infinite Dilution Activity Coefficients
Compound
CAS no.
Formula
H = γ ∞Pvp, atm
Pentane
Hexane
Heptane
Benzene
Toluene
o-Xylene
Cumene
Styrene
Formaldehyde
Acetaldehyde
Propanal
Acetone
Methyl ethyl ketone
Methyl n-propyl ketone
Formic acid
Methyl acetate
Ethyl acetate
Butyl acetate
Chloroethane
1-Chloropropane
Chlorobenzene
Methanol
Ethanol
Pyridine
Diethyl ether
Thiophene
109660
1100543
142825
71432
108883
95476
98,828
100425
50000
75070
123386
67641
78933
107879
64186
79209
141786
123864
75003
74986
108907
67561
64175
110861
60297
110021
C5H12
C6H14
C7H16
C6H6
C7H8
C8H10
C9H12
C8H8
CH2O
C2H4O
C3H6O
C3H6O
C4H8O
C5H10O
CH2O2
C3H6O2
C4H8O2
C6H12O2
C2H5Cl
C3H7Cl
C6H5Cl
CH4O
C2H6O
C5H5N
C4H10O
C4H4S
63700
84600
120000
309
344
267
613
145
14.3
4.54
5.45
2.13
3.11
4.60
0.0404
6.38
8.01
12.3
626
792
219
0.263
0.293
0.544
48.7
160
TABLE 2-24
Air*
t, °C
0
5
10
15
20
25
30
35
10−4 × H †
4.32
4.88
5.49
6.07
6.64
7.20
7.71
8.23
t, °C
40
45
50
60
70
80
90
100
10−4 × H †
8.70
9.11
9.46
10.1
10.5
10.7
10.8
10.7
∗International Critical Tables, vol. 3, p. 257.
†
H is calculated from the absorption coefficients of O2 and N2, taking into consideration the correction for constant argon content.
TABLE 2-25 Ammonia-Water at 10 and 20çC*
10°C
Mass fraction
NH3 in liquid
0.0
0.00467
0.00495
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Henry’s constant H at 25°C is the vapor pressure at 25°C times the infinite dilution
activity coefficient, also at 25°C. Infinite dilution activity coefficients are from Mitchell
and Jurs, J. Chem. Inf. Comput. Sci. 38: 200 (1998). Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if used for
calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of single-point values over the ambient temperature range (4°C < T < 50°C) are
presented in Sec. 22, pp. 22–49, under “Estimating Henry’s law constants.” Estimation
procedures for the larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H.
Harvey, “Avoid Common Pitfalls When Using Henry’s Law,” Chem. Eng. Prog., 103(9),
2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping for Removal
of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem.
Res., 31, pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the
databank of 404 compounds of environmental interest and other useful property data.)
P, kPa
1.23
1.37
7.07
20.07
47.37
99.84
184.44
292.15
399.03
486.44
554.33
615.05
20°C
Mass fraction
NH3 in vapor
0.0
0.1
P, kPa
2.34
0.84164
0.95438
0.98565
0.99544
0.99848
0.99943
0.99975
0.99988
0.99995
1.0
2.60
11.95
32.34
73.85
150.56
269.50
416.63
560.61
678.61
771.87
857.48
Mass fraction
NH3 in vapor
0.0
0.1
0.82096
0.94541
0.98199
0.99393
0.99783
0.99913
0.99960
0.99980
0.99991
1.0
∗Selected values from R. Tillner-Roth and D. G. Friend, J. Phys. Chem. Ref. Data 27:63
(1998). This reference lists solubilities for temperatures from −70 to 340°C. Densities,
enthalpies, and entropies are listed for both the two-phase and single-phase regions for
pressures up to 40 MPa.
TABLE 2-26 Carbon Dioxide (CO2)*
Liquid mol fraction CO2 × 103
Total pressure, atm
1
2
10
20
30
36
0°C
10°C
15°C
20°C
25°C
35°C
50°C
75°C
100°C
1.445
2.89
12.71
21.23
25.79
0.985
1.946
8.81
15.38
19.80
21.45
0.802
1.587
7.32
13.13
17.49
19.42
0.692
1.374
6.44
11.84
16.22
18.30
0.608
1.207
5.74
10.75
15.05
17.29
0.473
0.943
4.54
8.64
12.80
14.80
0.342
0.683
3.30
6.34
9.10
10.63
0.248
0.495
2.41
4.65
6.78
7.90
0.187
0.373
1.841
3.62
5.35
6.35
∗Values selected from G. Houghton, A. M. McLean, and P. D. Ritchie, Chem. Eng. Sci. 6:132–137, 1957.
SOLUBILITIES
TABLE 2-27 Chlorine (Cl2)
Partial
pressure
of Cl2,
mmHg
TABLE 2-28 Chlorine Dioxide (ClO2)
Solubility, g of Cl2 per liter
10°C
20°C
30°C
40°C
50°C
5
10
30
50
100
0.488
0.679
1.221
1.717
2.79
0.451
0.603
1.024
1.354
2.08
0.438
0.575
0.937
1.210
1.773
0.424
0.553
0.873
1.106
1.573
0.412
0.532
0.821
1.025
1.424
0.398
0.512
0.781
0.962
1.313
150
200
250
300
350
3.81
4.78
5.71
2.73
3.35
3.95
4.54
5.13
2.27
2.74
3.19
3.63
4.06
1.966
2.34
2.69
3.03
3.35
1.754
2.05
2.34
2.61
2.86
1.599
1.856
2.09
2.31
2.53
400
450
500
550
600
5.71
6.26
6.85
7.39
7.97
4.48
4.88
5.29
5.71
6.12
3.69
3.98
4.30
4.60
4.91
3.11
3.36
3.61
3.84
4.08
2.74
2.94
3.14
3.33
3.52
650
700
750
800
900
8.52
9.09
9.65
10.21
6.52
6.90
7.29
7.69
8.46
5.21
5.50
5.80
6.08
6.68
4.32
4.54
4.77
4.99
5.44
3.71
3.89
4.07
4.27
4.62
9.27
10.84
13.23
17.07
21.0
7.27
8.42
10.14
13.02
15.84
5.89
6.81
8.05
10.22
12.32
4.97
5.67
6.70
8.38
10.03
18.73
21.7
24.7
27.7
30.8
14.47
16.62
18.84
20.7
23.3
11.70
13.38
15.04
16.75
18.46
Cl2.8H2O2 separates
3000
3500
4000
4500
5000
Partial
pressure
of Cl2,
mmHg
Weight of ClO2, grams per liter of solution
Vol % of ClO2
in gas phase
0°C
1000
1200
1500
2000
2500
2-91
1
3
5
7
10
11
12
13
14
15
16
0°C
5°C
10°C
15°C
20°C
30°C
40°C
2.00
6.00
10.0
14.0
20.0
1.50
4.7
7.8
10.9
15.5
17.0
18.6
20.3
1.25
3.85
6.30
8.95
12.8
14.0
15.3
16.6
18.0
19.2
20.3
1.00
3.20
5.25
7.35
10.5
11.7
12.8
13.8
14.9
16.0
17.0
0.90
2.70
4.30
6.15
8.80
9.70
10.55
11.5
12.3
13.2
14.2
0.60
1.95
3.20
4.40
6.30
7.00
7.50
8.20
8.80
9.50
10.1
0.46
1.30
2.25
3.20
4.50
5.00
5.45
5.85
6.35
6.80
7.20
Ishi, Chem. Eng. (Japan), 22:153 (1958).
TABLE 2-29 Hydrogen Chloride (HCl)
Weights of
HCl per 100
weights of H2O
78.6
66.7
56.3
47.0
38.9
31.6
25.0
19.05
13.64
8.70
4.17
2.04
Partial pressure of HCl, mmHg
0°C
10°C
20°C
30°C
510
130
29.0
5.7
1.0
0.175
0.0316
0.0056
0.00099
0.000118
0.000018
840
233
56.4
11.8
2.27
0.43
0.084
0.016
0.00305
0.000583
0.000069
0.0000117
399
105.5
23.5
4.90
1.00
0.205
0.0428
0.0088
0.00178
0.00024
0.000044
627
188
44.5
9.90
2.17
0.48
0.106
0.0234
0.00515
0.00077
0.000151
Weights of
HCl per 100
weights of H2O
Solubility, g of Cl2 per liter
60°C
70°C
80°C
90°C
100°C
110°C
5
10
30
50
100
0.383
0.492
0.743
0.912
1.228
0.369
0.470
0.704
0.863
1.149
0.351
0.447
0.671
0.815
1.085
0.339
0.431
0.642
0.781
1.034
0.326
0.415
0.627
0.747
0.987
0.316
0.402
0.598
0.722
0.950
150
200
250
300
350
1.482
1.706
1.914
2.10
2.28
1.382
1.580
1.764
1.932
2.10
1.294
1.479
1.642
1.793
1.940
1.227
1.396
1.553
1.700
1.831
1.174
1.333
1.480
1.610
1.736
1.137
1.276
1.413
1.542
1.661
400
450
500
550
600
2.47
2.64
2.80
2.97
3.13
2.25
2.41
2.55
2.69
2.83
2.08
2.22
2.35
2.47
2.59
1.965
2.09
2.21
2.32
2.43
1.854
1.972
2.08
2.19
2.29
1.773
1.880
1.986
2.09
2.19
650
700
750
800
900
3.29
3.44
3.59
3.75
4.04
2.97
3.10
3.23
3.37
3.63
2.72
2.84
2.96
3.08
3.30
2.55
2.66
2.76
2.87
3.08
2.41
2.50
2.60
2.69
2.89
2.28
2.37
2.47
2.56
2.74
1000
1200
1500
2000
2500
4.36
4.92
5.76
7.14
8.48
3.88
4.37
5.09
6.26
7.40
3.53
3.95
4.58
5.63
6.61
3.28
3.67
4.23
5.17
6.05
3.07
3.43
3.95
4.78
5.59
2.91
3.25
3.74
4.49
5.25
3000
3500
4000
4500
5000
9.83
11.22
12.54
13.88
15.26
8.52
9.65
10.76
11.91
13.01
7.54
8.53
9.52
10.46
11.42
6.92
7.79
8.65
9.49
10.35
6.38
7.16
7.94
8.72
9.48
5.97
6.72
7.42
8.13
8.84
78.6
66.7
56.3
47.0
38.9
31.6
25.0
19.05
13.64
8.70
4.17
2.04
50°C
Partial pressure of HCl, mm Hg
80°C
535
141
35.7
8.9
2.21
0.55
0.136
0.0344
0.0064
0.00140
623
188
54.5
15.6
4.66
1.34
0.39
0.095
0.0245
110°C
760
253
83
28
9.3
3.10
0.93
0.280
Enthalpy and phase-equilibrium data for the binary system HCl-H2O are given by
Van Nuys, Trans. Am. Inst. Chem. Engrs., 39, 663 (1943).
TABLE 2-30 Hydrogen Sulfide (H2S)
t, °C
0
5
10
15
20
25
30
35
10−2 × H
2.68
3.15
3.67
4.23
4.83
5.45
6.09
6.76
t, °C
40
45
50
60
70
80
90
100
10−2 × H
7.45
8.14
8.84
10.3
11.9
13.5
14.4
14.8
International Critical Tables, vol. 3, p. 259.
2-92
PHYSICAL AnD CHEMICAL DATA
DEnSITIES
Unit Conversions Unless otherwise noted, densities are given in grams
per cubic centimeter. To convert to pounds per cubic foot, multiply by 62.43.
Temperature conversion: °F = 9⁄5°C + 32.
Additional References and Comments The aqueous solution data
tables are from International Critical Tables, vol. 3, pp. 115–129, unless otherwise stated. All compositions are in weight percent in vacuo. All density
values are d 4t = g/mL in vacuo. For more detailed data on densities, see also
the CRC Handbook of Chemistry and Physics, Chemical Rubber Publishing
Co., 97th ed.; or http://hbcponline.com.
DEnSITIES OF PURE SUBSTAnCES
TABLE 2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point to the Critical Point
T, K
ρ, kg/m3
T, K
ρ, kg/m3
T, K
ρ, kg/m3
T, K
ρ, kg/m3
T, K
ρ, kg/m3
273.160∗
274
276
278
280
282
284
286
288
290
292
294
296
298
300
302
304
306
308
310
312
314
316
318
320
322
324
326
328
330
332
334
336
338
340
342
344
346
348
350
999.793
999.843
999.914
999.919
999.862
999.746
999.575
999.352
999.079
998.758
998.392
997.983
997.532
997.042
996.513
995.948
995.346
994.711
994.042
993.342
992.610
991.848
991.056
990.235
989.387
988.512
987.610
986.682
985.728
984.750
983.747
982.721
981.671
980.599
979.503
978.386
977.247
976.086
974.904
973.702
352
354
356
358
360
362
364
366
368
370
372
374
376
378
380
382
384
386
388
390
392
394
396
398
400
402
404
406
408
410
412
414
416
418
420
422
424
426
428
430
972.479
971.235
969.972
968.689
967.386
966.064
964.723
963.363
961.984
960.587
959.171
957.737
956.285
954.815
953.327
951.822
950.298
948.758
947.199
945.624
944.030
942.420
940.793
939.148
937.486
935.807
934.111
932.398
930.668
928.921
927.157
925.375
923.577
921.761
919.929
918.079
916.212
914.328
912.426
910.507
432
434
436
438
440
442
444
446
448
450
452
454
456
458
460
462
464
466
468
470
472
474
476
478
480
482
484
486
488
490
492
494
496
498
500
502
504
506
508
510
908.571
906.617
904.645
902.656
900.649
898.624
896.580
894.519
892.439
890.341
888.225
886.089
883.935
881.761
879.569
877.357
875.125
872.873
870.601
868.310
865.997
863.664
861.310
858.934
856.537
854.118
851.678
849.214
846.728
844.219
841.686
839.130
836.549
833.944
831.313
828.658
825.976
823.269
820.534
817.772
512
514
516
518
520
522
524
526
528
530
532
534
536
538
540
542
544
546
548
550
552
554
556
558
560
562
564
566
568
570
572
574
576
578
580
582
584
586
588
590
814.982
812.164
809.318
806.441
803.535
800.597
797.629
794.628
791.594
788.527
785.425
782.288
779.115
775.905
772.657
769.369
766.042
762.674
759.263
755.808
752.308
748.762
745.169
741.525
737.831
734.084
730.283
726.425
722.508
718.530
714.489
710.382
706.206
701.959
697.638
693.238
688.757
684.190
679.533
674.781
592
594
596
598
600
602
604
606
608
610
612
614
616
618
620
622
624
626
628
630
632
634
636
638
640
641
642
643
644
645
646
647
647.096†
669.930
664.974
659.907
654.722
649.411
643.97
638.38
632.64
626.74
620.65
614.37
607.88
601.15
594.16
586.88
579.26
571.25
562.81
553.84
544.25
533.92
522.71
510.42
496.82
481.53
473.01
463.67
453.14
440.73
425.05
402.96
357.34
322
∗Triple point
†
Critical point
From Wagner, W., and Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,”
J. Phys. Chem. Ref. Data 31(2):387–535, 2002.
TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3)
Eqn
2-93
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
Cmpd.
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CF4
Cl2
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
7782-50-5
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
153.8227
88.0043
70.906
C1
1.711365
1.016
1.4486
0.79388
1.2332
1.0693
2.4507
1.3261
1.2414
1.0379
2.8963
3.5383
0.77488
3.8469
0.7371
1.0259
0.83573
0.71587
0.72184
0.43743
0.59867
0.60917
0.70797
0.52257
2.1872
0.8226
1.3285
1.796
1.187
1.2346
1.0677
0.81696
0.81856
0.98279
0.97552
1.0877
1.1591
1.1448
0.67794
0.50812
0.89458
0.89137
1.3409
1.033873
0.88443
0.79716
2.768
1.7968
2.897
0.99835
1.955
2.23
C2
0.26355
0.21845
0.25892
0.24119
0.25886
0.20656
0.27448
0.26124
0.25822
0.22465
0.26733
0.25443
0.26114
0.2881
0.25487
0.26666
0.26326
0.24812
0.24606
0.24833
0.22849
0.26925
0.25982
0.25833
0.29527
0.26632
0.2708
0.27065
0.26114
0.27216
0.27188
0.24755
0.24967
0.2683
0.26339
0.26454
0.27085
0.27154
0.2637
0.25238
0.27463
0.27365
0.27892
0.266739
0.25828
0.23168
0.26212
0.28749
0.27532
0.274
0.27884
0.27645
C3
466
761
591.95
606
508.2
545.5
308.3
506
615
540
132.45
405.65
645.6
150.86
824
562.05
689
751
702.3
830
720.15
662
718
773
584.15
670.15
503.8
464
452
425
425.12
680
676
563.1
535.9
419.5
435.5
428.6
575.4
660.5
570.1
554
440
537.2
615.7
585.4
304.21
552
132.92
556.35
227.51
417.15
C4
0.28571
0.26116
0.2529
0.29817
0.2913
0.24699
0.28752
0.2489
0.30701
0.28921
0.27341
0.2888
0.28234
0.29783
0.28571
0.28394
0.30798
0.2857
0.28789
0.27555
0.23567
0.2632
0.32144
0.27026
0.3295
0.2821
0.3012
0.28947
0.3065
0.28707
0.28688
0.24535
0.22023
0.25488
0.26864
0.2843
0.28116
0.28419
0.29318
0.29373
0.28512
0.2953
0.29661
0.28571
0.248
0.28071
0.2908
0.3226
0.2813
0.287
0.28571
0.2926
C5
C6
C7
Tmin, K
149.78
353.33
289.81
200.15
178.45
229.32
192.40
185.45
286.15
189.63
59.15
195.41
235.65
83.78
403.00
278.68
258.27
395.45
260.28
321.35
257.85
275.65
243.95
342.20
265.85
242.43
154.25
173.00
136.95
164.25
134.86
220.00
196.15
183.85
158.45
87.80
134.26
167.62
199.65
185.30
157.46
133.02
147.43
176.80
267.95
161.30
216.58
161.11
68.15
250.33
89.56
172.12
Density
at Tmin
21.423
16.936
17.492
11.626
15.683
20.544
23.692
16.822
14.693
17.254
33.279
43.141
9.6675
35.491
8.9381
11.422
10.074
8.8935
10.008
5.9496
9.9051
7.0651
8.8623
6.4251
20.109
9.9087
15.809
20.787
15.123
14.058
12.62
11.734
11.872
12.035
12.473
14.264
13.894
13.08
8.3365
7.0264
10.585
10.761
14.901
12.602
11.087
13.087
26.828
19.064
30.18
10.843
21.211
24.242
Tmax, K
466.00
761.00
591.95
606.00
508.20
545.50
308.30
506.00
615.00
540.00
132.45
405.65
645.60
150.86
824.00
562.05
689.00
751.00
702.30
830.00
720.15
662.00
718.00
773.00
584.15
670.15
503.80
464.00
452.00
425.00
425.12
680.00
676.00
563.10
535.90
419.50
435.50
428.60
575.40
660.50
570.10
554.00
440.00
537.20
615.70
585.40
304.21
552.00
132.92
556.35
227.51
417.15
Density
at Tmax
6.4935
4.6509
5.5948
3.2915
4.7640
5.1767
8.9285
5.0762
4.8075
4.6201
10.8340
13.9070
2.9673
13.3530
2.8921
3.8472
3.1745
2.8852
2.9336
1.7615
2.6201
2.2625
2.7248
2.0229
7.4075
3.0888
4.9058
6.6359
4.5455
4.5363
3.9271
3.3002
3.2786
3.6630
3.7037
4.1117
4.2795
4.2160
2.5709
2.0133
3.2574
3.2573
4.8075
3.8760
3.4243
3.4408
10.5600
6.2500
10.5220
3.6436
7.0112
8.0666
(Continued )
2-94
TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued )
Eqn
Cmpd.
no.
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
Name
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Di–sopropyl amine
Di–sopropyl ether
Di–sopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Formula
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
CAS
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
Mol. wt.
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
90.121
104.14758
C1
0.8711
1.39625
1.0841
1.8651
1.12465
1.1202
0.9061
0.95937
1.1503
0.58711
1.7805
1.3931
0.88998
0.8243
0.86464
0.92997
1.0897
1.1035
1.7411
0.78578
0.478542
0.41084
0.39348
0.38208
0.43981
0.44289
0.46877
5.2115
0.95523
1.0132
1.1136
0.55941
0.74495
0.74404
0.74858
1.1055
1.2591
1.3897
0.9551
0.89833
0.68184
0.85379
0.9554
0.82227
1.4345
1.173
1.9973
0.6181
0.69213
0.64619
0.89368
0.76327
C2
0.26805
0.26867
0.2581
0.2627
0.2728
0.27669
0.28268
0.2882
0.31861
0.25583
0.26846
0.29255
0.27376
0.26545
0.26888
0.27056
0.28356
0.27035
0.28205
0.27882
0.275162
0.25175
0.2492
0.24645
0.25661
0.27636
0.25875
0.315
0.26364
0.26634
0.24834
0.27243
0.26147
0.26112
0.26276
0.26533
0.27698
0.25678
0.27794
0.26142
0.23796
0.25675
0.26847
0.26314
0.25774
0.22856
0.24653
0.25786
0.26974
0.26881
0.26599
0.26742
C3
632.35
460.35
536.4
416.25
503.15
489
705.85
697.55
704.65
631
400.15
459.93
553.8
650.1
653
560.4
511.7
507
398
664
674
617.7
722.1
688
616.6
696
619.85
38.35
628
650.15
611
584.1
683.95
705
684.75
523
561.6
510
560
572
736.6
496.6
466.7
557.15
386.44
445
351.26
523.1
500.05
576
507.8
543
C4
0.2799
0.28571
0.2741
0.28571
0.28571
0.27646
0.2707
0.2857
0.30104
0.28498
0.26079
0.24913
0.28571
0.28495
0.29943
0.28943
0.25142
0.28699
0.29598
0.31067
0.28571
0.28571
0.28571
0.26125
0.29148
0.27668
0.29479
0.28571
0.29825
0.28571
0.27583
0.29932
0.31526
0.30815
0.30788
0.287
0.30492
0.2902
0.24132
0.2868
0.2062
0.27027
0.2814
0.27369
0.28178
0.28571
0.28153
0.271
0.28571
0.28036
0.28571
0.28571
C5
C6
C7
Tmin, K
227.95
136.75
209.63
175.43
150.35
155.97
285.39
304.19
307.93
177.14
245.25
182.48
279.69
296.60
242.00
169.67
179.28
138.13
145.59
189.64
285.00
243.51
304.55
280.05
206.89
247.56
229.15
18.73
210.15
282.85
220.60
175.30
248.39
256.15
326.14
176.19
237.49
178.01
192.50
172.71
301.15
223.35
156.85
169.20
154.56
179.60
136.95
176.85
187.65
204.81
159.95
226.10
Density
at Tmin
10.385
17.055
13.702
22.272
13.333
12.855
9.6115
9.5725
9.4494
7.9387
18.517
14.074
9.3804
9.4693
10.09
11.16
11.906
13.47
18.658
8.9048
5.2396
5.3927
5.1809
5.2609
5.7328
5.0048
5.8954
42.945
11.799
11.704
15.358
6.6071
9.1207
9.1658
8.5175
13.549
13.462
17.974
10.925
11.526
10.39
10.575
11.487
10.47
18.006
18.336
27.399
8.0541
8.0673
7.6796
11.029
8.8431
Tmax, K
632.35
460.35
536.40
416.25
503.15
489.00
705.85
697.55
704.65
631.00
400.15
459.93
553.80
650.10
653.00
560.40
511.70
507.00
398.00
664.00
674.00
617.70
722.10
688.00
616.60
696.00
619.85
38.35
628.00
650.15
611.00
584.10
683.95
705.00
684.75
523.00
561.60
510.00
560.00
572.00
736.60
496.60
466.70
557.15
386.44
445.00
351.26
523.10
500.05
576.00
507.80
543.00
Density
at Tmax
3.2498
5.1969
4.2003
7.0997
4.1226
4.0486
3.2054
3.3288
3.6104
2.2949
6.6323
4.7619
3.2509
3.1053
3.2157
3.4372
3.8429
4.0817
6.1730
2.8182
1.7391
1.6319
1.5790
1.5503
1.7139
1.6026
1.8117
16.5440
3.6232
3.8042
4.4842
2.0534
2.8491
2.8494
2.8489
4.1665
4.5458
5.4120
3.4364
3.4363
2.8654
3.3254
3.5587
3.1248
5.5657
5.1321
8.1017
2.3970
2.5659
2.4039
3.3598
2.8542
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
240.46774
114.18546
1.1717
1.5436
0.7565
0.55873
0.52953
0.54405
1.1058
1.5693
0.89615
0.72352
0.47977
1.0214
1.4029
1.1096
0.48611
1.1819
0.52133
0.659
0.33267
0.18166
1.9122
1.6288
0.8996
1.0936
0.70041
0.48864
0.66085
0.63566
0.61587
0.71751
2.0961
0.7842
1.315
1.3462
1.836
1.1343
0.47428
0.55729
0.8185
0.68162
1.3047
0.7405
0.7908
0.61243
4.2895
1.0146
1.693858
2.2261
3.897011
1.2486
1.938
1.1339
7.2475
0.21897
0.577362
0.25895
0.27784
0.27305
0.25143
0.24358
0.25026
0.27866
0.2679
0.23478
0.28629
0.25428
0.26351
0.27991
0.25189
0.25715
0.2813
0.26218
0.26428
0.24664
0.23351
0.27937
0.27469
0.25856
0.22636
0.26162
0.23894
0.25707
0.25613
0.26477
0.26903
0.27657
0.20702
0.25125
0.23289
0.26024
0.26168
0.25028
0.2714
0.26929
0.25152
0.2694
0.25563
0.266
0.24681
0.28587
0.27277
0.269323
0.25072
0.331636
0.20352
0.24225
0.24741
0.41865
0.23642
0.250575
473.2
437.2
500
591.15
606.15
596.15
615
400.1
649.6
537.3
766
402
503.04
729
777.4
587
766.8
550
658
768
305.32
514
523.3
456.15
617.15
698
655
571
609.15
569.5
282.34
593
720
537
469.15
508.4
674.6
583
489
567
499.15
546
500.23
559.95
144.12
560.09
375.31
317.42
420
771
588
490.15
5.2
736
620
0.27289
0.2572
0.27408
0.27758
0.26809
0.2658
0.31082
0.2882
0.28091
0.27121
0.30722
0.28421
0.2741
0.3311
0.28571
0.3047
0.31033
0.2766
0.28571
0.28571
0.29187
0.23178
0.278
0.25522
0.28454
0.28421
0.31103
0.27829
0.28054
0.27733
0.29147
0.20254
0.21868
0.23357
0.2696
0.2791
0.25442
0.29538
0.30621
0.3182
0.27866
0.2795
0.292
0.30858
0.28776
0.28291
0.28571
0.27343
0.28571
0.25178
0.24435
0.2612
0.24096
0.28571
0.28571
240.91
180.96
145.19
239.66
223.16
184.99
188.44
131.65
212.72
141.23
274.18
122.93
174.88
291.67
413.79
284.95
300.03
210.15
263.57
309.58
90.35
159.05
189.60
192.15
178.20
238.45
258.15
175.15
161.84
134.71
104.00
284.29
260.15
195.20
160.65
193.55
155.15
180.00
140.00
204.15
125.26
199.25
145.65
167.55
53.48
230.94
129.95
131.35
155.15
275.60
281.45
187.55
2.20
295.13
229.80
13.767
16.964
9.031
7.3417
7.5783
7.6258
12.413
18.95
13.954
7.9932
6.2334
12.898
15.556
14.111
5.6397
11.838
6.2648
7.9929
4.5205
2.7293
21.64
19.41
11.478
17.588
9.0407
7.2908
8.2198
8.4912
7.8679
9.0179
23.326
15.055
18.31
21.45
23.477
14.006
6.926
6.612
9.9236
8.9749
16.242
9.6317
9.8474
8.6934
44.888
11.374
20.099
29.345
30.92
25.488
26.806
15.702
37.115
3.2189
7.7462
473.20
437.20
500.00
591.15
606.15
596.15
615.00
400.10
649.60
537.30
766.00
402.00
503.04
729.00
777.40
587.00
766.80
550.00
658.00
768.00
305.32
514.00
523.30
456.15
617.15
698.00
655.00
571.00
609.15
569.50
282.34
593.00
720.00
537.00
469.15
508.40
674.60
583.00
489.00
567.00
499.15
546.00
500.23
559.95
144.12
560.09
375.31
317.42
420.00
771.00
588.00
490.15
5.20
736.00
620.00
4.5248
5.5557
2.7706
2.2222
2.1739
2.1739
3.9683
5.8578
3.8170
2.5272
1.8868
3.8761
5.0120
4.4051
1.8904
4.2016
1.9884
2.4936
1.3488
0.7780
6.8447
5.9296
3.4793
4.8312
2.6772
2.0450
2.5707
2.4818
2.3261
2.6670
7.5789
3.7880
5.2338
5.7804
7.0550
4.3347
1.8950
2.0534
3.0395
2.7100
4.8430
2.8968
2.9729
2.4814
15.0050
3.7196
6.2893
8.8788
11.7510
6.1350
8.0000
4.5831
17.3120
0.9262
2.3041
2-95
(Continued )
2-96
TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued )
Eqn
Cmpd.
no.
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
Name
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Formula
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CAS
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
Mol. wt.
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
C1
0.61259
0.53066
0.55687
0.59339
0.59268
0.58247
0.66016
0.58622
0.67304
0.23289
0.668504
0.70824
0.62833
0.70093
0.67393
0.67816
0.67666
0.76925
0.78045
0.66372
0.84427
0.76277
1.0516
5.414
2.832
3.342
1.3413
2.8061
2.7672
0.88575
1.2801
0.87969
0.87025
2.9214
2.3267
0.88268
1.13
1.6085
0.97286
1.39
0.53382
0.84623
0.91991
0.72762
0.8189
0.91619
0.93391
1.1157
0.8363
0.75509
0.94575
0.76983
C2
0.26211
0.24729
0.24725
0.2602
0.25663
0.25279
0.26657
0.2726
0.26045
0.23659
0.252695
0.26411
0.25598
0.26776
0.25948
0.25634
0.25578
0.26809
0.26065
0.27345
0.27185
0.25248
0.16613
0.34893
0.2832
0.2729
0.18589
0.19362
0.27369
0.25736
0.2828
0.24543
0.24383
0.28976
0.27073
0.23568
0.2593
0.26436
0.26267
0.21405
0.23274
0.24625
0.27815
0.25244
0.26974
0.26752
0.27275
0.27671
0.27514
0.27183
0.26008
0.26173
C3
540.2
677.3
632.3
608.3
606.6
611.4
537.4
645
547
723
594
507.6
660.2
611.3
585.3
587.61
582.82
504
544
623
516.2
549
653.15
33.19
363.15
324.65
456.65
461.15
373.53
605
471.85
834
662
190.56
512.5
718
506.55
402.4
536
430.05
693
490
460.4
643
577.2
465
470
492
512.74
593
463.2
554.5
C4
0.28141
0.28289
0.31471
0.26968
0.27766
0.29818
0.28571
0.29644
0.28388
0.28571
0.28571
0.27537
0.25304
0.24919
0.26552
0.28365
0.27746
0.28571
0.28571
0.29185
0.2771
0.31611
0.1898
0.2706
0.28571
0.3217
0.28206
0.29847
0.29015
0.26265
0.2972
0.28571
0.28571
0.28881
0.24713
0.27379
0.2764
0.27987
0.2508
0.2275
0.28147
0.29041
0.28667
0.28571
0.23573
0.28164
0.2578
0.30821
0.27553
0.29127
0.30807
0.26879
C5
C6
C7
Tmin, K
182.57
265.83
239.15
220.00
234.15
238.15
154.12
229.92
192.22
291.31
214.93
177.83
269.25
228.55
223.00
217.35
217.50
133.39
170.05
192.62
141.25
183.65
274.69
13.95
185.15
158.97
259.83
189.79
187.68
227.15
177.95
409.15
288.15
90.69
175.47
301.15
175.15
170.45
196.32
179.69
260.75
159.53
113.25
193.00
155.95
135.58
139.39
160.15
157.48
175.30
183.45
187.35
Density
at Tmin
7.6998
7.2212
7.5022
7.5173
7.5751
7.5514
8.2257
6.7277
8.4922
3.415
8.8708
8.747
8.0964
8.456
8.5181
8.7319
8.7631
9.5815
10.021
7.7733
10.23
10.133
31.934
38.487
27.985
34.854
27.202
58.861
29.13
11.42
13.561
11.417
11.834
28.18
27.915
13.012
14.475
19.031
12.203
25.378
8.2202
11.994
10.764
9.9915
10.248
11.332
11.216
12.581
9.7581
9.0056
11.519
9.7638
Tmax, K
540.20
677.30
632.30
608.30
606.60
611.40
537.40
645.00
547.00
723.00
594.00
507.60
660.20
611.30
585.30
587.61
582.82
504.00
544.00
623.00
516.20
549.00
653.15
33.19
363.15
324.65
456.65
461.15
373.53
605.00
471.85
834.00
662.00
190.56
512.50
718.00
506.55
402.40
536.00
430.05
693.00
490.00
460.40
643.00
577.20
465.00
470.00
492.00
512.74
593.00
463.20
554.50
Density
at Tmax
2.3371
2.1459
2.2523
2.2805
2.3095
2.3042
2.4765
2.1505
2.5841
0.9844
2.6455
2.6816
2.4546
2.6178
2.5972
2.6455
2.6455
2.8694
2.9942
2.4272
3.1056
3.0211
6.3300
15.5160
10.0000
12.2460
7.2156
14.4930
10.1110
3.4417
4.5265
3.5843
3.5691
10.0820
8.5942
3.7452
4.3579
6.0845
3.7037
6.4938
2.2936
3.4365
3.3072
2.8823
3.0359
3.4248
3.4241
4.0320
3.0395
2.7778
3.6364
2.9413
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
CH3NO2
N2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
1.0674
0.73109
0.7013
0.70973
0.72836
0.84758
0.88824
0.9109
0.97608
1.2635
0.93767
1.067
1.525
0.84005
0.71687
1.0228
0.97887
0.86567
0.78912
1.9323
0.7761
0.4416
0.72701
0.71004
1.0631
0.92128
1.1446
0.9147
0.96145
0.87496
1.3052
0.64856
0.817948
1.2587
0.6348
7.3718
1.0024
3.2091
2.3736
1.3728
2.781
5.246
0.19199
0.473233
0.46321
0.41582
0.43682
0.419258
0.48661
0.47377
0.52152
0.20448
0.525901
0.5266
0.48251
0.26257
0.26971
0.266
0.26544
0.27241
0.27037
0.26914
0.276
0.28209
0.27878
0.25035
0.27102
0.2634
0.27638
0.26453
0.20692
0.27017
0.26836
0.25915
0.28018
0.25068
0.2521
0.26754
0.26981
0.27506
0.25442
0.2724
0.2594
0.26536
0.26862
0.26757
0.25877
0.269105
0.26433
0.25838
0.3067
0.23655
0.2861
0.2817
0.23793
0.27244
0.3044
0.23337
0.256918
0.25444
0.24284
0.25161
0.241912
0.25722
0.27052
0.25918
0.23474
0.25664
0.25693
0.25196
442
572.1
686
614
617
532.7
542
526
483
437.8
535.5
533
487.2
497
574.6
488
464.48
553.4
553.1
469.95
566
694
497.7
546.49
407.8
506.2
417.9
530.6
476.25
565
352.5
654
497.1
437
748.4
44.4
593
126.2
234
588.15
309.57
180.15
758
658.5
594.6
710.7
670.9
649.5
593.1
681
598.05
747
638.9
568.7
694.26
0.26569
0.29185
0.28571
0.26016
0.2478
0.28258
0.27874
0.26756
0.22529
0.2744
0.29964
0.29364
0.2806
0.27645
0.28918
0.28571
0.28998
0.28364
0.26512
0.28523
0.29773
0.28532
0.28268
0.29974
0.2758
0.27586
0.28172
0.2774
0.30088
0.30259
0.28799
0.31444
0.28571
0.25819
0.27727
0.2786
0.278
0.2966
0.29529
0.29601
0.2882
0.242
0.28571
0.28571
0.28571
0.30036
0.2498
0.28571
0.28571
0.30284
0.29177
0.28571
0.28571
0.28571
0.26842
139.05
146.58
285.15
280.15
269.15
130.73
146.62
168.54
182.55
160.00
186.48
167.23
174.15
188.00
189.15
256.15
127.93
180.15
171.64
150.18
224.95
240.00
119.55
176.00
113.54
298.97
132.81
185.65
133.97
160.17
116.34
249.95
164.55
151.15
333.15
24.56
183.63
63.15
66.46
244.60
182.30
109.50
305.04
267.30
219.66
285.55
268.15
238.15
191.91
253.05
223.15
301.31
251.65
216.38
289.65
13.626
9.0173
8.2091
8.2931
8.2628
10.491
10.98
10.538
10.789
13.995
12.663
12.671
18.811
9.3871
8.8617
17.666
11.933
10.46
10.352
21.564
10.176
5.938
9.2041
8.445
12.574
10.556
13.507
11.678
12.043
10.689
15.791
8.0099
9.7955
15.691
7.7545
61.796
15.556
31.063
26.555
19.632
27.928
44.487
2.8889
5.9415
6.0427
5.7592
5.8496
6.0223
6.3717
5.4532
6.5369
3.0418
6.6608
6.7049
6.3107
442.00
572.10
686.00
614.00
617.00
532.70
542.00
526.00
483.00
437.80
535.50
533.00
487.20
497.00
574.60
488.00
464.48
553.40
553.10
469.95
566.00
694.00
497.70
546.49
407.80
506.20
417.90
530.60
476.25
565.00
352.50
654.00
497.10
437.00
748.40
44.40
593.00
126.20
234.00
588.15
309.57
180.15
758.00
658.50
594.60
710.70
670.90
649.50
593.10
681.00
598.05
747.00
638.90
568.70
694.26
4.0652
2.7107
2.6365
2.6738
2.6738
3.1349
3.3003
3.3004
3.4602
4.5322
3.7454
3.9370
5.7897
3.0395
2.7100
4.9430
3.6232
3.2258
3.0450
6.8966
3.0960
1.7517
2.7174
2.6316
3.8650
3.6211
4.2019
3.5262
3.6232
3.2572
4.8780
2.5063
3.0395
4.7619
2.4568
24.0360
4.2376
11.2170
8.4260
5.7698
10.2080
17.2340
0.8227
1.8420
1.8205
1.7123
1.7361
1.7331
1.8918
1.7513
2.0122
0.8711
2.0492
2.0496
1.9150
2-97
(Continued )
2-98
TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued )
Eqn
Cmpd.
no.
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
Name
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Formula
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
CAS
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
Mol. wt.
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
C1
0.48979
0.52497
0.50006
0.5108
0.55449
0.52577
0.58945
1.1911
3.9143
3.3592
0.25142
0.85658
0.84947
0.73455
0.81754
0.81577
0.90411
0.71811
0.89816
0.65858
0.75345
0.8491
0.92099
0.45554
1.3798
0.63163
0.5393
1.6087
1.3757
1.2457
1.1799
0.61255
1.2861
1.0969
0.91281
0.73041
0.9195
0.57233
1.4403
0.915
1.093
1.0714
1.0923
0.83228
1.1945
0.7397
C2
0.24931
0.26186
0.24851
0.25386
0.25952
0.27234
0.26052
0.27038
0.28772
0.29884
0.23837
0.26811
0.26726
0.25636
0.26732
0.26594
0.27207
0.24129
0.26608
0.25367
0.27047
0.2352
0.25419
0.2523
0.31598
0.23373
0.22704
0.26543
0.27453
0.27281
0.2644
0.26769
0.26236
0.25568
0.22125
0.25456
0.23878
0.25171
0.26852
0.26134
0.27762
0.27214
0.26106
0.25385
0.24128
0.2603
C3
652.3
629.8
632.7
627.7
566.9
667.3
574
828
154.58
261
708
566.1
469.7
639.16
588.1
561
561.08
560.95
464.8
584.3
598
481.2
519
869
694.25
653
791
394
369.83
536.8
508.3
636
503.6
600.81
561.3
549.73
496.95
638.35
364.85
538
517
536.6
626
683
259
636
C4
0.27824
0.25257
0.29942
0.26735
0.28571
0.30063
0.28532
0.28571
0.2924
0.28523
0.28571
0.27354
0.27789
0.25522
0.25348
0.25551
0.30669
0.27996
0.28571
0.28571
0.30583
0.353
0.31077
0.24841
0.32768
0.28571
0.248
0.29895
0.29359
0.23994
0.24653
0.28571
0.3004
0.26857
0.26811
0.27666
0.2461
0.29616
0.28775
0.28
0.29781
0.29481
0.20459
0.23658
0.16693
0.3009
C5
C6
C7
Tmin, K
257.65
241.55
252.85
255.55
171.45
223.95
193.55
462.65
54.35
80.15
283.07
191.59
143.42
239.15
195.56
200.00
196.29
234.18
108.02
160.75
197.45
167.45
163.83
372.38
314.06
243.15
404.15
136.87
85.47
146.95
185.26
199.00
165.00
252.45
180.37
178.15
188.36
173.55
87.89
180.25
142.61
159.95
213.15
388.85
186.35
242.54
Density
at Tmin
6.5738
6.5625
6.6477
6.6283
7.2155
6.0987
7.4832
12.405
40.77
33.361
3.6423
10.353
10.474
9.5869
10.061
10.017
10.398
10.102
11.521
9.073
8.8575
12.532
12.24
5.9853
11.244
9.6466
8.2218
19.479
16.583
15.206
14.663
7.4763
16.075
13.935
16.067
9.7941
13.764
7.9821
18.07
11.59
12.61
12.716
14.363
10.082
15.635
9.1088
Tmax, K
652.30
629.80
632.70
627.70
566.90
667.30
574.00
828.00
154.58
261.00
708.00
566.10
469.70
639.16
588.10
561.00
561.08
560.95
464.80
584.30
598.00
481.20
519.00
869.00
694.25
653.00
791.00
394.00
369.83
536.80
508.30
636.00
503.60
600.81
561.30
549.73
496.95
638.35
364.85
538.00
517.00
536.60
626.00
683.00
259.00
636.00
Density
at Tmax
1.9646
2.0048
2.0122
2.0121
2.1366
1.9306
2.2626
4.4053
13.6050
11.2410
1.0547
3.1949
3.1784
2.8653
3.0583
3.0675
3.3231
2.9761
3.3755
2.5962
2.7857
3.6101
3.6232
1.8055
4.3667
2.7024
2.3754
6.0607
5.0111
4.5662
4.4626
2.2883
4.9020
4.2901
4.1257
2.8693
3.8508
2.2738
5.3638
3.5012
3.9370
3.9369
4.1841
3.2786
4.9507
2.8417
105
105
105
105
105
105
100
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
105
100
119
105
105
105
313
314
315
316
317
318
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
342
343
344
345
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
Water
m-Xylene
o-Xylene
p-Xylene
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
H2O
C8H10
C8H10
C8H10
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
7732-18-5
108-38-3
95-47-6
106-42-3
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
18.01528
106.165
106.165
106.165
0.65882
2.106
1.3587
1.4969
0.41922
0.3448
5.7136
0.27248
1.2543
0.67717
1.1628
0.58988
1.2874
0.8792
0.9062
0.29934
0.7035
1.0116
0.6531
0.60394
0.59059
0.6028
0.48195
0.37378
0.36703
0.33113
0.9591
1.2703
1.5115
0.59595
–13.851
17.874
0.68902
0.69962
0.67752
0.21741
0.25842
0.2701
0.19013
0.17775
0.25116
–0.003474
0.24007
0.28084
0.27772
0.28954
0.27201
0.28194
0.27136
0.25475
0.2433
0.27386
0.25683
0.27002
0.25956
0.27424
0.27446
0.23093
0.21379
0.24876
0.23676
0.2593
0.26041
0.2707
0.24314
0.64038
35.618
0.26086
0.26143
0.25887
838
430.75
318.69
490.85
883.6
857
0.28571
0.2895
0.2921
0.4359
0.28571
0.29268
693
540.15
720
631.95
568
579.35
591.75
602
675
535.15
433.25
664.5
649.1
543.8
573.5
846
828
639
703.9
519.13
454
432
543.15
–0.0019124
19.655
617
630.3
616.2
0.28571
0.2912
0.2878
0.28674
0.27341
0.30781
0.29241
0.31
0.28571
0.2872
0.2696
0.26268
0.27713
0.2847
0.2741
0.28571
0.29905
0.28571
0.2762
0.27448
0.297
0.2716
0.24856
1.8211E-06
–9.1306
0.27479
0.27365
0.27596
–31.367 –813.56 – 17421000
460.85
197.67
223.15
289.95
700.15
329.35
288.15
279.01
164.65
237.38
176.99
373.96
234.94
178.18
236.50
267.76
158.45
156.08
243.15
229.33
165.78
172.22
398.40
354.00
247.57
288.45
180.35
173.15
119.36
178.35
273.16
273.16
225.30
247.98
286.41
10.21
25.298
12.631
24.241
7.102
4.5526
4.7126
3.889
13.998
7.638
12.408
5.7242
13.43
10.487
11.478
4.1817
8.2843
13.144
7.7278
7.689
6.9146
7.0934
7.0825
6.4521
4.9453
4.8594
12.287
15.664
18.481
8.8236
55.497
55.487
8.648
8.6229
8.1614
838.00
430.75
318.69
490.85
883.60
857.00
313.19
693.00
540.15
720.00
631.95
568.00
579.35
591.75
602.00
675.00
535.15
433.25
664.50
649.10
543.80
573.50
846.00
828.00
639.00
703.90
519.13
454.00
432.00
543.15
353.15
647.096
617.00
630.30
616.20
3.0303
8.1495
5.0304
7.8730
2.3585
1.3728
4.6256
1.1350
4.4662
2.4383
4.0160
2.1686
4.5662
3.2400
3.5572
1.2303
2.5688
3.9388
2.4187
2.3268
2.1536
2.1963
2.0870
1.7484
1.4754
1.3986
3.6988
4.8781
5.5837
2.4511
54.0010
17.8740
2.6413
2.6761
2.6172
Except for o-terphenyl and water, liquid density ρ is calculated by Eqn 105: ρ = C1/(C2[1 + (1 – T/C3)^C4]) where ρ is in mol/dm3 and T is in K. The pressure is equal to the vapor pressure for pressures greater than 1 atm and equal to 1 atm
when the vapor pressure is less than 1 atm.
Equation (2-100), used for the limited temperature ranges as noted for o-terphenyl and water, is ρ = C1 + C2T + C3T 2 + C4T 3.
Equation (2-119), used for water, is ρ = C1 + C2τ1/3 + C3τ2/3 + C4τ5/3 + C5τ16/3 + C6τ43/3 + C7τ110/3 where τ = 1 − T/TC, and TC = critical temperature (647.096 K).
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and
reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data
Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016).
2-99
2-100
PHYSICAL AnD CHEMICAL DATA
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
TABLE 2-33
Ammonia (nH3)*
% −15°C −10°C
1
2
4
8
12
16
20
24
28
30
−5°C
0°C
5°C
10°C
20°C
25°C
TABLE 2-38 Ferric nitrate
[Fe(nO3)3]*
d 415
%
0.9943 0.9954 0.9959 0.9958 0.9955 0.9939 0.993 32 0.889
.9906 .9915 .9919 .9917 .9913 .9895 .988 36 .877
.9834 .9840 .9842 .9837 .9832 .9811 .980 40 .865
0.970 .9701 .9701 .9695 .9686 .9677 .9651 .964 45 .849
.958 .9576 .9571 .9561 .9548 .9534 .9501 .948 50 .832
.947 .9461 .9450 .9435 .9420 .9402 .9362 .934 60 .796
.9353 .9335 .9316 .9296 .9275 .9229
70 .755
.9249 .9226 .9202 .9179 .9155 .9101
80 .711
.9150 .9122 .9094 .9067 .9040 .8980
90 .665
.9101 .9070 .9040 .9012 .8983 .8920
100 .618
0°C
10°C
20°C
30°C
50°C
80°C
100°C
1
2
4
8
12
16
20
24
1.0033
1.0067
1.0135
1.0266
1.0391
1.0510
1.0625
1.0736
1.0029
1.0062
1.0126
1.0251
1.0370
1.0485
1.0596
1.0705
1.0013
1.0045
1.0107
1.0227
1.0344
1.0457
1.0567
1.0674
0.9987
1.0018
1.0077
1.0195
1.0310
1.0422
1.0532
1.0641
0.9910
.9940
.9999
1.0116
1.0231
1.0343
1.0454
1.0564
0.9749
.9780
.9842
.9963
1.0081
1.0198
1.0312
1.0426
0.9617
.9651
.9718
.9849
.9975
1.0096
1.0213
1.0327
∗International Critical Tables, vol. 3, p. 60.
TABLE 2-35 Calcium Chloride (CaCl2)*
2
4
8
12
16
20
25
30
35
40
1.0708
1.1083
1.1471
1.1874
1
2
4
8
12
16
20
25
1.0065
1.0144
1.0304
1.0636
1.0989
1.1359
1.1748
1.2281
Ammonium Chloride (nH4Cl)*
%
% −5°C
d4
∗International Critical Tables,
vol. 3, p. 68.
∗International Critical Tables, vol. 3, p. 59.
TABLE 2-34
18
%
0°C
20°C
30°C
40°C
60°C
80°C 100°C 120°C† 140°C
1.0171
1.0346
1.0703
1.1072
1.1454
1.1853
1.2376
1.2922
1.0148
1.0316
1.0659
1.1015
1.1386
1.1775
1.2284
1.2816
1.3373
1.3957
1.0120
1.0286
1.0626
1.0978
1.1345
1.1730
1.2236
1.2764
1.3316
1.3895
1.0084
1.0249
1.0586
1.0937
1.1301
1.1684
1.2186
1.2709
1.3255
1.3826
0.9994
1.0158
1.0492
1.0840
1.1202
1.1581
1.2079
1.2597
1.3137
1.3700
0.9881
1.0046
1.0382
1.0730
1.1092
1.1471
1.1965
1.2478
1.3013
1.3571
0.9748
0.9915
1.0257
1.0610
1.0973
1.1352
1.1846
1.2359
1.2893
1.3450
0.9596
0.9765
1.0111
1.0466
1.0835
1.1219
0.9428
0.9601
0.9954
1.0317
1.0691
1.1080
∗International Critical Tables, vol. 3, pp. 72–73.
†
Corrected to atmospheric pressure.
TABLE 2-36 Ferric Chloride (FeCl3)*
%
0°C
10°C
20°C
30°C
1
2
4
8
12
16
20
25
30
35
40
45
50
1.0086
1.0174
1.0347
1.0703
1.1088
1.1475
1.1870
1.2400
1.2970
1.3605
1.4280
1.0084
1.0168
1.0341
1.0692
1.1071
1.1449
1.1847
1.2380
1.2950
1.3580
1.4235
1.4920
1.5610
1.0068
1.0152
1.0324
1.0669
1.1040
1.1418
1.1820
1.2340
1.2910
1.3530
1.4175
1.4850
1.5510
1.0040
1.0122
1.0292
1.0636
1.1006
1.1386
1.1786
1.2290
1.2850
1.3475
1.4115
TABLE 2-37 Ferric Sulfate
[Fe2(SO4)3]*
1
2
4
8
12
16
20
30
40
50
60
%
15°C
18°C
TABLE 2-40 Hydrogen
Cyanide (HCn)*
20°C
0.2
1.00068
1.0002
0.4
1.00275
1.0022
0.8
1.00645
1.0062
1.0 1.0090
1.0085
1.0082
4.0 1.0380
1.0375
8.0 1.0790
1.0785
12.0 1.1235
1.1220
16.0 1.1690
1.1675
20.0 1.2150
1.2135
∗International Critical Tables, vol. 3,
p. 68.
17.5
d4
1.0072
1.0157
1.0327
1.0670
1.1028
1.1409
1.1811
1.3073
1.4487
1.6127
1.7983
∗International Critical Tables, vol. 3, p. 68.
15
%
d4
1
2
4
8
12
16
82
90
100
0.998
0.996
0.993
0.984
0.971
0.956
0.752
0.724
0.691
∗International Critical Tables,
vol. 3, p. 61.
TABLE 2-41 Hydrogen Chloride (HCl)
%
−5°C
0°C
10°C
20°C
40°C
60°C
80°C
100°C
1
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
1.0048
1.0104
1.0213
1.0321
1.0428
1.0536
1.0645
1.0754
1.0864
1.0975
1.1087
1.1200
1.1314
1.1426
1.1537
1.1648
1.0052
1.0106
1.0213
1.0319
1.0423
1.0528
1.0634
1.0741
1.0849
1.0958
1.1067
1.1177
1.1287
1.1396
1.1505
1.1613
1.0048
1.0100
1.0202
1.0303
1.0403
1.0504
1.0607
1.0711
1.0815
1.0920
1.1025
1.1131
1.1238
1.1344
1.1449
1.1553
1.0032
1.0082
1.0181
1.0279
1.0376
1.0474
1.0574
1.0675
1.0776
1.0878
1.0980
1.1083
1.1187
1.1290
1.1392
1.1493
1.1593
1.1691
1.1789
1.1885
1.1980
0.9970
1.0019
1.0116
1.0211
1.0305
1.0400
1.0497
1.0594
1.0692
1.0790
1.0888
1.0986
1.1085
1.1183
1.1280
1.1376
0.9881
0.9930
1.0026
1.0121
1.0215
1.0310
1.0406
1.0502
1.0598
1.0694
1.0790
1.0886
1.0982
1.1076
1.1169
1.1260
0.9768
0.9819
0.9919
1.0016
1.0111
1.0206
1.0302
1.0398
1.0494
1.0590
1.0685
1.0780
1.0874
1.0967
1.1058
1.1149
0.9636
0.9688
0.9791
0.9892
0.9992
1.0090
1.0188
1.0286
1.0383
1.0479
1.0574
1.0668
1.0761
1.0853
1.0942
1.1030
∗International Critical Tables, vol. 3, p. 54.
TABLE 2-42 Hydrogen
Peroxide (H2O2)*
∗International Critical Tables, vol. 3, p. 68.
%
TABLE 2-39 Ferrous Sulfate
(FeSO4)*
18
18
%
d4
%
d4
1
2
4
6
8
10
12
14
16
18
20
22
24
1.0022
1.0058
1.0131
1.0204
1.0277
1.0351
1.0425
1.0499
1.0574
1.0649
1.0725
1.0802
1.0880
26
28
30
35
40
45
50
55
60
70
80
90
100
1.0959
1.1040
1.1122
1.1327
1.1536
1.1749
1.1966
1.2188
1.2416
1.2897
1.3406
1.3931
1.4465
∗International Critical Tables, vol. 3,
p. 54.
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
2-101
TABLE 2-43 nitric Acid (HnO3)*
%
0°C
5°C
10°C
15°C
20°C
25°C
30°C
40°C
50°C
60°C
80°C
100°C
1
2
3
4
1.0058
1.0117
1.0176
1.0236
1.00572
1.01149
1.01730
1.02315
1.00534
1.01099
1.01668
1.02240
1.00464
1.01018
1.01576
1.02137
1.00364
1.00909
1.01457
1.02008
1.00241
1.00778
1.01318
1.01861
1.0009
1.0061
1.0114
1.0168
0.9973
1.0025
1.0077
1.0129
0.9931
0.9982
1.0033
1.0084
0.9882
0.9932
0.9982
1.0033
0.9767
0.9816
0.9865
0.9915
0.9632
0.9681
0.9730
0.9779
5
6
7
8
9
1.0296
1.0357
1.0418
1.0480
1.0543
1.02904
1.03497
1.0410
1.0471
1.0532
1.02816
1.03397
1.0399
1.0458
1.0518
1.02702
1.03272
1.0385
1.0443
1.0502
1.02563
1.03122
1.0369
1.0427
1.0485
1.02408
1.02958
1.0352
1.0409
1.0466
1.0222
1.0277
1.0333
1.0389
1.0446
1.0182
1.0235
1.0289
1.0344
1.0399
1.0136
1.0188
1.0241
1.0295
1.0349
1.0084
1.0136
1.0188
1.0241
1.0294
0.9965
1.0015
1.0066
1.0117
1.0169
0.9829
0.9879
0.9929
0.9980
1.0032
10
11
12
13
14
1.0606
1.0669
1.0733
1.0797
1.0862
1.0594
1.0656
1.0718
1.0781
1.0845
1.0578
1.0639
1.0700
1.0762
1.0824
1.0561
1.0621
1.0681
1.0742
1.0803
1.0543
1.0602
1.0661
1.0721
1.0781
1.0523
1.0581
1.0640
1.0699
1.0758
1.0503
1.0560
1.0618
1.0676
1.0735
1.0455
1.0511
1.0567
1.0624
1.0681
1.0403
1.0458
1.0513
1.0568
1.0624
1.0347
1.0401
1.0455
1.0509
1.0564
1.0221
1.0273
1.0326
1.0379
1.0432
1.0083
1.0134
1.0186
1.0238
1.0289
15
16
17
18
19
1.0927
1.0992
1.1057
1.1123
1.1189
1.0909
1.0973
1.1038
1.1103
1.1168
1.0887
1.0950
1.1014
1.1078
1.1142
1.0865
1.0927
1.0989
1.1052
1.1115
1.0842
1.0903
1.0964
1.1026
1.1088
1.0818
1.0879
1.0940
1.1001
1.1062
1.0794
1.0854
1.0914
1.0974
1.1034
1.0739
1.0797
1.0855
1.0913
1.0972
1.0680
1.0737
1.0794
1.0851
1.0908
1.0619
1.0675
1.0731
1.0787
1.0843
1.0485
1.0538
1.0592
1.0646
1.0700
1.0341
1.0393
1.0444
1.0496
1.0547
20
21
22
23
24
1.1255
1.1322
1.1389
1.1457
1.1525
1.1234
1.1300
1.1366
1.1433
1.1501
1.1206
1.1271
1.1336
1.1402
1.1469
1.1178
1.1242
1.1306
1.1371
1.1437
1.1150
1.1213
1.1276
1.1340
1.1404
1.1123
1.1185
1.1247
1.1310
1.1374
1.1094
1.1155
1.1217
1.1280
1.1343
1.1031
1.1090
1.1150
1.1210
1.1271
1.0966
1.1024
1.1083
1.1142
1.1201
1.0899
1.0956
1.1013
1.1070
1.1127
1.0754
1.0808
1.0862
1.0917
1.0972
1.0598
1.0650
1.0701
1.0753
1.0805
25
26
27
28
29
1.1594
1.1663
1.1733
1.1803
1.1874
1.1569
1.1638
1.1707
1.1777
1.1847
1.1536
1.1603
1.1670
1.1738
1.1807
1.1503
1.1569
1.1635
1.1702
1.1770
1.1469
1.1534
1.1600
1.1666
1.1733
1.1438
1.1502
1.1566
1.1631
1.1697
1.1406
1.1469
1.1533
1.1597
1.1662
1.1332
1.1394
1.1456
1.1519
1.1582
1.1260
1.1320
1.1381
1.1442
1.1503
1.1185
1.1244
1.1303
1.1362
1.1422
1.1027
1.1083
1.1139
1.1195
1.1251
1.0857
1.0910
1.0963
1.1016
1.1069
30
31
32
33
34
1.1945
1.2016
1.2088
1.2160
1.2233
1.1917
1.1988
1.2059
1.2131
1.2203
1.1876
1.1945
1.2014
1.2084
1.2155
1.1838
1.1906
1.1974
1.2043
1.2113
1.1800
1.1867
1.1934
1.2002
1.2071
1.1763
1.1829
1.1896
1.1963
1.2030
1.1727
1.1792
1.1857
1.1922
1.1988
1.1645
1.1708
1.1772
1.1836
1.1901
1.1564
1.1625
1.1687
1.1749
1.1812
1.1482
1.1542
1.1602
1.1662
1.1723
1.1307
1.1363
1.1419
1.1476
1.1533
1.1122
1.1175
1.1228
1.1281
1.1335
35
36
37
38
39
1.2306
1.2375
1.2444
1.2513
1.2581
1.2275
1.2344
1.2412
1.2479
1.2546
1.2227
1.2294
1.2361
1.2428
1.2494
1.2183
1.2249
1.2315
1.2381
1.2446
1.2140
1.2205
1.2270
1.2335
1.2399
1.2098
1.2163
1.2227
1.2291
1.2354
1.2055
1.2119
1.2182
1.2245
1.2308
1.1966
1.2028
1.2089
1.2150
1.2210
1.1876
1.1936
1.1995
1.2054
1.2112
1.1784
1.1842
1.1899
1.1956
1.2013
1.1591
1.1645
1.1699
1.1752
1.1805
1.1390
1.1440
1.1490
1.1540
1.1589
40
41
42
43
44
1.2649
1.2717
1.2786
1.2854
1.2922
1.2613
1.2680
1.2747
1.2814
1.2880
1.2560
1.2626
1.2692
1.2758
1.2824
1.2511
1.2576
1.2641
1.2706
1.2771
1.2463
1.2527
1.2591
1.2655
1.2719
1.2417
1.2480
1.2543
1.2606
1.2669
1.2370
1.2432
1.2494
1.2556
1.2618
1.2270
1.2330
1.2390
1.2450
1.2510
1.2170
1.2229
1.2287
1.2345
1.2403
1.2069
1.2126
1.2182
1.2238
1.2294
1.1858
1.1911
1.1963
1.2015
1.2067
1.1638
1.1687
1.1735
1.1783
1.1831
45
46
47
48
49
1.2990
1.3058
1.3126
1.3194
1.3263
1.2947
1.3014
1.3080
1.3147
1.3214
1.2890
1.2955
1.3021
1.3087
1.3153
1.2836
1.2901
1.2966
1.3031
1.3096
1.2783
1.2847
1.2911
1.2975
1.3040
1.2732
1.2795
1.2858
1.2921
1.2984
1.2680
1.2742
1.2804
1.2867
1.2929
1.2570
1.2630
1.2690
1.2750
1.2811
1.2461
1.2519
1.2577
1.2635
1.2693
1.2350
1.2406
1.2462
1.2518
1.2575
1.2119
1.2171
1.2223
1.2275
1.2328
1.1879
1.1927
1.1976
1.2024
1.2073
50
51
52
53
54
1.3327
1.3391
1.3454
1.3517
1.3579
1.3277
1.3339
1.3401
1.3462
1.3523
1.3215
1.3277
1.3338
1.3399
1.3459
1.3157
1.3218
1.3278
1.3338
1.3397
1.3100
1.3160
1.3219
1.3278
1.3336
1.3043
1.3102
1.3160
1.3218
1.3275
1.2987
1.3045
1.3102
1.3159
1.3215
1.2867
1.2923
1.2978
1.3033
1.3087
1.2748
1.2802
1.2856
1.2909
1.2961
1.2628
1.2680
1.2731
1.2782
1.2833
1.2377
1.2425
1.2473
1.2521
1.2568
1.2118
1.2163
1.2208
1.2252
1.2296
55
56
57
58
59
1.3640
1.3700
1.3759
1.3818
1.3875
1.3583
1.3642
1.3700
1.3757
1.3813
1.3518
1.3576
1.3634
1.3691
1.3747
1.3455
1.3512
1.3569
1.3625
1.3680
1.3393
1.3449
1.3505
1.3560
1.3614
1.3331
1.3386
1.3441
1.3495
1.3548
1.3270
1.3324
1.3377
1.3430
1.3482
1.3141
1.3194
1.3246
1.3298
1.3348
1.3013
1.3064
1.3114
1.3164
1.3213
1.2883
1.2932
1.2981
1.3029
1.3077
1.2615
1.2661
1.2706
1.2751
1.2795
1.2339
1.2382
1.2424
1.2466
1.2507
60
61
62
63
64
1.3931
1.3986
1.4039
1.4091
1.3868
1.3922
1.3975
1.4027
1.4078
1.3801
1.3855
1.3907
1.3958
1.4007
1.3734
1.3787
1.3838
1.3888
1.3936
1.3667
1.3719
1.3769
1.3818
1.3866
1.3600
1.3651
1.3700
1.3748
1.3795
1.3533
1.3583
1.3632
1.3679
1.3725
1.3398
1.3447
1.3494
1.3540
1.3261
1.3308
1.3354
1.3398
1.3124
1.3169
1.3213
1.3255
1.2839
1.2881
1.2922
1.2962
1.2547
1.2587
1.2625
1.2661
(Continued )
2-102
PHYSICAL AnD CHEMICAL DATA
TABLE 2-43 nitric Acid (HnO3) (Continued )
%
5°C
10°C
15°C
20°C
25°C
30°C
65
66
67
68
69
0°C
1.4128
1.4177
1.4224
1.4271
1.4317
1.4055
1.4103
1.4150
1.4196
1.4241
1.3984
1.4031
1.4077
1.4122
1.4166
1.3913
1.3959
1.4004
1.4048
1.4091
1.3841
1.3887
1.3932
1.3976
1.4019
1.3770
1.3814
1.3857
1.3900
1.3942
70
71
72
73
74
1.4362
1.4406
1.4449
1.4491
1.4532
1.4285
1.4328
1.4371
1.4413
1.4454
1.4210
1.4252
1.4294
1.4335
1.4376
1.4134
1.4176
1.4218
1.4258
1.4298
1.4061
1.4102
1.4142
1.4182
1.4221
1.3983
1.4023
1.4063
1.4103
1.4142
75
76
77
78
79
1.4573
1.4613
1.4652
1.4690
1.4727
1.4494
1.4533
1.4572
1.4610
1.4647
1.4415
1.4454
1.4492
1.4529
1.4565
1.4337
1.4375
1.4413
1.4450
1.4486
1.4259
1.4296
1.4333
1.4369
1.4404
1.4180
1.4217
1.4253
1.4288
1.4323
80
81
82
83
84
1.4764
1.4800
1.4835
1.4869
1.4903
1.4683
1.4718
1.4753
1.4787
1.4820
1.4601
1.4636
1.4670
1.4704
1.4737
1.4521
1.4555
1.4589
1.4622
1.4655
1.4439
1.4473
1.4507
1.4540
1.4572
1.4357
1.4391
1.4424
1.4456
1.4487
85
86
87
88
89
1.4936
1.4968
1.4999
1.5029
1.5058
1.4852
1.4883
1.4913
1.4942
1.4970
1.4769
1.4799
1.4829
1.4858
1.4885
1.4686
1.4716
1.4745
1.4773
1.4800
1.4603
1.4633
1.4662
1.4690
1.4716
1.4518
1.4548
1.4577
1.4605
1.4631
90
91
92
93
94
1.5085
1.5111
1.5136
1.5156
1.5177
1.4997
1.5023
1.5048
1.5068
1.5088
1.4911
1.4936
1.4960
1.4979
1.4999
1.4826
1.4850
1.4873
1.4892
1.4912
1.4741
1.4766
1.4789
1.4807
1.4826
1.4656
1.4681
1.4704
1.4722
1.4741
95
96
97
98
99
100
1.5198
1.5220
1.5244
1.5278
1.5327
1.5402
1.5109
1.5130
1.5152
1.5187
1.5235
1.5310
1.5019
1.5040
1.5062
1.5096
1.5144
1.5217
1.4932
1.4952
1.4974
1.5008
1.5056
1.5129
1.4846
1.4867
1.4889
1.4922
1.4969
1.5040
1.4761
1.4781
1.4802
1.4835
1.4881
1.4952
40°C
50°C
60°C
80°C
100°C
∗International Critical Tables, vol. 3, pp. 58–59.
TABLE 2-44 Perchloric Acid (HClO4)*
15
%
d4
1
2
4
6
8
10
12
14
16
18
20
22
24
26
1.0050
1.0109
1.0228
1.0348
1.0471
1.0597
1.0726
1.0589
1.0995
1.1135
1.1279
1.1428
1.1581
1.1738
20
d4
25
50
TABLE 2-46 Potassium Bicarbonate (KHCO3)*
15
20
50
d4
d4
%
d4
d4
d4
1.0020
1.0070
1.0169
1.0270
1.0372
1.0475
0.9933
0.9986
0.9906
1.0205
1.0320
1.0440
1.0560
1.0680
1.0810
1.0940
1.1070
1.1205
1.1345
1.1490
28
30
32
34
36
38
40
45
50
55
60
65
70
1.1900
1.2067
1.2239
1.2418
1.2603
1.2794
1.2991
1.3521
1.4103
1.4733
1.5389
1.6059
1.6736
1.1851
1.2013
1.2183
1.2359
1.2542
1.2732
1.2927
1.3450
1.4018
1.4636
1.5298
1.5986
1.6680
1.1645
1.1800
1.1960
1.2130
1.2310
1.2490
1.2680
1.3180
1.3730
1.4320
1.4950
1.5620
1.6290
1.1697
∗International Critical Tables, vol. 3, p. 54.
2%
6%
14%
20%
26%
0 1.0113 1.0339 1.0811 1.1192
10 1.0109 1.0330 1.0792 1.1167 1.1567
20 1.0092 1.0309 1.0764 1.1134 1.1529
30 1.0065 1.0279 1.0728 1.1094 1.1484
40 1.0029 1.0241 1.0685 1.1048
∗International Critical Tables, vol. 3, p. 61.
1%
2%
4%
0
1.0066
1.0134
1.0270
10
1.0064
1.0132
1.0268
15
1.0058
1.0125
1.0260
20
1.0049
1.0117
1.0252
30
1.0024
1.0092
1.0228
40
0.9990
1.0058
1.0195
50
0.9949
1.0017
1.0154
60
0.9901
0.9969
1.0106
80
0.9786
0.9855
0.9993
100
0.9653
0.9722
0.9860
∗International Critical Tables, vol. 3, p. 90.
6%
8%
10%
1.0396
1.0534
1.0674
TABLE 2-47 Potassium Carbonate (K2CO3)*
TABLE 2-45 Phosphoric Acid (H3PO4)*
°C
°C
35%
50%
75%
100%
1.221
1.216
1.211
1.341
1.335
1.329
1.579
1.572
1.870
1.862
%
0°C
10°C
20°C
40°C
60°C
80°C
100°C
1
2
4
8
12
16
20
24
28
30
35
40
45
50
1.0094
1.0189
1.0381
1.0768
1.1160
1.1562
1.1977
1.2405
1.2846
1.3071
1.3646
1.4244
1.4867
1.5517
1.0089
1.0182
1.0369
1.0746
1.1131
1.1530
1.1941
1.2366
1.2804
1.3028
1.3600
1.4195
1.4815
1.5462
1.0072
1.0163
1.0345
1.0715
1.1096
1.1490
1.1898
1.2320
1.2756
1.2979
1.3548
1.4141
1.4759
1.5404
1.0010
1.0098
1.0276
1.0640
1.1013
1.1399
1.1801
1.2219
1.2652
1.2873
1.3440
1.4029
1.4644
1.5285
0.9919
1.0005
1.0180
1.0538
1.0906
1.1290
1.1690
1.2106
1.2538
1.2759
1.3324
1.3913
1.4528
1.5169
0.9803
0.9889
1.0063
1.0418
1.0786
1.1170
1.1570
1.1986
1.2418
1.2640
1.3206
1.3795
1.4408
1.5048
0.9670
0.9756
0.9951
1.0291
1.0663
1.1049
1.1451
1.1869
1.2301
1.2522
1.3089
1.3678
1.4290
1.4928
∗International Critical Tables, vol. 3, p. 90.
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
TABLE 2-48 Potassium Chloride (KCl)*
2-103
TABLE 2-52 Sodium Carbonate (na2CO3)*
%
0°C
20°C
25°C
40°C
60°C
80°C
100°C
%
0°C
10°C
20°C
30°C
40°C
60°C
80°C
100°C
1.0
2.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
1.00661
1.01335
1.02690
1.05431
1.08222
1.11068
1.13973
1.00462
1.01103
1.02391
1.05003
1.07679
1.10434
1.13280
1.16226
1.00342
1.00977
1.02255
1.04847
1.07506
1.10245
1.13072
1.15995
0.99847
1.00471
1.01727
1.04278
1.06897
1.09600
1.12399
1.15299
1.18304
0.9894
0.9956
1.0080
1.0333
1.0592
1.0861
1.1138
1.1425
1.1723
0.9780
0.9842
0.9966
1.0219
1.0478
1.0746
1.1024
1.1311
1.1609
0.9646
0.9708
0.9634
1.0888
1.0350
1.0619
1.0897
1.1185
1.1483
1
2
4
8
12
14
16
18
20
24
28
30
1.0109
1.0219
1.0439
1.0878
1.1319
1.1543
1.0103
1.0210
1.0423
1.0850
1.1284
1.1506
1.0086
1.0190
1.0398
1.0816
1.1244
1.1463
1.0058
1.0159
1.0363
1.0775
1.1200
1.1417
1.1636
1.1859
1.2086
1.2552
1.3031
1.3274
1.0022
1.0122
1.0323
1.0732
1.1150
1.1365
0.9929
1.0027
1.0223
1.0625
1.1039
1.1251
0.9814
0.9910
1.0105
1.0503
1.0914
1.1125
0.9683
0.9782
0.9980
1.0380
1.0787
1.0996
%
110°C
120°C
130°C
3.79
7.45
13.62
0.9733
0.9978
1.0388
0.9663
0.9899
1.0313
0.9583
0.9827
1.0238
140°C
0.9502
0.9745
1.0159
∗International Critical Tables, vol. 3, pp. 82–83.
∗International Critical Tables, vol. 3, p. 87.
TABLE 2-53 Sodium Chloride (naCl)*
TABLE 2-49 Potassium
Hydroxide (KOH)*
%
d
15
4
1.0
1.0083
2.0
1.0175
4.0
1.0359
6.0
1.0544
8.0
1.0730
10.0
1.0918
15.0
1.1396
20.0
1.1884
25.0
1.2387
30.0
1.2905
35.0
1.3440
40.0
1.3991
45.0
1.4558
50.0
1.5143
51.7
1.5355 (sat’d. soln.)
∗International Critical Tables, vol. 3,
p. 86.
0°C
10°C
20°C
1
2
4
8
12
16
20
24
1.00654
1.01326
1.02677
1.05419
1.08221
1.00615
1.01262
1.02566
1.05226
1.07963
1.00447
1.01075
1.02344
1.04940
1.07620
1.10392
1.13261
1.16233
10°C
25°C
40°C
60°C
80°C
100°C
1.00747
1.01509
1.03038
1.06121
1.09244
1.12419
1.15663
1.18999
1.20709
1.00707
1.01442
1.02920
1.05907
1.08946
1.12056
1.15254
1.18557
1.20254
1.00409
1.01112
1.02530
1.05412
1.08365
1.11401
1.14533
1.17776
1.19443
0.99908
1.00593
1.01977
1.04798
1.07699
1.10688
1.13774
1.16971
1.18614
0.9900
0.9967
1.0103
1.0381
1.0667
1.0962
1.1268
1.1584
1.1747
0.9785
0.9852
0.9988
1.0264
1.0549
1.0842
1.1146
1.1463
1.1626
0.9651
0.9719
0.9855
1.0134
1.0420
1.0713
1.1017
1.1331
1.1492
TABLE 2-54 Sodium Hydroxide (naOH)*
40°C
60°C
80°C
100°C
0.99825
1.00430
1.01652
1.04152
1.06740
1.09432
1.12240
1.15175
0.9890
0.9949
1.0068
1.0313
1.0567
1.0831
1.1106
1.1391
0.9776
0.9834
0.9951
1.0192
1.0442
1.0703
1.0974
1.1256
0.9641
0.9699
0.9816
1.0056
1.0304
1.0562
1.0831
1.1110
∗International Critical Tables, vol. 3, p. 89.
0°C
1
2
4
8
12
16
20
24
26
∗International Critical Tables, vol. 3, p. 79.
TABLE 2-50 Potassium nitrate (KnO3)*
%
%
%
0°C
15°C
20°C
40°C
60°C
80°C
100°C
1
2
4
8
12
16
20
24
28
32
36
40
44
48
50
1.0124
1.0244
1.0482
1.0943
1.1399
1.1849
1.2296
1.2741
1.3182
1.3614
1.4030
1.4435
1.4825
1.5210
1.5400
1.01065
1.02198
1.04441
1.08887
1.13327
1.17761
1.22183
1.26582
1.3094
1.3520
1.3933
1.4334
1.4720
1.5102
1.5290
1.0095
1.0207
1.0428
1.0869
1.1309
1.1751
1.2191
1.2629
1.3064
1.3490
1.3900
1.4300
1.4685
1.5065
1.5253
1.0033
1.0139
1.0352
1.0780
1.1210
1.1645
1.2079
1.2512
1.2942
1.3362
1.3768
1.4164
1.4545
1.4922
1.5109
0.9941
1.0045
1.0254
1.0676
1.1101
1.1531
1.1960
1.2388
1.2814
1.3232
1.3634
1.4027
1.4405
1.4781
1.4967
0.9824
0.9929
1.0139
1.0560
1.0983
1.1408
1.1833
1.2259
1.2682
1.3097
1.3498
1.3889
1.4266
1.4641
1.4827
0.9693
0.9797
1.0009
1.0432
1.0855
1.1277
1.1700
1.2124
1.2546
1.2960
1.3360
1.3750
1.4127
1.4503
1.4690
∗International Critical Tables, vol. 3, p. 79.
TABLE 2-51 Sodium Acetate
(naC2H3O2)*
20
%
d4
1
2
4
8
12
18
20
26
28
1.0033
1.0084
1.0186
1.0392
1.0598
1.0807
1.1021
1.1351
1.1462
∗International Critical Tables, vol. 3,
p. 83.
2-104
PHYSICAL AnD CHEMICAL DATA
TABLE 2-55 Sulfuric Acid (H2SO4)*
%
0°C
10°C
15°C
20°C
25°C
30°C
40°C
50°C
60°C
80°C
100°C
1
2
3
4
1.0074
1.0147
1.0219
1.0291
1.0068
1.0138
1.0206
1.0275
1.0060
1.0129
1.0197
1.0264
1.0051
1.0118
1.0184
1.0250
1.0038
1.0104
1.0169
1.0234
1.0022
1.0087
1.0152
1.0216
0.9986
1.0050
1.0113
1.0176
0.9944
1.0006
1.0067
1.0129
0.9895
0.9956
1.0017
1.0078
0.9779
0.9839
0.9900
0.9961
0.9645
0.9705
0.9766
0.9827
5
6
7
8
9
1.0364
1.0437
1.0511
1.0585
1.0660
1.0344
1.0414
1.0485
1.0556
1.0628
1.0332
1.0400
1.0469
1.0539
1.0610
1.0317
1.0385
1.0453
1.0522
1.0591
1.0300
1.0367
1.0434
1.0502
1.0571
1.0281
1.0347
1.0414
1.0481
1.0549
1.0240
1.0305
1.0371
1.0437
1.0503
1.0192
1.0256
1.0321
1.0386
1.0451
1.0140
1.0203
1.0266
1.0330
1.0395
1.0022
1.0084
1.0146
1.0209
1.0273
0.9888
0.9950
1.0013
1.0076
1.0140
10
11
12
13
14
1.0735
1.0810
1.0886
1.0962
1.1039
1.0700
1.0773
1.0846
1.0920
1.0994
1.0681
1.0753
1.0825
1.0898
1.0971
1.0661
1.0731
1.0802
1.0874
1.0947
1.0640
1.0710
1.0780
1.0851
1.0922
1.0617
1.0686
1.0756
1.0826
1.0897
1.0570
1.0637
1.0705
1.0774
1.0844
1.0517
1.0584
1.0651
1.0719
1.0788
1.0460
1.0526
1.0593
1.0661
1.0729
1.0338
1.0403
1.0469
1.0536
1.0603
1.0204
1.0269
1.0335
1.0402
1.0469
15
16
17
18
19
1.1116
1.1194
1.1272
1.1351
1.1430
1.1069
1.1145
1.1221
1.1298
1.1375
1.1045
1.1120
1.1195
1.1271
1.1347
1.1020
1.1094
1.1168
1.1243
1.1318
1.0994
1.1067
1.1141
1.1215
1.1290
1.0968
1.1040
1.1113
1.1187
1.1261
1.0914
1.0985
1.1057
1.1129
1.1202
1.0857
1.0927
1.0998
1.1070
1.1142
1.0798
1.0868
1.0938
1.1009
1.1081
1.0671
1.0740
1.0809
1.0879
1.0950
1.0537
1.0605
1.0674
1.0744
1.0814
20
21
22
23
24
1.1510
1.1590
1.1670
1.1751
1.1832
1.1453
1.1531
1.1609
1.1688
1.1768
1.1424
1.1501
1.1579
1.1657
1.1736
1.1394
1.1471
1.1548
1.1626
1.1704
1.1365
1.1441
1.1517
1.1594
1.1672
1.1335
1.1410
1.1486
1.1563
1.1640
1.1275
1.1349
1.1424
1.1500
1.1576
1.1215
1.1288
1.1362
1.1437
1.1512
1.1153
1.1226
1.1299
1.1373
1.1448
1.1021
1.1093
1.1166
1.1239
1.1313
1.0885
1.0957
1.1029
1.1102
1.1176
25
26
27
28
29
1.1914
1.1996
1.2078
1.2160
1.2243
1.1848
1.1929
1.2010
1.2091
1.2173
1.1816
1.1896
1.1976
1.2057
1.2138
1.1783
1.1862
1.1942
1.2023
1.2104
1.1750
1.1829
1.1909
1.1989
1.2069
1.1718
1.1796
1.1875
1.1955
1.2035
1.1653
1.1730
1.1808
1.1887
1.1966
1.1588
1.1665
1.1742
1.1820
1.1898
1.1523
1.1599
1.1676
1.1753
1.1831
1.1388
1.1463
1.1539
1.1616
1.1693
1.1250
1.1325
1.1400
1.1476
1.1553
30
31
32
33
34
1.2326
1.2409
1.2493
1.2577
1.2661
1.2255
1.2338
1.2421
1.2504
1.2588
1.2220
1.2302
1.2385
1.2468
1.2552
1.2185
1.2267
1.2349
1.2432
1.2515
1.2150
1.2232
1.2314
1.2396
1.2479
1.2115
1.2196
1.2278
1.2360
1.2443
1.2046
1.2126
1.2207
1.2289
1.2371
1.1977
1.2057
1.2137
1.2218
1.2300
1.1909
1.1988
1.2068
1.2148
1.2229
1.1771
1.1849
1.1928
1.2008
1.2088
1.1630
1.1708
1.1787
1.1866
1.1946
35
36
37
38
39
1.2746
1.2831
1.2917
1.3004
1.3091
1.2672
1.2757
1.2843
1.2929
1.3016
1.2636
1.2720
1.2805
1.2891
1.2978
1.2599
1.2684
1.2769
1.2855
1.2941
1.2563
1.2647
1.2732
1.2818
1.2904
1.2526
1.2610
1.2695
1.2780
1.2866
1.2454
1.2538
1.2622
1.2707
1.2793
1.2383
1.2466
1.2550
1.2635
1.2720
1.2311
1.2394
1.2477
1.2561
1.2646
1.2169
1.2251
1.2334
1.2418
1.2503
1.2027
1.2109
1.2192
1.2276
1.2361
40
41
42
43
44
1.3179
1.3268
1.3357
1.3447
1.3538
1.3103
1.3191
1.3280
1.3370
1.3461
1.3065
1.3153
1.3242
1.3332
1.3423
1.3028
1.3116
1.3205
1.3294
1.3384
1.2991
1.3079
1.3167
1.3256
1.3346
1.2953
1.3041
1.3129
1.3218
1.3308
1.2880
1.2967
1.3055
1.3144
1.3234
1.2806
1.2893
1.2981
1.3070
1.3160
1.2732
1.2819
1.2907
1.2996
1.3086
1.2589
1.2675
1.2762
1.2850
1.2939
1.2446
1.2532
1.2619
1.2707
1.2796
45
46
47
48
49
1.3630
1.3724
1.3819
1.3915
1.4012
1.3553
1.3646
1.3740
1.3835
1.3931
1.3515
1.3608
1.3702
1.3797
1.3893
1.3476
1.3569
1.3663
1.3758
1.3854
1.3437
1.3530
1.3624
1.3719
1.3814
1.3399
1.3492
1.3586
1.3680
1.3775
1.3325
1.3417
1.3510
1.3604
1.3699
1.3251
1.3343
1.3435
1.3528
1.3623
1.3177
1.3269
1.3362
1.3455
1.3549
1.3029
1.3120
1.3212
1.3305
1.3399
1.2886
1.2976
1.3067
1.3159
1.3253
50
51
52
53
54
1.4110
1.4209
1.4310
1.4412
1.4515
1.4029
1.4128
1.4228
1.4329
1.4431
1.3990
1.4088
1.4188
1.4289
1.4391
1.3951
1.4049
1.4148
1.4248
1.4350
1.3911
1.4009
1.4109
1.4209
1.4310
1.3872
1.3970
1.4069
1.4169
1.4270
1.3795
1.3893
1.3991
1.4091
1.4191
1.3719
1.3816
1.3914
1.4013
1.4113
1.3644
1.3740
1.3837
1.3936
1.4036
1.3494
1.3590
1.3687
1.3785
1.3884
1.3348
1.3444
1.3540
1.3637
1.3735
55
56
57
58
59
1.4619
1.4724
1.4830
1.4937
1.5045
1.4535
1.4640
1.4746
1.4852
1.4959
1.4494
1.4598
1.4703
1.4809
1.4916
1.4453
1.4557
1.4662
1.4768
1.4875
1.4412
1.4516
1.4621
1.4726
1.4832
1.4372
1.4475
1.4580
1.4685
1.4791
1.4293
1.4396
1.4500
1.4604
1.4709
1.4214
1.4317
1.4420
1.4524
1.4629
1.4137
1.4239
1.4342
1.4446
1.4551
1.3984
1.4085
1.4187
1.4290
1.4393
1.3834
1.3934
1.4035
1.4137
1.4240
60
61
62
63
64
1.5154
1.5264
1.5375
1.5487
1.5600
1.5067
1.5177
1.5287
1.5398
1.5510
1.5024
1.5133
1.5243
1.5354
1.5465
1.4983
1.5091
1.5200
1.5310
1.5421
1.4940
1.5048
1.5157
1.5267
1.5378
1.4898
1.5006
1.5115
1.5225
1.5335
1.4816
1.4923
1.5031
1.5140
1.5250
1.4735
1.4842
1.4950
1.5058
1.5167
1.4656
1.4762
1.4869
1.4977
1.5086
1.4497
1.4602
1.4708
1.4815
1.4923
1.4344
1.4449
1.4554
1.4660
1.4766
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
2-105
TABLE 2-55 Sulfuric Acid (H2SO4) (Continued )
%
0°C
10°C
15°C
20°C
25°C
30°C
40°C
50°C
60°C
80°C
100°C
65
66
67
68
69
1.5714
1.5828
1.5943
1.6059
1.6176
1.5623
1.5736
1.5850
1.5965
1.6081
1.5578
1.5691
1.5805
1.5920
1.6035
1.5533
1.5646
1.5760
1.5874
1.5989
1.5490
1.5602
1.5715
1.5829
1.5944
1.5446
1.5558
1.5671
1.5785
1.5899
1.5361
1.5472
1.5584
1.5697
1.5811
1.5277
1.5388
1.5499
1.5611
1.5724
1.5195
1.5305
1.5416
1.5528
1.5640
1.5031
1.5140
1.5249
1.5359
1.5470
1.4873
1.4981
1.5089
1.5198
1.5307
70
71
72
73
74
1.6293
1.6411
1.6529
1.6648
1.6768
1.6198
1.6315
1.6433
1.6551
1.6670
1.6151
1.6268
1.6385
1.6503
1.6622
1.6105
1.6221
1.6338
1.6456
1.6574
1.6059
1.6175
1.6292
1.6409
1.6526
1.6014
1.6130
1.6246
1.6363
1.6480
1.5925
1.6040
1.6155
1.6271
1.6387
1.5838
1.5952
1.6067
1.6182
1.6297
1.5753
1.5867
1.5981
1.6095
1.6209
1.5582
1.5694
1.5806
1.5919
1.6031
1.5417
1.5527
1.5637
1.5747
1.5857
75
76
77
78
79
1.6888
1.7008
1.7128
1.7247
1.7365
1.6789
1.6908
1.7026
1.7144
1.7261
1.6740
1.6858
1.6976
1.7093
1.7209
1.6692
1.6810
1.6927
1.7043
1.7158
1.6644
1.6761
1.6878
1.6994
1.7108
1.6597
1.6713
1.6829
1.6944
1.7058
1.6503
1.6619
1.6734
1.6847
1.6959
1.6412
1.6526
1.6640
1.6751
1.6862
1.6322
1.6435
1.6547
1.6657
1.6766
1.6142
1.6252
1.6361
1.6469
1.6575
1.5966
1.6074
1.6181
1.6286
1.6390
80
81
82
83
84
1.7482
1.7597
1.7709
1.7815
1.7916
1.7376
1.7489
1.7599
1.7704
1.7804
1.7323
1.7435
1.7544
1.7649
1.7748
1.7272
1.7383
1.7491
1.7594
1.7693
1.7221
1.7331
1.7437
1.7540
1.7639
1.7170
1.7279
1.7385
1.7487
1.7585
1.7069
1.7177
1.7281
1.7382
1.7479
1.6971
1.7077
1.7180
1.7279
1.7375
1.6873
1.6978
1.7080
1.7179
1.7274
1.6680
1.6782
1.6882
1.6979
1.7072
1.6493
1.6594
1.6692
1.6787
1.6878
85
86
87
88
89
1.8009
1.8095
1.8173
1.8243
1.8306
1.7897
1.7983
1.8061
1.8132
1.8195
1.7841
1.7927
1.8006
1.8077
1.8141
1.7786
1.7872
1.7951
1.8022
1.8087
1.7732
1.7818
1.7897
1.7968
1.8033
1.7678
1.7763
1.7842
1.7914
1.7979
1.7571
1.7657
1.7736
1.7809
1.7874
1.7466
1.7552
1.7632
1.7705
1.7770
1.7364
1.7449
1.7529
1.7602
1.7669
1.7161
1.7245
1.7324
1.7397
1.7464
1.6966
1.7050
1.7129
1.7202
1.7269
90
91
92
93
94
1.8361
1.8410
1.8453
1.8490
1.8520
1.8252
1.8302
1.8346
1.8384
1.8415
1.8198
1.8248
1.8293
1.8331
1.8363
1.8144
1.8195
1.8240
1.8279
1.8312
1.8091
1.8142
1.8188
1.8227
1.8260
1.8038
1.8090
1.8136
1.8176
1.8210
1.7933
1.7986
1.8033
1.8074
1.8109
1.7829
1.7883
1.7932
1.7974
1.8011
1.7729
1.7783
1.7832
1.7876
1.7914
1.7525
1.7581
1.7633
1.7681
1.7331
1.7388
1.7439
1.7485
95
96
97
98
99
100
1.8544
1.8560
1.8569
1.8567
1.8551
1.8517
1.8439
1.8457
1.8466
1.8463
1.8445
1.8409
1.8388
1.8406
1.8414
1.8411
1.8393
1.8357
1.8337
1.8355
1.8364
1.8361
1.8342
1.8305
1.8286
1.8305
1.8314
1.8310
1.8292
1.8255
1.8236
1.8255
1.8264
1.8261
1.8242
1.8205
1.8137
1.8157
1.8166
1.8163
1.8145
1.8107
1.8040
1.8060
1.8071
1.8068
1.8050
1.8013
1.7944
1.7965
1.7977
1.7976
1.7958
1.7922
%
d 45.96
%
d 413.00
d 418.00
0.005
.01
.02
.03
.04
1.000 0140
1.000 0576
1.000 1434
1.000 2276
1.000 3104
0.05
0.1
0.2
0.3
0.4
0.999 810
1.000 185
1.000 912
1.001 623
1.002 326
0.999 028
0.999 400
1.000 119
1.000 820
1.001 512
.05
.06
.07
.08
.09
1.000 3920
1.000 4726
1.000 5523
1.000 6313
1.000 7098
0.5
0.6
0.8
1.0
1.2
1.003 023
1.003 716
1.005 090
1.006 452
1.007 807
1.002 197
1.002 877
1.004 227
1.005 570
1.006 909
.10
.15
.20
.25
.30
1.000 7880
1.001 1732
1.001 5514
1.001 9254
1.002 2961
1.4
1.6
1.8
2.0
2.2
1.009 159
1.010 510
1.011 860
1.013 209
1.014 557
1.008 247
1.009 583
1.010 918
1.012 252
1.013 586
.35
.40
.45
.50
1.002 6639
1.003 0292
1.003 3923
1.003 7534
2.4
1.015 904
1.014 919
∗International Critical Tables, vol. 3, pp. 56–57.
2-106
PHYSICAL AnD CHEMICAL DATA
DEnSITIES OF AQUEOUS ORGAnIC SOLUTIOnS
TABLE 2-56 Acetic Acid (CH3COOH)
%
0°C
10°C
15°C
20°C
25°C
30°C
40°C
%
0°C
10°C
15°C
20°C
25°C
30°C
40°C
0
1
2
3
4
0.9999
1.0016
1.0033
1.0051
1.0070
0.9997
1.0013
1.0029
1.0044
1.0060
0.9991
1.0006
1.0021
1.0036
1.0051
0.9982
0.9996
1.0012
1.0025
1.0040
0.9971
0.9987
1.0000
1.0013
1.0027
0.9957
0.9971
0.9984
0.9997
1.0011
0.9922
0.9934
0.9946
0.9958
0.9970
50
51
52
53
54
1.0729
1.0738
1.0748
1.0757
1.0765
1.0654
1.0663
1.0671
1.0679
1.0687
1.0613
1.0622
1.0629
1.0637
1.0644
1.0575
1.0582
1.0590
1.0597
1.0604
1.0534
1.0542
1.0549
1.0555
1.0562
1.0492
1.0499
1.0506
1.0512
1.0518
1.0408
1.0414
1.0421
1.0427
1.0432
5
6
7
8
9
1.0088
1.0106
1.0124
1.0142
1.0159
1.0076
1.0092
1.0108
1.0124
1.0140
1.0066
1.0081
1.0096
1.0111
1.0126
1.0055
1.0069
1.0083
1.0097
1.0111
1.0041
1.0055
1.0068
1.0081
1.0094
1.0024
1.0037
1.0050
1.0063
1.0076
0.9982
0.9994
1.0006
1.0018
1.0030
55
56
57
58
59
1.0774
1.0782
1.0790
1.0798
1.0805
1.0694
1.0701
1.0708
1.0715
1.0722
1.0651
1.0658
1.0665
1.0672
1.0678
1.0611
1.0618
1.0624
1.0631
1.0637
1.0568
1.0574
1.0580
1.0586
1.0592
1.0525
1.0531
1.0536
1.0542
1.0547
1.0438
1.0443
1.0448
1.0453
1.0458
10
11
12
13
14
1.0177
1.0194
1.0211
1.0228
1.0245
1.0156
1.0171
1.0187
1.0202
1.0217
1.0141
1.0155
1.0170
1.0184
1.0199
1.0125
1.0139
1.0154
1.0168
1.0182
1.0107
1.0120
1.0133
1.0146
1.0159
1.0089
1.0102
1.0115
1.0127
1.0139
1.0042
1.0054
1.0065
1.0077
1.0088
60
61
62
63
64
1.0813
1.0820
1.0826
1.0833
1.0838
1.0728
1.0734
1.0740
1.0746
1.0752
1.0684
1.0690
1.0696
1.0701
1.0706
1.0642
1.0648
1.0653
1.0658
1.0662
1.0597
1.0602
1.0607
1.0612
1.0616
1.0552
1.0557
1.0562
1.0566
1.0571
1.0462
1.0466
1.0470
1.0473
1.0477
15
16
17
18
19
1.0262
1.0278
1.0295
1.0311
1.0327
1.0232
1.0247
1.0262
1.0276
1.0291
1.0213
1.0227
1.0241
1.0255
1.0269
1.0195
1.0209
1.0223
1.0236
1.0250
1.0172
1.0185
1.0198
1.0210
1.0223
1.0151
1.0163
1.0175
1.0187
1.0198
1.0099
1.0110
1.0121
1.0132
1.0142
65
66
67
68
69
1.0844
1.0850
1.0856
1.0860
1.0865
1.0757
1.0762
1.0767
1.0771
1.0775
1.0711
1.0716
1.0720
1.0725
1.0729
1.0666
1.0671
1.0675
1.0678
1.0682
1.0621
1.0624
1.0628
1.0631
1.0634
1.0575
1.0578
1.0582
1.0585
1.0588
1.0480
1.0483
1.0486
1.0489
1.0491
20
21
22
23
24
1.0343
1.0358
1.0374
1.0389
1.0404
1.0305
1.0319
1.0333
1.0347
1.0361
1.0283
1.0297
1.0310
1.0323
1.0336
1.0263
1.0276
1.0288
1.0301
1.0313
1.0235
1.0248
1.0260
1.0272
1.0283
1.0210
1.0222
1.0233
1.0244
1.0256
1.0153
1.0164
1.0174
1.0185
1.0195
70
71
72
73
74
1.0869
1.0874
1.0877
1.0881
1.0884
1.0779
1.0783
1.0786
1.0789
1.0792
1.0732
1.0736
1.0738
1.0741
1.0743
1.0685
1.0687
1.0690
1.0693
1.0694
1.0637
1.0640
1.0642
1.0644
1.0645
1.0590
1.0592
1.0594
1.0595
1.0596
1.0493
1.0495
1.0496
1.0497
1.0498
25
26
27
28
29
1.0419
1.0434
1.0449
1.0463
1.0477
1.0375
1.0388
1.0401
1.0414
1.0427
1.0349
1.0362
1.0374
1.0386
1.0399
1.0326
1.0338
1.0349
1.0361
1.0372
1.0295
1.0307
1.0318
1.0329
1.0340
1.0267
1.0278
1.0289
1.0299
1.0310
1.0205
1.0215
1.0225
1.0234
1.0244
75
76
77
78
79
1.0887
1.0889
1.0891
1.0893
1.0894
1.0794
1.0796
1.0797
1.0798
1.0798
1.0745
1.0746
1.0747
1.0747
1.0747
1.0696
1.0698
1.0699
1.0700
1.0700
1.0647
1.0648
1.0648
1.0648
1.0648
1.0597
1.0598
1.0598
1.0598
1.0597
1.0499
1.0499
1.0499
1.0498
1.0497
30
31
32
33
34
1.0491
1.0505
1.0519
1.0532
1.0545
1.0440
1.0453
1.0465
1.0477
1.0489
1.0411
1.0423
1.0435
1.0446
1.0458
1.0384
1.0395
1.0406
1.0417
1.0428
1.0350
1.0361
1.0372
1.0382
1.0392
1.0320
1.0330
1.0341
1.0351
1.0361
1.0253
1.0262
1.0272
1.0281
1.0289
80
81
82
83
84
1.0895
1.0895
1.0895
1.0895
1.0893
1.0798
1.0797
1.0796
1.0795
1.0793
1.0747
1.0745
1.0743
1.0741
1.0738
1.0700
1.0699
1.0698
1.0696
1.0693
1.0647
1.0646
1.0644
1.0642
1.0638
1.0596
1.0594
1.0592
1.0589
1.0585
1.0495
1.0493
1.0490
1.0487
1.0483
35
36
37
38
39
1.0558
1.0571
1.0584
1.0596
1.0608
1.0501
1.0513
1.0524
1.0535
1.0546
1.0469
1.0480
1.0491
1.0501
1.0512
1.0438
1.0449
1.0459
1.0469
1.0479
1.0402
1.0412
1.0422
1.0432
1.0441
1.0371
1.0380
1.0390
1.0399
1.0408
1.0298
1.0306
1.0314
1.0322
1.0330
85
86
87
88
89
1.0891
1.0887
1.0883
1.0877
1.0872
1.0790
1.0787
1.0783
1.0778
1.0773
1.0735
1.0731
1.0726
1.0721
1.0715
1.0689
1.0685
1.0680
1.0675
1.0668
1.0635
1.0630
1.0626
1.0620
1.0613
1.0582
1.0576
1.0571
1.0564
1.0557
1.0479
1.0473
1.0467
1.0460
1.0453
40
41
42
43
44
1.0621
1.0633
1.0644
1.0656
1.0667
1.0557
1.0568
1.0578
1.0588
1.0598
1.0522
1.0532
1.0542
1.0551
1.0561
1.0488
1.0498
1.0507
1.0516
1.0525
1.0450
1.0460
1.0469
1.0477
1.0486
1.0416
1.0425
1.0433
1.0441
1.0449
1.0338
1.0346
1.0353
1.0361
1.0368
90
91
92
93
94
1.0865
1.0857
1.0848
1.0838
1.0826
1.0766
1.0758
1.0749
1.0739
1.0727
1.0708
1.0700
1.0690
1.0680
1.0667
1.0661
1.0652
1.0643
1.0632
1.0619
1.0605
1.0597
1.0587
1.0577
1.0564
1.0549
1.0541
1.0530
1.0518
1.0506
1.0445
1.0436
1.0426
1.0414
1.0401
45
46
47
48
49
1.0679
1.0689
1.0699
1.0709
1.0720
1.0608
1.0618
1.0627
1.0636
1.0645
1.0570
1.0579
1.0588
1.0597
1.0605
1.0534
1.0542
1.0551
1.0559
1.0567
1.0495
1.0503
1.0511
1.0518
1.0526
1.0456
1.0464
1.0471
1.0479
1.0486
1.0375
1.0382
1.0389
1.0395
1.0402
95
96
97
98
99
1.0813
1.0798
1.0780
1.0759
1.0730
1.0714
1.0652
1.0632
1.0611
1.0590
1.0567
1.0605
1.0588
1.0570
1.0549
1.0524
1.0551
1.0535
1.0516
1.0495
1.0468
1.0491
1.0473
1.0454
1.0431
1.0407
1.0386
1.0368
1.0348
1.0325
1.0299
100
1.0697
1.0545
1.0498
1.0440
1.0380
1.0271
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
2-107
TABLE 2-57 Methyl Alcohol (CH3OH)*
%
0°C
10°C
20°C
15°C
%
0°C
10°C
20°C
15°C
%
0°C
10°C
20°C
15°C
0
1
2
3
4
0.9999
0.9981
0.9963
0.9946
0.9930
0.9997
0.9980
0.9962
0.9945
0.9929
15.56°C
0.9990
0.9973
0.9955
0.9938
0.9921
0.9982
0.9965
0.9948
0.9931
0.9914
0.99913
0.99727
0.99543
0.99370
0.99198
35
36
37
38
39
0.9534
0.9520
0.9505
0.9490
0.9475
0.9484
0.9469
0.9453
0.9437
0.9420
15.56°C
0.9456
0.9440
0.9422
0.9405
0.9387
0.9433
0.9416
0.9398
0.9381
0.9363
0.94570
0.94404
0.94237
0.94067
0.93894
70
71
72
73
74
0.8869
0.8847
0.8824
0.8801
0.8778
0.8794
0.8770
0.8747
0.8724
0.8699
15.56°C
0.8748
0.8726
0.8702
0.8678
0.8653
0.8715
0.8690
0.8665
0.8641
0.8616
0.87507
0.87271
0.87033
0.86792
0.86546
5
6
7
8
9
0.9914
0.9899
0.9884
0.9870
0.9856
0.9912
0.9896
0.9881
0.9865
0.9849
0.9904
0.9889
0.9872
0.9857
0.9841
0.9896
0.9880
0.9863
0.9847
0.9831
0.99029
0.98864
0.98701
0.98547
0.98394
40
41
42
43
44
0.9459
0.9443
0.9427
0.9411
0.9395
0.9403
0.9387
0.9370
0.9352
0.9334
0.9369
0.9351
0.9333
0.9315
0.9297
0.9345
0.9327
0.9309
0.9290
0.9272
0.93720
0.93543
0.93365
0.93185
0.93001
75
76
77
78
79
0.8754
0.8729
0.8705
0.8680
0.8657
0.8676
0.8651
0.8626
0.8602
0.8577
0.8629
0.8604
0.8579
0.8554
0.8529
0.8592
0.8567
0.8542
0.8518
0.8494
0.86300
0.86051
0.85801
0.85551
0.85300
10
11
12
13
14
0.9842
0.9829
0.9816
0.9804
0.9792
0.9834
0.9820
0.9805
0.9791
0.9778
0.9826
0.9811
0.9796
0.9781
0.9766
0.9815
0.9799
0.9784
0.9768
0.9754
0.98241
0.98093
0.97945
0.97802
0.97660
45
46
47
48
49
0.9377
0.9360
0.9342
0.9324
0.9306
0.9316
0.9298
0.9279
0.9260
0.9240
0.9279
0.9261
0.9242
0.9223
0.9204
0.9252
0.9234
0.9214
0.9196
0.9176
0.92815
0.92627
0.92436
0.92242
0.92048
80
81
82
83
84
0.8634
0.8610
0.8585
0.8560
0.8535
0.8551
0.8527
0.8501
0.8475
0.8449
0.8503
0.8478
0.8452
0.8426
0.8400
0.8469
0.8446
0.8420
0.8394
0.8366
0.85048
0.84794
0.84536
0.84274
0.84009
15
16
17
18
19
0.9780
0.9769
0.9758
0.9747
0.9736
0.9764
0.9751
0.9739
0.9726
0.9713
0.9752
0.9738
0.9723
0.9709
0.9695
0.9740
0.9725
0.9710
0.9696
0.9681
0.97518
0.97377
0.97237
0.97096
0.96955
50
51
52
53
54
0.9287
0.9269
0.9250
0.9230
0.9211
0.9221
0.9202
0.9182
0.9162
0.9142
0.9185
0.9166
0.9146
0.9126
0.9106
0.9156
0.9135
0.9114
0.9094
0.9073
0.91852
0.91653
0.91451
0.91248
0.91044
85
86
87
88
89
0.8510
0.8483
0.8456
0.8428
0.8400
0.8422
0.8394
0.8367
0.8340
0.8314
0.8374
0.8347
0.8320
0.8294
0.8267
0.8340
0.8314
0.8286
0.8258
0.8230
0.83742
0.83475
0.83207
0.82937
0.82667
20
21
22
23
24
0.9725
0.9714
0.9702
0.9690
0.9678
0.9700
0.9687
0.9673
0.9660
0.9646
0.9680
0.9666
0.9652
0.9638
0.9624
0.9666
0.9651
0.9636
0.9622
0.9607
0.96814
0.96673
0.96533
0.96392
0.96251
55
56
57
58
59
0.9191
0.9172
0.9151
0.9131
0.9111
0.9122
0.9101
0.9080
0.9060
0.9039
0.9086
0.9065
0.9045
0.9024
0.9002
0.9052
0.9032
0.9010
0.8988
0.8968
0.90839
0.90631
0.90421
0.90210
0.89996
90
91
92
93
94
0.8374
0.8347
0.8320
0.8293
0.8266
0.8287
0.8261
0.8234
0.8208
0.8180
0.8239
0.8212
0.8185
0.8157
0.8129
0.8202
0.8174
0.8146
0.8118
0.8090
0.82396
0.82124
0.81849
0.81568
0.81285
25
26
27
28
29
0.9666
0.9654
0.9642
0.9629
0.9616
0.9632
0.9618
0.9604
0.9590
0.9575
0.9609
0.9595
0.9580
0.9565
0.9550
0.9592
0.9576
0.9562
0.9546
0.9531
0.96108
0.95963
0.95817
0.95668
0.95518
60
61
62
63
64
0.9090
0.9068
0.9046
0.9024
0.9002
0.9018
0.8998
0.8977
0.8955
0.8933
0.8980
0.8958
0.8936
0.8913
0.8890
0.8946
0.8924
0.8902
0.8879
0.8856
0.89781
0.89563
0.89341
0.89117
0.88890
95
96
97
98
99
0.8240
0.8212
0.8186
0.8158
0.8130
0.8152
0.8124
0.8096
0.8068
0.8040
0.8101
0.8073
0.8045
0.8016
0.7987
0.8062
0.8034
0.8005
0.7976
0.7948
0.80999
0.80713
0.80428
0.80143
0.79859
30
31
32
33
34
0.9604
0.9590
0.9576
0.9563
0.9549
0.9560
0.9546
0.9531
0.9516
0.9500
0.9535
0.9521
0.9505
0.9489
0.9473
0.9515
0.9499
0.9483
0.9466
0.9450
0.95366
0.95213
0.95056
0.94896
0.94734
65
66
67
68
69
0.8980
0.8958
0.8935
0.8913
0.8891
0.8911
0.8888
0.8865
0.8842
0.8818
0.8867
0.8844
0.8820
0.8797
0.8771
0.8834
0.8811
0.8787
0.8763
0.8738
0.88662
0.88433
0.88203
0.87971
0.87739
100
0.8102
0.8009
0.7959
0.7917
0.79577
∗It should be noted that the values for 100 percent do not agree with some data available elsewhere, e.g., American Institute of Physics Handbook, McGraw-Hill,
New York, 1957. Also, see Atack, Handbook of Chemical Data, Reinhold, New York, 1957. Also, see Tables 2-120 and 2-135 for pure methanol and water densities.
2-108
PHYSICAL AnD CHEMICAL DATA
TABLE 2-58 Ethyl Alcohol (C2H5OH)*
%
10°C
15°C
20°C
25°C
30°C
35°C
40°C
%
10°C
15°C
20°C
25°C
30°C
35°C
40°C
0
1
2
3
4
0.99973
785
602
426
258
0.99913
725
542
365
195
0.99823
636
453
275
103
0.99708
520
336
157
0.98984
0.99568
379
194
014
0.98839
0.99406
217
031
0.98849
672
0.99225
034
0.98846
663
485
50
51
52
53
54
0.92126
0.91943
723
502
279
0.91776
555
333
110
0.90885
0.91384
160
0.90936
711
485
0.90985
760
534
307
079
0.90580
353
125
0.89896
667
0.90168
0.89940
710
479
248
0.89750
519
288
056
0.88823
5
6
7
8
9
098
0.98946
801
660
524
032
0.98877
729
584
442
0.98938
780
627
478
331
817
656
500
346
193
670
507
347
189
031
501
335
172
009
0.97846
311
142
0.97975
808
641
55
56
57
58
59
055
0.90831
607
381
154
659
433
207
0.89980
752
258
031
0.89803
574
344
0.89850
621
392
162
0.88931
437
206
0.88975
744
512
016
0.88784
552
319
085
589
356
122
0.87888
653
10
11
12
13
14
393
267
145
026
0.97911
304
171
041
0.97914
790
187
047
0.97910
775
643
043
0.97897
753
611
472
0.97875
723
573
424
278
685
527
371
216
063
475
312
150
0.96989
829
60
61
62
63
64
0.89927
698
468
237
006
523
293
062
0.88830
597
113
0.88882
650
417
183
699
466
233
0.87998
763
278
044
0.87809
574
337
0.87851
615
379
142
0.86905
417
180
0.86943
705
466
15
16
17
18
19
800
692
583
473
363
669
552
433
313
191
514
387
259
129
0.96997
334
199
062
0.96923
782
133
0.96990
844
697
547
0.96911
760
607
452
294
670
512
352
189
023
65
66
67
68
69
0.88774
541
308
074
0.87839
364
130
0.87895
660
424
0.87948
713
477
241
004
527
291
054
0.86817
579
100
0.86863
625
387
148
667
429
190
0.85950
710
227
0.85987
747
507
266
20
21
22
23
24
252
139
024
0.96907
787
068
0.96944
818
689
558
864
729
592
453
312
639
495
348
199
048
395
242
087
0.95929
769
134
0.95973
809
643
476
0.95856
687
516
343
168
70
71
72
73
74
602
365
127
0.86888
648
187
0.86949
710
470
229
0.86766
527
287
047
0.85806
340
100
0.85859
618
376
0.85908
667
426
184
0.84941
470
228
0.84986
743
500
025
0.84783
540
297
053
25
26
27
28
29
665
539
406
268
125
424
287
144
0.95996
844
168
020
0.95867
710
548
0.95895
738
576
410
241
607
442
272
098
0.94922
306
133
0.94955
774
590
0.94991
810
625
438
248
75
76
77
78
79
408
168
0.85927
685
442
0.85988
747
505
262
018
564
322
079
0.84835
590
134
0.84891
647
403
158
698
455
211
0.83966
720
257
013
0.83768
523
277
0.83809
564
319
074
0.82827
30
31
32
33
34
0.95977
823
665
502
334
686
524
357
186
011
382
212
038
0.94860
679
067
0.94890
709
525
337
741
557
370
180
0.93986
403
214
021
0.93825
626
055
0.93860
662
461
257
80
81
82
83
84
197
0.84950
702
453
203
0.84772
525
277
028
0.83777
344
096
0.83848
599
348
0.83911
664
415
164
0.82913
473
224
0.82974
724
473
029
0.82780
530
279
027
578
329
079
0.81828
576
35
36
37
38
39
162
0.94986
805
620
431
0.94832
650
464
273
079
494
306
114
0.93919
720
146
0.93952
756
556
353
790
591
390
186
0.92979
425
221
016
0.92808
597
051
0.92843
634
422
208
85
86
87
88
89
0.83951
697
441
181
0.82919
525
271
014
0.82754
492
095
0.82840
583
323
062
660
405
148
0.81888
626
220
0.81965
708
448
186
0.81774
519
262
003
0.80742
322
067
0.80811
552
291
40
41
42
43
44
238
042
0.93842
639
433
0.93882
682
478
271
062
518
314
107
0.92897
685
148
0.92940
729
516
301
770
558
344
128
0.91910
385
170
0.91952
733
513
0.91992
774
554
332
108
90
91
92
93
94
654
386
114
0.81839
561
227
0.81959
688
413
134
0.81797
529
257
0.80983
705
362
094
0.80823
549
272
0.80922
655
384
111
0.79835
478
211
0.79941
669
393
028
0.79761
491
220
0.78947
45
46
47
48
49
226
017
0.92806
593
379
0.92852
640
426
211
0.91995
472
257
041
0.91823
604
085
0.91868
649
429
208
692
472
250
028
0.90805
291
069
0.90845
621
396
0.90884
660
434
207
0.89979
95
96
97
98
99
278
0.80991
698
399
094
0.80852
566
274
0.79975
670
424
138
0.79846
547
243
0.79991
706
415
117
0.78814
555
271
0.78981
684
382
114
0.78831
542
247
0.77946
670
388
100
0.77806
507
100
0.79784
360
0.78934
506
075
641
203
∗For data from −78° to 78°C, see p. 2-142, Table 2N-5, American Institute of Physics Handbook, McGraw-Hill, New York, 1957. See Tables 2-115 and 2-135 for pure
ethanol and pure water densities.
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
2-109
TABLE 2-59 n-Propyl Alcohol (C3H7OH)
%
0°C
15°C
30°C
%
0°C
15°C
30°C
%
0°C
15°C
30°C
%
0°C
15°C
30°C
%
0°C
15°C
30°C
0
1
2
3
4
0.9999
0.9982
0.9967
0.9952
0.9939
0.9991
0.9974
0.9960
0.9944
0.9929
0.9957
0.9940
0.9924
0.9908
0.9893
20
21
22
23
24
0.9789
0.9776
0.9763
0.9748
0.9733
0.9723
0.9705
0.9688
0.9670
0.9651
0.9643
0.9622
0.9602
0.9583
0.9563
40
41
42
43
44
0.9430
0.9411
0.9391
0.9371
0.9352
0.9331
0.9310
0.9290
0.9269
0.9248
0.9226
0.9205
0.9184
0.9164
0.9143
60
61
62
63
64
0.9033
0.9013
0.8994
0.8974
0.8954
0.8922
0.8902
0.8882
0.8861
0.8841
0.8807
0.8786
0.8766
0.8745
0.8724
80
81
82
83
84
0.8634
0.8614
0.8594
0.8574
0.8554
0.8516
0.8496
0.8475
0.8454
0.8434
0.8394
0.8373
0.8352
0.8332
0.8311
5
6
7
8
9
0.9926
0.9914
0.9904
0.9894
0.9883
0.9915
0.9902
0.9890
0.9877
0.9864
0.9877
0.9862
0.9848
0.9834
0.9819
25
26
27
28
29
0.9717
0.9700
0.9682
0.9664
0.9646
0.9633
0.9614
0.9594
0.9576
0.9556
0.9543
0.9522
0.9501
0.9481
0.9460
45
46
47
48
49
0.9332
0.9311
0.9291
0.9272
0.9252
0.9228
0.9207
0.9186
0.9165
0.9145
0.9122
0.9100
0.9079
0.9057
0.9036
65
66
67
68
69
0.8934
0.8913
0.8894
0.8874
0.8854
0.8820
0.8800
0.8779
0.8759
0.8739
0.8703
0.8682
0.8662
0.8641
0.8620
85
86
87
88
89
0.8534
0.8513
0.8492
0.8471
0.8450
0.8413
0.8393
0.8372
0.8351
0.8330
0.8290
0.8269
0.8248
0.8227
0.8206
10
11
12
13
14
0.9874
0.9865
0.9857
0.9849
0.9841
0.9852
0.9840
0.9828
0.9817
0.9806
0.9804
0.9790
0.9775
0.9760
0.9746
30
31
32
33
34
0.9627
0.9608
0.9589
0.9570
0.9550
0.9535
0.9516
0.9495
0.9474
0.9454
0.9439
0.9418
0.9396
0.9375
0.9354
50
51
52
53
54
0.9232
0.9213
0.9192
0.9173
0.9153
0.9124
0.9104
0.9084
0.9064
0.9044
0.9015
0.8994
0.8973
0.8952
0.8931
70
71
72
73
74
0.8835
0.8815
0.8795
0.8776
0.8756
0.8719
0.8700
0.8680
0.8659
0.8639
0.8600
0.8580
0.8559
0.8539
0.8518
90
91
92
93
94
0.8429
0.8408
0.8387
0.8364
0.8342
0.8308
0.8287
0.8266
0.8244
0.8221
0.8185
0.8164
0.8142
0.8120
0.8098
15
16
17
18
19
0.9833
0.9825
0.9817
0.9808
0.9800
0.9793
0.9780
0.9768
0.9752
0.9739
0.9730
0.9714
0.9698
0.9680
0.9661
35
36
37
38
39
0.9530
0.9511
0.9491
0.9471
0.9450
0.9434
0.9413
0.9392
0.9372
0.9351
0.9333
0.9312
0.9289
0.9269
0.9247
55
56
57
58
59
0.9132
0.9112
0.9093
0.9073
0.9053
0.9023
0.9003
0.8983
0.8963
0.8942
0.8911
0.8890
0.8869
0.8849
0.8828
75
76
77
78
79
0.8736
0.8716
0.8695
0.8675
0.8655
0.8618
0.8598
0.8577
0.8556
0.8536
0.8497
0.8477
0.8456
0.8435
0.8414
95
96
97
98
99
0.8320
0.8296
0.8272
0.8248
0.8222
0.8199
0.8176
0.8153
0.8128
0.8104
0.8077
0.8054
0.8031
0.8008
0.7984
100
0.8194
0.8077
0.7958
TABLE 2-60 Isopropyl Alcohol (C3H7OH)
%
0°C
15°C∗
15°C∗
20°C
30°C
%
0°C
15°C∗
20°C
30°C
%
0°C
15°C∗
15°C∗
20°C
30°C
0
1
2
3
4
0.9999
0.9980
0.9962
0.9946
0.9930
0.9991
0.9973
0.9956
0.9938
0.9922
0.99913
0.9972
0.9954
0.9936
0.9920
0.9982
0.9962
0.9944
0.9926
0.9909
0.9957
0.9939
0.9921
0.9904
0.9887
35
36
37
38
39
0.9557
0.9536
0.9514
0.9493
0.9472
15°C∗
0.9446
0.9424
0.9401
0.9379
0.9356
0.9419
0.9399
0.9377
0.9355
0.9333
0.9338
0.9315
0.9292
0.9269
0.9246
70
71
72
73
74
0.8761
0.8738
0.8714
0.8691
0.8668
0.8639
0.8615
0.8592
0.8568
0.8545
0.86346
0.8611
0.8588
0.8564
0.8541
0.8584
0.8560
0.8537
0.8513
0.8489
0.8511
0.8487
0.8464
0.8440
0.8416
5
6
7
8
9
0.9916
0.9902
0.9890
0.9878
0.9866
0.9906
0.9892
0.9878
0.9864
0.9851
0.9904
0.9890
0.9875
0.9862
0.9849
0.9893
0.9877
0.9862
0.9847
0.9833
0.9871
0.9855
0.9839
0.9824
0.9809
40
41
42
43
44
0.9450
0.9428
0.9406
0.9384
0.9361
0.93333
0.9311
0.9288
0.9266
0.9243
0.9310
0.9287
0.9264
0.9239
0.9215
0.9224
0.9201
0.9177
0.9154
0.9130
75
76
77
78
79
0.8644
0.8621
0.8598
0.8575
0.8551
0.8521
0.8497
0.8474
0.8450
0.8426
0.8517
0.8493
0.8470
0.8446
0.8422
0.8464
0.8439
0.8415
0.8391
0.8366
0.8392
0.8368
0.8344
0.8321
0.8297
10
11
12
13
14
0.9856
0.9846
0.9838
0.9829
0.9821
0.9838
0.9826
0.9813
0.9802
0.9790
0.98362
0.9824
0.9812
0.9800
0.9788
0.9820
0.9808
0.9797
0.9876
0.9776
0.9794
0.9778
0.9764
0.9750
0.9735
45
46
47
48
49
0.9338
0.9315
0.9292
0.9270
0.9247
0.9220
0.9197
0.9174
0.9150
0.9127
0.9191
0.9165
0.9141
0.9117
0.9093
0.9106
0.9082
0.9059
0.9036
0.9013
80
81
82
83
84
0.8528
0.8503
0.8479
0.8456
0.8432
0.8403
0.8379
0.8355
0.8331
0.8307
0.83979
0.8374
0.8350
0.8326
0.8302
0.8342
0.8317
0.8292
0.8268
0.8243
0.8273
0.8248
0.8224
0.8200
0.8175
15
16
17
18
19
0.9814
0.9806
0.9799
0.9792
0.9784
0.9779
0.9768
0.9756
0.9745
0.9730
0.9777
0.9765
0.9753
0.9741
0.9728
0.9765
0.9754
0.9743
0.9731
0.9717
0.9720
0.9705
0.9690
0.9675
0.9658
50
51
52
53
54
0.9224
0.9201
0.9178
0.9155
0.9132
0.91043
0.9081
0.9058
0.9035
0.9011
0.9069
0.9044
0.9020
0.8996
0.8971
0.8990
0.8966
0.8943
0.8919
0.8895
85
86
87
88
89
0.8408
0.8384
0.8360
0.8336
0.8311
0.8282
0.8259
0.8234
0.8209
0.8184
0.8278
0.8254
0.8229
0.8205
0.8180
0.8219
0.8194
0.8169
0.8145
0.8120
0.8151
0.8127
0.8201
0.8078
0.8053
20
21
22
23
24
0.9777
0.9768
0.9759
0.9749
0.9739
0.9719
0.9704
0.9690
0.9675
0.9660
0.97158
0.9703
0.9689
0.9674
0.9659
0.9703
0.9688
0.9669
0.9651
0.9634
0.9642
0.9624
0.9606
0.9587
0.9569
55
56
57
58
59
0.9109
0.9086
0.9063
0.9040
0.9017
0.8988
0.8964
0.8940
0.8917
0.8893
0.8946
0.8921
0.8896
0.8874
0.8850
0.8871
0.8847
0.8823
0.8800
0.8777
90
91
92
93
94
0.8287
0.8262
0.8237
0.8212
0.8186
0.8161
0.8136
0.8110
0.8085
0.8060
0.81553
0.8130
0.8104
0.8079
0.8052
0.8096
0.8072
0.8047
0.8023
0.7998
0.8029
0.8004
0.7979
0.7954
0.7929
25
26
27
28
29
0.9727
0.9714
0.9699
0.9684
0.9669
0.9643
0.9626
0.9608
0.9590
0.9570
0.9642
0.9624
0.9605
0.9586
0.9568
0.9615
0.9597
0.9577
0.9558
0.9540
0.9549
0.9529
0.9509
0.9488
0.9467
60
61
62
63
64
0.8994
0.8970
0.8947
0.8924
0.8901
0.8829
0.8805
0.8781
0.88690
0.8845
0.8821
0.8798
0.8775
0.8825
0.8800
0.8776
0.8751
0.8727
0.8752
0.8728
0.8704
0.8680
0.8656
95
96
97
98
99
0.8160
0.8133
0.8106
0.8078
0.8048
0.8034
0.8008
0.7981
0.7954
0.7926
0.8026
0.7999
0.7972
0.7945
0.7918
0.7973
0.7949
0.7925
0.7901
0.7877
0.7904
0.7878
0.7852
0.7826
0.7799
30
31
32
33
34
0.9652
0.9634
0.9615
0.9596
0.9577
0.9551
0.95493
0.9530
0.9510
0.9489
0.9468
0.9520
0.9500
0.9481
0.9460
0.9440
0.9446
0.9426
0.9405
0.9383
0.9361
65
66
67
68
69
0.8878
0.8854
0.8831
0.8807
0.8784
0.8757
0.8733
0.8710
0.8686
0.8662
0.8752
0.8728
0.8705
0.8682
0.8658
0.8702
0.8679
0.8656
0.8632
0.8609
0.8631
0.8607
0.8583
0.8559
0.8535
100
0.8016
0.7896
0.78913
0.7854
0.7770
∗Two different observers; see International Critical Tables, vol. 3, p. 120.
2-110
PHYSICAL AnD CHEMICAL DATA
TABLE 2-61 Glycerol*
Density
Density
Density
Glycerol,
%
15°C
15.5°C
20°C
25°C
30°C
Glycerol,
%
15°C
15.5°C
20°C
25°C
30°C
Glycerol,
%
15°C
15.5°C
20°C
25°C
30°C
100
99
98
97
96
1.26415
1.26160
1.25900
1.25645
1.25385
1.26381
1.26125
1.25865
1.25610
1.25350
1.26108
1.25850
1.25590
1.25335
1.25080
1.15802
1.25545
1.25290
1.25030
1.24770
1.25495
1.25235
1.24975
1.24710
1.24450
65
64
63
62
61
1.17030
1.16755
1.16480
1.16200
1.15925
1.17000
1.16725
1.16445
1.16170
1.15895
1.16750
1.16475
1.16205
1.15930
1.15655
1.16475
1.16200
1.15925
1.15655
1.15380
1.16195
1.15925
1.15650
1.15375
1.15100
30
29
28
27
26
1.07455
1.07195
1.06935
1.06670
1.06410
1.07435
1.07175
1.06915
1.06655
1.06390
1.07270
1.07010
1.06755
1.06495
1.06240
1.07070
1.06815
1.06560
1.06305
1.06055
1.06855
1.06605
1.06355
1.06105
1.05855
95
94
93
92
91
1.25130
1.24865
1.24600
1.24340
1.24075
1.25095
1.24830
1.24565
1.24305
1.24040
1.24825
1.24560
1.24300
1.24035
1.23770
1.24515
1.24250
1.23985
1.23725
1.23460
1.24190
1.23930
1.23670
1.23410
1.23150
60
59
58
57
56
1.15650
1.15370
1.15095
1.14815
1.14535
1.15615
1.15340
1.15065
1.14785
1.14510
1.15380
1.15105
1.14830
1.14555
1.14280
1.15105
1.14835
1.14560
1.14285
1.14015
1.14830
1.14555
1.14285
1.14010
1.13740
25
24
23
22
21
1.06150
1.05885
1.05625
1.05365
1.05100
1.06130
1.05870
1.05610
1.05350
1.05090
1.05980
1.05720
1.05465
1.05205
1.04950
1.05800
1.05545
1.05290
1.05035
1.04780
1.05605
1.05350
1.05100
1.04850
1.04600
90
89
88
87
86
1.23810
1.23545
1.23280
1.23015
1.22750
1.23775
1.23510
1.23245
1.22980
1.22710
1.23510
1.23245
1.22975
1.22710
1.22445
1.23200
1.22935
1.22665
1.22400
1.22135
1.22890
1.22625
1.22360
1.22095
1.21830
55
54
53
52
51
1.14260
1.13980
1.13705
1.13425
1.13150
1.14230
1.13955
1.13680
1.13400
1.13125
1.14005
1.13730
1.13455
1.13180
1.12905
1.13740
1.13465
1.13195
1.12920
1.12650
1.13470
1.13195
1.12925
1.12650
1.12380
20
19
18
17
16
1.04840
1.04590
1.04335
1.04085
1.03835
1.04825
1.04575
1.04325
1.04075
1.03825
1.04690
1.04440
1.04195
1.03945
1.03695
1.04525
1.04280
1.04035
1.03790
1.03545
1.04350
1.04105
1.03860
1.03615
1.03370
85
84
83
82
81
1.22485
1.22220
1.21955
1.21690
1.21425
1.22445
1.22180
1.21915
1.21650
1.21385
1.22180
1.21915
1.21650
1.21380
1.21115
1.21870
1.21605
1.21340
1.21075
1.20810
1.21565
1.21300
1.21035
1.20770
1.20505
50
49
48
47
46
1.12870
1.12600
1.12325
1.12055
1.11780
1.12845
1.12575
1.12305
1.12030
1.11760
1.12630
1.12360
1.12090
1.11820
1.11550
1.12375
1.12110
1.11840
1.11575
1.11310
1.12110
1.11845
1.11580
1.11320
1.11055
15
14
13
12
11
1.03580
1.03330
1.03080
1.02830
1.02575
1.03570
1.03320
1.03070
1.02820
1.02565
1.03450
1.03200
1.02955
1.02705
1.02455
1.03300
1.03055
1.02805
1.02560
1.02315
1.03130
1.02885
1.02640
1.02395
1.02150
80
79
78
77
76
1.21160
1.20885
1.20610
1.20335
1.20060
1.21120
1.20845
1.20570
1.20300
1.20025
1.20850
1.20575
1.20305
1.20030
1.19760
1.20545
1.20275
1.20005
1.19735
1.19465
1.20240
1.19970
1.19705
1.19435
1.19170
45
44
43
42
41
1.11510
1.11235
1.10960
1.10690
1.10415
1.11490
1.11215
1.10945
1.10670
1.10400
1.11280
1.11010
1.10740
1.10470
1.10200
1.11040
1.10775
1.10510
1.10240
1.09975
1.10795
1.10530
1.10265
1.10005
1.09740
10
9
8
7
6
1.02325
1.02085
1.01840
1.01600
1.01360
1.02315
1.02075
1.01835
1.01590
1.01350
1.02210
1.01970
1.01730
1.01495
1.01255
1.02070
1.01835
1.01600
1.01360
1.01125
1.01905
1.01670
1.01440
1.01205
1.00970
75
74
73
72
71
1.19785
1.19510
1.19235
1.18965
1.18690
1.19750
1.19480
1.19205
1.18930
1.18655
1.19485
1.19215
1.18940
1.18670
1.18395
1.19195
1.18925
1.18650
1.18380
1.18110
1.18900
1.18635
1.18365
1.18100
1.17830
40
39
38
37
36
1.10145
1.09875
1.09605
1.09340
1.09070
1.10130
1.09860
1.09590
1.09320
1.09050
1.09930
1.09665
1.09400
1.09135
1.08865
1.09710
1.09445
1.09180
1.08915
1.08655
1.09475
1.09215
1.08955
1.08690
1.08430
5
4
3
2
1
1.01120
1.00875
1.00635
1.00395
1.00155
1.01110
1.00870
1.00630
1.00385
1.00145
1.01015
1.00780
1.00540
1.00300
1.00060
1.00890
1.00655
1.00415
1.00180
0.99945
1.00735
1.00505
1.00270
1.00035
0.99800
70
69
68
67
66
1.18415
1.18135
1.17860
1.17585
1.17305
1.18385
1.18105
1.17830
1.17555
1.17275
1.18125
1.17850
1.17575
1.17300
1.17025
1.17840
1.17565
1.17295
1.17020
1.16745
1.17565
1.17290
1.17020
1.16745
1.16470
35
34
33
32
31
1.08800
1.08530
1.08265
1.07995
1.07725
1.08780
1.08515
1.08245
1.07975
1.07705
1.08600
1.08335
1.08070
1.07800
1.07535
1.08390
1.08125
1.07860
1.07600
1.07335
1.08165
1.07905
1.07645
1.07380
1.07120
0
0.99913 0.99905 0.99823 0.99708 0.99568
∗Bosart and Snoddy, Ind. Eng. Chem., 20, (1928): 1378.
TABLE 2-62 Hydrazine (n2H4)*
%
d 415
%
d 415
1
2
4
8
12
16
20
24
28
1.0002
1.0013
1.0034
1.0077
1.0121
1.0164
1.0207
1.0248
1.0286
30
40
50
60
70
80
90
100
1.0305
1.038
1.044
1.047
1.046
1.040
1.030
1.011
∗International Critical Tables, vol. 3, p. 55.
DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM
2-111
TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds*
d, dw, and ds are the density of the solution, pure water, and pure liquid solute, respectively, all in g/mL. ps is the wt % solute. 0.03255 means 2.55 × 10−4.
Section A
Name
Acetaldehyde
Acetamide
Formula
C2H4O
C2H5NO
Acetone
C3H6O
Acetonitrile
Allyl alcohol
Benzenepentacarboxylic acid
Butyl alcohol (n-)
C2H3N
C3H6O
C11H6O10
C4H10O
Butyric acid (n-)
C4H8O2
Chloral hydrate
C2H3Cl3O2
Chloroacetic acid
C2H3ClO2
Citric acid (hydrate)
C6H3O7 + H2O
Dichloroacetic acid
C2H2Cl2O2
Diethylamine hydrochloride
Ethylamine hydrochloride
C4H12ClN
C2H8ClN
Ethylene glycol
C2H6O2
Ethyl ether
C4H10O
tartrate
Formaldehyde
Formamide
C8H14O6
CH2O
CH3NO
Furfural
C5H4O2
Isoamyl alcohol
C5H12O
Isobutyl alcohol
C4H10O
Isobutyric acid
C4H8O2
Isovaleric acid
Lactic acid
Maleic acid
C5H10O2
C3H6O
C4H4O4
Malic acid
C4H6O5
Malonic acid
Methyl acetate
C3H4O4
C3H6O2
glucoside (α-)
Nicotine
Nitrophenol (p-)
Oxalic acid
C7H14O6
C10H14N2
C6H5NO3
C2H2O4
Phenol
C6H6O
Phenylglycolic acid
Picoline (α-)
(β-)
C8H8O3
C6H7N
C6H7N
Propionic acid
C3H6O2
Pyridine
Resorcinol
Succinic acid
C5H5N
C6H6O2
C4H6O4
Tartaric acid (d, l, or dl)
C4H6O6
∗From International Critical Tables, vol. 3, pp. 111–114.
d = d w + Aps + Bp s2 + Cps3
t, °C
Range, ps
A
B
18
15
0
4
15
20
25
15
0
25
20
18
25
0
15
30
20
25
18
20
25
21
21
0
15
20
25
15
15
25
20
25
20
15
20
15
18
25
25
25
25
20
25
20
20
0
30
20
15
0
15
17.5
20
25
15
80
25
25
25
18
25
25
18
25
15
17.5
20
30
40
50
60
0–30
0–6
0–100
0–100
0–100
0–100
0–100
0–16
0–89
0–0.6
0–7.9
0–10
0–62
0–70
0–78
0–90
0–32
0–86
0–50
0–30
0–97
0–36
0–65
0–100
0–6
0–5
0–4.5
0–95
0–40
22–96
0–8
0–8
0–2.5
0–8
0–8
0–9
0–9
0–12
0–5
0–9
0–40
0–40
0–40
0–40
0–20
26–51
26–51
0–60
0–1.5
0–4
0–4
0–9
0–4
0–4
0–5
0–65
0–11
0–70
0–60
0–10
0–40
0–60
0–52
0–5.5
0–15
0–50
0–50
0–50
0–50
0–50
0–50
+0.03255
+0.03639
−0.03856
−0.027648
−0.021009
−0.021233
−0.021171
−0.021175
−0.033729
+0.025615
−0.021651
+0.03414
+0.035135
+0.024489
+0.024455
+0.024401
+0.023648
+0.023602
+0.023824
+0.024427
+0.024427
+0.0334
+0.021193
+0.021483
+0.02133
−0.02221
−0.02221
+0.022367
+0.022518
+0.021217
+0.021827
+0.021664
+0.02155
−0.02146
−0.02169
+0.0352
+0.0345
+0.0337
+0.03253
+0.02231
+0.0234
+0.023933
+0.023736
+0.02389
+0.0340
+0.023336
+0.023151
+0.03642
+0.023216
+0.025898
+0.02494
+0.02494
+0.025264
+0.025108
+0.02111
+0.03462
+0.02207
−0.04386
−0.04683
+0.0395
+0.039245
+0.03229
+0.02201
+0.02304
+0.024482
+0.024455
+0.024432
+0.024335
+0.024265
+0.024205
+0.024155
−0.0516
+0.04171
−0.05449
−0.041193
−0.059682
−0.053529
−0.05904
−0.042024
−0.041232
−0.02117
+0.04285
+0.04131
−0.04166
+0.042802
+0.042198
+0.041887
+0.05302
+0.05552
+0.041141
+0.05537
+0.05537
+0.0676
−0.05307
+0.052992
−0.05108
+0.0448
+0.0435
+0.05358
−0.05658
+0.053199
+0.05366
+0.0421
+0.043
+0.056
+0.0438
−0.04282
+0.05186
+0.0575
+0.05957
+0.04175
+0.041066
−0.0574
+0.05996
+0.05975
+0.05454
−0.0455
−0.033185
−0.058
−0.058
−0.031996
−0.031607
−0.04283
−0.0686
+0.0423
−0.051405
−0.0513
−0.04172
−0.0599
−0.05204
+0.05519
C
−0.07588
+0.08272
−0.08624
−0.075327
−0.0856
+0.072984
+0.0611
−0.071291
+0.074366
+0.076549
+0.0722
+0.0717
+0.077534
+0.077534
−0.0747
−0.075248
−0.076005
+0.06542
−0.072529
+0.01544
+0.08978
−0.07687
+0.0441
+0.04254
+0.04208
−0.074167
+0.07361
−0.0828
−0.0819
+0.04185
+0.04185
+0.041837
+0.04185
+0.04185
+0.04185
+0.04185
(Continued )
2-112
PHYSICAL AnD CHEMICAL DATA
TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds (Continued )
d = d w + Aps + Bp s2 + Cps3 (Cont.)
Section A
Name
t, °C
Formula
Tetraethyl ammonium chloride
Thiourea
C8H20ClN
CH4N2S
Trichloroacetic acid
C2HCl3O2
Triethylamine hydrochloride
C6H16ClN
Trimethyl carbinol
C4H10O
Urea
CH4N2O
Urethane
Valeric acid (n-)
C3H7NO2
C5H10O2
Section B
Name
Formula
Butyl alcohol (n-)
Butyric acid (n-)
Ethyl ether
C4H10O
C4H8O2
C4H10O
Isobutyl alcohol
C4H10O
Isobutyric acid
Nicotine
Picoline (α-)
(β-)
Pyridine
Trimethyl carbinol
C4H8O2
C10H14N2
C6H7N
C6H7N
C5H5N
C4H10O
ds
0.8097
0.9534
0.7077
0.8170
0.8055
0.9425
1.0093
0.9404
0.9515
0.9776
0.7856
Section C
Name
Formula
Allyl alcohol
Butyl alcohol (n-)
C3H6O
C4H10O
Chloral hydrate
C2H3Cl3O2
Ethyl tartrate
C7H14O6
Furfural
C5H4O2
Pyridine
C5H5N
Range, ps
21
15
12.5
20
25
21
20
25
14.8
18
20
25
20
25
ps
76.60
80.95
2.00
10.00
5.00
10.00
25.00
4.62
5.69
6.56
9.34
21.20
29.50
40.40
0–63
0–7
0–61
10–30
0–94
0–54
0–100
0–100
0–12
0–51
0–35
0–10
0–56
0–3
A
B
C
+0.031884
+0.022995
+0.02499
+0.025053
+0.025051
+0.046
−0.02117
−0.021286
+0.023213
+0.022718
+0.022702
+0.022728
+0.021278
+0.0334
+0.056
+0.05374
+0.04153
+0.041387
+0.056119
+0.05558
−0.041908
−0.04176
−0.044802
+0.051552
+0.053712
−0.041817
−0.05245
−0.0427
+0.07122
+0.061038
−0.0869
+0.07957
+0.07887
+0.051216
+0.072573
−0.072285
+0.051379
−0.073437
d = ds + Apw + Bp w2 + Cp w3
t, °C
Range, pw
A
B
20
25
25
0
15
26
20
25
25
25
20
0–20
0–38
0–1.1
0–14
0–16
0–80
0–40
0–30
0–40
0–40
0–20
+0.022103
+0.021854
+0.0234
+0.022437
+0.02224
+0.021808
+0.02199
+0.022715
+0.021925
+0.021157
+0.022287
−0.04113
−0.042314
+0.0336
−0.04285
−0.04129
−0.042358
−0.04331
−0.04393
−0.04352
−0.05536
+0.05275
C
+0.061253
+0.07315
+0.0625
−0.062
dt = do + At + Bt2
do
Range, °C
A
B
0.9122
0.8614
1.0094
1.0476
1.0150
1.0270
1.0665
1.0125
1.0140
1.0155
1.0055
1.0115
1.0145
1.0182
0–45
0–43
7–80
7–80
15–80
15–80
15–80
22–74
22–74
22–74
11–73
14–73
12–72
9–74
−0.038
−0.037292
−0.042597
−0.047955
−0.032103
−0.032116
−0.03401
−0.03232
−0.03221
−0.03211
−0.03171
−0.03378
−0.03463
−0.03605
−0.0527
−0.0675
−0.054313
−0.054253
−0.052544
−0.062929
−0.0523
−0.05254
−0.05268
−0.05290
−0.053615
−0.05248
−0.05235
−0.05167
DEnSITIES OF MISCELLAnEOUS MATERIALS
2-113
DEnSITIES OF MISCELLAnEOUS MATERIALS
TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids*
Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material.
Substance
Metals, Alloys, Ores
Aluminum, cast-hammered
bronze
Brass, cast-rolled
Bronze, 7.9 to 14% Sn
phosphor
Sp. gr.
Aver.
density
lb/ft 3
Substance
Sp. gr.
Aver.
density
lb/ft 3
Timber, Air-dry
Apple
Ash, black
white
Birch, sweet, yellow
Cedar, white, red
0.66–0.74
0.55
0.64–0.71
0.71–0.72
0.35
44
34
42
44
22
2.55–2.80
7.7
8.4–8.7
7.4–8.9
8.88
165
481
534
509
554
Copper, cast-rolled
ore, pyrites
German silver
Gold, cast-hammered
coin (U.S.)
8.8–8.95
4.1–4.3
8.58
19.25–19.35
17.18–17.2
556
262
536
1205
1073
Cherry, wild red
Chestnut
Cypress
Elm, white
Fir, Douglas
0.43
0.48
0.45–0.48
0.56
0.48–0.55
27
30
29
35
32
Iridium
Iron, gray cast
cast, pig
wrought
spiegeleisen
21.78–22.42
7.03–7.13
7.2
7.6–7.9
7.5
1383
442
450
485
468
balsam
Hemlock
Hickory
Locust
Mahogany
0.40
0.45–0.50
0.74–0.80
0.67–0.77
0.56–0.85
25
29
48
45
44
ferro-silicon
ore, hematite
ore, limonite
ore, magnetite
slag
6.7–7.3
5.2
3.6–4.0
4.9–5.2
2.5–3.0
437
325
237
315
172
Maple, sugar
white
Oak, chestnut
live
red, black
0.68
0.53
0.74
0.87
0.64–0.71
43
33
46
54
42
Lead
ore, galena
Manganese
ore, pyrolusite
Mercury
11.34
7.3–7.6
7.42
3.7–4.6
13.6
710
465
475
259
849
8.97
8.9
21.5
10.4–10.6
7.83
7.80
7.70–7.73
7.2–7.5
6.4–7.0
19.22
555
537
1330
656
489
487
481
459
418
1200
white
Pine, Norway
Oregon
red
Southern
white
0.77
0.55
0.51
0.48
0.61–0.67
0.43
48
34
32
30
38–42
27
Poplar
Redwood, California
Spruce, white, red
Teak, African
Indian
Walnut, black
Willow
0.43
0.42
0.45
0.99
0.66–0.88
0.59
0.42–0.50
27
26
28
62
48
37
28
6.9–7.2
3.9–4.2
440
253
Various Solids
Cereals, oats, bulk
barley, bulk
corn, rye, bulk
wheat, bulk
Cork
0.51
0.62
0.73
0.77
0.22–0.26
26
39
45
48
15
Various Liquids
Alcohol, ethyl (100%)
methyl (100%)
Acid, muriatic, 40%
nitric, 91%
sulfuric, 87%
0.789
0.796
1.20
1.50
1.80
49
50
75
94
112
Cotton, flax, hemp
Fats
Flour, loose
pressed
Glass, common
1.47–1.50
0.90–0.97
0.40–0.50
0.70–0.80
2.40–2.80
93
58
28
47
162
Chloroform
Ether
Lye, soda, 66%
Oils, vegetable
mineral, lubricants
1.500
0.736
1.70
0.91–0.94
0.88–0.94
95
46
106
58
57
plate or crown
crystal
dint
Hay and straw, bales
Leather
2.45–2.72
2.90–3.00
3.2–4.7
0.32
0.86–1.02
161
184
247
20
59
0.861–0.867
1.0
0.9584
0.88–0.92
0.125
54
62.428
59.830
56
8
1.02–1.03
64
Paper
Potatoes, piled
Rubber, caoutchouc
goods
Salt, granulated, piled
0.70–1.15
0.67
0.92–0.96
1.0–2.0
0.77
58
44
59
94
48
Ashlar Masonry
Bluestone
Granite, syenite, gneiss
Limestone
Marble
Sandstone
2.3–2.6
2.4–2.7
2.1–2.8
2.4–2.8
2.0–2.6
153
159
153
162
143
Saltpeter
Starch
Sulfur
Wool
1.07
1.53
1.93–2.07
1.32
67
96
125
82
Rubble Masonry
Bluestone
Granite, syenite, gneiss
Limestone
Marble
Sandstone
2.2–2.5
2.3–2.6
2.0–2.7
2.3–2.7
1.9–2.5
147
153
147
156
137
Monel metal, rolled
Nickel
Platinum, cast-hammered
Silver, cast-hammered
Steel, cold-drawn
machine
tool
Tin, cast-hammered
cassiterite
Tungsten
Zinc, cast-rolled
blende
Turpentine
Water, 4°C max. density
100°C
ice
snow, fresh fallen
sea water
∗From Marks’ Standard Handbook for Mechanical Engineers, 10th ed., McGraw-Hill, 1996.
Sp. gr.
Aver.
density
lb/ft 3
Dry Rubble Masonry
Granite, syenite, gneiss
Limestone, marble
Sandstone, bluestone
1.9–2.3
1.9–2.1
1.8–1.9
130
125
110
Brick Masonry
Hard brick
Medium brick
Soft brick
Sand-lime brick
1.8–2.3
1.6–2.0
1.4–1.9
1.4–2.2
128
112
103
112
Concrete Masonry
Cement, stone, sand
slag, etc.
cinder, etc.
2.2–2.4
1.9–2.3
1.5–1.7
144
130
100
0.64–0.72
1.5
0.85–1.00
1.4–1.9
2.08–2.25
40–45
94
53–64
103
94–135
Portland cement
Slags, bank slag
bank screenings
machine slag
slag sand
3.1–3.2
1.1–1.2
1.5–1.9
1.5
0.8–0.9
196
67–72
98–117
96
49–55
Earth, etc., Excavated
Clay, dry
damp plastic
and gravel, dry
Earth, dry, loose
dry, packed
moist, loose
moist, packed
mud, flowing
mud, packed
Riprap, limestone
1.0
1.76
1.6
1.2
1.5
1.3
1.6
1.7
1.8
1.3–1.4
63
110
100
76
95
78
96
108
115
80–85
1.4
1.7
1.4–1.7
1.6–1.9
1.89–2.16
90
105
90–105
100–120
126
1.28
1.44
0.96
1.00
1.12
1.00
80
90
60
65
70
65
Minerals
Asbestos
Barytes
Basait
Bauxite
Bluestone
2.1–2.8
4.50
2.7–3.2
2.55
2.5–2.6
153
281
184
159
159
Borax
Chalk
Clay, marl
Dolomite
Feldspar, orthoclase
1.7–1.8
1.8–2.8
1.8–2.6
2.9
2.5–2.7
109
143
137
181
162
Gneiss
Granite
Greenstone, trap
Gypsum, alabaster
Hornblende
Limestone
Marble
Magnesite
Phosphate rock, apatite
Porphyry
2.7–2.9
2.6–2.7
2.8–3.2
2.3–2.8
3.0
2.1–2.86
2.6–2.86
3.0
3.2
2.6–2.9
175
165
187
159
187
155
170
187
200
172
Substance
Various Building Materials
Ashes, cinders
Cement, Portland, loose
Lime, gypsum, loose
Mortar, lime, set
Portland cement
Riprap, sandstone
Riprap, shale
Sand, gravel, dry, loose
gravel, dry, packed
gravel, wet
Excavations in Water
Clay
River mud
Sand or gravel
and clay
Soil
Stone riprap
(Continued )
2-114
PHYSICAL AnD CHEMICAL DATA
TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids (Continued )
Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material.
Substance
Aver.
density
lb/ft3
Substance
0.37–0.90
2.5–2.8
2.0–2.6
2.7–2.8
2.6–2.9
40
165
143
171
172
Bituminous Substances
Asphaltum
Coal, anthracite
bituminous
lignite
peat, turf, dry
1.1–1.5
1.4–1.8
1.2–1.5
1.1–1.4
0.65–0.85
81
97
84
78
47
2.6–2.8
2.6–2.7
169
165
1.5
1.7
1.5
1.3
1.5
96
107
95
82
92
charcoal, pine
charcoal, oak
coke
Graphite
Paraffin
0.28–0.44
0.47–0.57
1.0–1.4
1.64–2.7
0.87–0.91
23
33
75
135
56
Sp. gr.
Minerals (Cont.)
Pumice, natural
Quartz, flint
Sandstone
Serpentine
Shale, slate
Soapstone, talc
Syenite
Stone, Quarried, Piled
Basalt, granite, gneiss
Greenstone, hornblende
Limestone, marble, quartz
Sandstone
Shale
Aver.
density
lb/ft 3
Sp. gr.
Substance
Sp. gr.
Aver.
density
lb/ft3
Bituminous Substances (Cont.)
Petroleum
refined (kerosene)
benzine
gasoline
Pitch
Tar, bituminous
0.87
0.78–0.82
0.73–0.75
0.70–0.75
1.07–1.15
1.20
54
50
46
45
69
75
Coal and Coke, Piled
Coal, anthracite
bituminous, lignite
peat, turf
charcoal
coke
0.75–0.93
0.64–0.87
0.32–0.42
0.16–0.23
0.37–0.51
47–58
40–54
20–26
10–14
23–32
note: To convert pounds per cubic foot to kilograms per cubic meter, multiply by 16.02. °F = 9⁄5°C + 32.
TABLE 2-65 Density (kg/m3) of Selected Elements as a Function of Temperature
Element symbol
Temperature,
K∗
Al
Be†
Cr
Cu
Au
Ir
Fe
Pb
Mo
Ni
Pt
Ag
Zn†
50
100
150
200
250
2736
2732
2726
2719
2710
3650
3640
3630
3620
3610
7160
7155
7150
7145
7140
9019
9009
8992
8973
8951
19,490
19,460
19,420
19,380
19,340
22,600
22,580
22,560
22,540
22,520
7910
7900
7890
7880
7870
11,570
11,520
11,470
11,430
11,380
10,260
10,260
10,250
10,250
10,250
8960
8950
8940
8930
8910
21,570
21,550
21,530
21,500
21,470
10,620
10,600
10,575
10,550
10,520
7280
7260
7230
7200
7170
300
400
500
600
800
2701
2681
2661
2639
2591
3600
3580
3555
3530
7135
7120
7110
7080
7040
8930
8885
8837
8787
8686
19,300
19,210
19,130
19,040
18,860
22,500
22,450
22,410
22,360
22,250
7860
7830
7800
7760
7690
11,330
11,230
11,130
11,010
10,430
10,240
10,220
10,210
10,190
10,160
8900
8860
8820
8780
8690
21,450
21,380
21,330
21,270
21,140
10,490
10,430
10,360
10,300
10,160
7135
7070
7000
6935
6430
1000
1200
1400
1600
1800
2365
2305
2255
7000
6945
6890
6760
6700
8568
8458
7920
7750
7600
18,660
18,440
17,230
16,950
22,140
22,030
21,920
21,790
21,660
7650
7620
7520
7420
7320
10,190
9,940
10,120
10,080
10,040
10,000
9,950
8610
8510
8410
8320
7690
21,010
20,870
20,720
20,570
20,400
10,010
9,850
9,170
8,980
6260
21,510
7030
9,900
7450
20,220
2000
7460
note: Above the horizontal line the condensed phase is solid; below the line, it is liquid.
∗°R = 9⁄ 5 K.
†
Polycrystalline form tabulated. Similar tables for an additional 45 elements appear in the Handbook of Heat Transfer, 2d ed., McGraw-Hill, New York, 1984.
LATEnT HEATS
Unit Conversions For this subsection, the following unit conversions
are applicable: °F = 9⁄ 5°C + 32.
To convert calories per gram to British thermal units per pound, multiply
by 1.799.
To convert millimeters of mercury to pounds-force per square inch, multiply by 1.934 × 10−2.
LATEnT HEATS
2-115
TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds*
Unless stated otherwise, the values have been taken from the compilations by K. K. Kelley on “Heats of Fusion of Inorganic Compounds,” U.S. Bur. Mines Bull. 393 (1936),
and “The Free Energies of Vaporization and Vapor Pressures of Inorganic Substances,” U.S. Bur. Mines Bull. 383 (1935).
Substance
mp, °C
Heat of
fusion,a,b
cal/mol
bp at
1 atm, °C
Aluminum
Al
660.0
2,550
Al2Br6
97.5
5,420
Al2Cl6
192.5
16,960
1000
16,380
AlF3⋅3NaF
Al2I6
191.0
7,960
Al2O3
2045
(26,000)
Antimony
Sb
630.5
4,770
97
3,510
SbBr3
SbCl3
73.4
3,030
SbCl5
4
2,400
655
(27,000)
Sb4O6
Sb4S6
546
11,200
Argon
A
−189.3
290
Arsenic
As
814
(6,620)
AsBr3
31
2,810
AsCl3
−16
2,420
AsF5
−80.7
2,800
As4O6
313
8,000
Barium
Ba
704
(1,400)e
847
6,000
BaBr2
BaCl2
960
5,370
BaF2
1287
3,000
Ba(NO3)2
595
(5,980)
Ba3(PO4)2
1730
18,600
BaSO4
1350
9,700
Beryllium
Be
1280
2,500e
Bismuth
Bi
271.3
2,505
BiBr3
BiCl3
224
2,600
Bi2O3
817
6,800
Bi2S5
747
8,900
Boron
BBr3
BCl3
BF3
−128
480
B2H6
−165.5
B3H10
−119.8
B5H9
−46.9
B5H11
B10H14
99.7
7,800
B2H5Br
−104
B3N3H6
−58
Bromine
Br2
−7.2
2,580
BrF5
−61.3
1,355
Cadmium
Cd
320.9
1,460
CdBr2
568
(5,000)
CdCl2
568
5,300
CdF2
1110
(5,400)
CdI2
387
3,660
CdO
CdSO4
1000
4,790
Calcium
Ca
851
2,230
CaBr2
730
4,180
CaCO3
1282
(12,700)
CaCl2
782
6,100
CaF2
1392
4,100
Ca(NO3)2
561
5,120
CaO
2707
(12,240)
CaO⋅Al2O3⋅2SiO2
1550
29,400
CaO⋅MgO⋅2SiO2
1392
(18,200)
CaO⋅SiO2
1512
13,400
CaSO4
1297
6,700
Carbon
C (graphite)
3600
11,000e
CBr4
90
1,050
CCl4
−24.0
644
CF4
CH4
−182.5
224
C2N2
−27.8
1,938u
CNBr
52
CNCl
−5
2,240
∗See also subsection “Thermodynamic Properties.”
Heat of
vaporization,a,b
cal/mol
2057
256.4
180.2c
61,020
10,920
26,750c
385.5
3000
15,360
1440
46,670
219
172d
1425
10,360
11,570
17,820
−185.8
1,590
610c
31,000c
122
−52.8
457.2
7,570
4,980
14,300
1638
35,670
1420
461
441
18,020
17,350
91.3
12.5
−100.9
−92.4
16
58
67
f
16
50.4
7,300
5,680
4,620
3,685
6,470
7,700
8,500
11,600
6,230
7,670
58.0
40.4
7,420
7,470
765
23,870
967
29,860
796
1559c
25,400
53,820c
1487
36,580
77
−127.9
−161.4
−21.1
13
7,280
3,110
2,040
5,576u
11,010c
6,300
Substance
Carbon (Cont.)
CNF
CNI
CO
CO2
COS
COCl2
CS2
Cerium
Ce
Cesium
Cs
CsBr
CsCl
CsF
CsI
CsNO3
Chlorine
Cl2
ClF
ClF3
Cl2O
ClO2
Cl2O7
Chromium
Cr
Cr O2Cl2
Cobalt
Co
CoCl2
Copper
Cu
Cu2Br2
Cu2Cl2
CuI
Cu2(CN)2
Cu2O
CuO
Cu2S
Fluorine
F2
F2O
Gallium
Ga
Germanium
Ge
GeH4
Ge2H6
Ge3H8
GeHCl3
GeBr4
GeCl4
Ge(CH3)4
Gold
Au
Helium
He
Hydrogen
H2
HBr
HCl
HCN
HF
(HF)6
HI
H2O
H22O (= D2O)
H2O2
HNO3
H3PO2
H3PO3
H3PO4
H4P2O6
H2S
H2S2
H2SO4
H2Se
H2SeO4
H2Te
Indium
In
mp, °C
Heat of
fusion,a,b
cal/mol
−205.0
−57.5
−138.8
200
1,900
1,129 k
−112.0
1,049 l
775
2,120
28.4
500
642
715
3,600
(2,450)
407
3,250
−101.0
1,531m
1550
3,930
1490
727
3,660
7,390
1083.0
3,110
430
4,890
473
1230
1447
1127
(5,400)
(13,400)
2,820
5,500
−223
29.8
bp at
1 atm, °C
−72.8
141
−191.5
−78.4c
−50.2
8.0
5,780c
13,980c
1,444
6,030 c, r
4,423 k
5,990
690
1300
1300
1251
1280
16,320
35,990
35,690
34,330
35,930
−34.1
−101
11.3
2.0
10.9
79
959
−165
−109
−105.6
−71
26.1
−49.5
−88
(8,300)
1063.0
3,030
−271.4
−259.2
−86.9
−114.2
−13.2
−83.0
28
575
476
2,009i
1,094
−50.8
0.0
3.8
−2
−47
17.4
74
42.4
55
−85.5
−87.6
10.5
686
1,436
1,501s
2,520c
600
2,310
3,070
2,520
8,300
568t
1,805
2,360
58
−48.9
3,450
1,670
156.4
781
4,878 m
5,890
6,280
7,100
8,480
2475
117
8,250
1050
27,170
2595
1355
1490
1336
72,810
16,310
11,920
15,940
−188.2
−144.8
1,336
Heat of
vaporization,a,b
cal/mol
1,640
2,650
2071
−89.1
31.4
110.6
75g
189
84
44
2966
3,580
5,900
7,550
8,000
8,560
7,030
6,460
81,800
−268.4
22
−252.7
−66.7
−85.0
25.7
33.3
51.2
216
4,210
3,860
6,027i
7,460
5,020
100.0
101.4
158
9,729 h,q
9,945 r,q
10,270
−60.3
4,463 t
−41.3
4,880
−2.2
5,650
(Continued )
2-116
PHYSICAL AnD CHEMICAL DATA
TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued )
Substance
Iodine
I2
ICl(α)
ICl(β)
IF7
Iron
Fe
FeCl2
Fe2Cl6
Fe(CO)5
FeO
FeS
Krypton
Kr
Lead
Pb
PbBr2
PbCl2
PbF2
PbI2
PbMoO4
PbO
PbS
PbSO4
PbWO4
Lithium
Li
LiBO2
LiBr
LiCl
LiF
LiI
LiOH
Li2MoO4
LiNO3
Li2SiO3
Li4SiO4
Li2SO4
Li2WO4
Magnesium
Mg
MgBr2
MgCl2
MgF2
MgO
Mg3(PO4)2
MgSiO3
MgSO4
MgZn2
Manganese
Mn
MnCl2
MnSiO3
MnTiO3
Mercury
Hg
HgBr2
HgCl2
HgI2
HgSO4
Molybdenum
Mo
MoF6
MoO3
Neon
Ne
Nickel
Ni
NiCl2
Ni(CO)4
Ni2S
Ni3S2
Nitrogen
N2
NF3
NH3
NH4CNS
NH4NO3
N2O
NO
N2O4
N2O5
NOCl
Osmium
OsF8
OsO4 (yellow)
OsO4 (white)
Oxygen
O2
O3
mp, °C
113.0
17.2
13.9
1530
677
304
−21
1380
1195
−157
Heat of
fusion,a,b
cal/mol
bp at
1 atm, °C
Heat of
vaporization,a,b
cal/mol
3,650
2,660
2,270
183
4c
7,460c
3,560
7,800
20,590
3,250
(7,700)
5,000
2735
1026
319
105
84,600
30,210
12,040
9,000
360
e
152.9
10,390
2,310
e
327.4
488
498
824
412
1065
890
1114
1087
1123
1,224
4,290
5,650
1,860
5,970
(25,800)
2,820
4,150
9,600
(15,200)
179
845
552
614
847
440
462
705
1,100
(5,570)
2,900
3,200
(2,360)
(1,420)
2,480
4,200
1177
1249
857
742
7,210
7,430
3,040
(6,700)
650
711
712
1221
2642
1184
1524
1127
589
2,160
8,300
8,100
5,900
18,500
(11,300)
14,700
3,500
(8,270)
1107
32,520
1418
32,690
1220
650
1274
1404
3,450
7,340
(8,200)
(7,960)
2152
1190
55,150
29,630
557
3,960
4,150
4,500
(1,440)
361
319
304
354
13,980
14,080
14,080
14,260
(6,660)
2,500
(2,500)
(4800)
36
1151
(128,000)
6,000
−38.9
241
277
250
850
2622
17
745
−248.5
1744
914
954
1293
872
42,060
27,700
29,600
38,300
24,850
1472
1281
51,310
(50,000)
1372
32,250
1310
1382
1681
1171
35,420
35,960
50,970
40,770
77
−246.0
440e
1455
4,200
645
790
(2,980)
5,800
2730
987c
42.5
87,300
48,360c
7,000
−195.8
−129.0
−33.4
1,336
3,000
5,581n
−88.5
−151.7
30
32.4
−6.4
3,950
3,307
7,040
13,800c
6,140
47.4
130
6,840
9,450
−183.0
−111
1,629
2,880
−210.0
−77.7
146
169.6
−90.8
−163.6
−13
56
42
−218.9
172
1,352
(4,700)
1,460
1,563
550
5,540
n
4,060
2,340
106
Substance
Palladium
Pd
Phosphorus
P4 (yellow)
P4 (violet)
P4 (black)
PCl3
PH3
P4O6
P4O10(α)
P4O10(β)
POCl3
P 2S 3
Platinum
Pt
Potassium
K
KBO2
KBr
KCl
KCN
KCNS
K2CO3
K2Cr O4
K2Cr2O7
KF
KI
K2MoO4
KNO3
KOH
KPO3
K3PO4
K4P2O7
K2SO4
K2TiO3
K2WO4
Praseodymium
Pr
Radon
Rn
Rhenium
Re
Re2O7
Re2O8
Rubidium
Rb
RbBr
RbCl
RbF
RbI
RbNO3
Selenium
Se2
Se6
SeF6
SeO2
SeOCl2
Silicon
Si
SiCl4
Si2Cl6
Si3Cl8
(SiCl3)2O
SiF4
Si2F6
SiF3Cl
SiF2Cl2
SiH4
Si2H6
Si3H8
Si4H10
SiH3Br
SiH2Br2
SiHCl3
(SiH3)3N
(SiH3)2O
SiO2 (quartz)
SiO2 (cristobalite)
Silver
Ag
AgBr
AgCl
AgCN
AgI
AgNO3
Ag2S
Ag2SO4
Sodium
Na
NaBO2
mp, °C
1554
Heat of
fusion,a,b
cal/mol
bp at
1 atm, °C
Heat of
vaporization,a,b
cal/mol
4,120
44.2
615
−133.8
23.8
569
270o
3,360
17,080
1.1
3,110
1773.5
4,700
(4400)
(107,000)
63.5
947
742
770
623
179
897
984
398
857
682
922
338
360
817
1340
1092
1074
810
927
574
(5,700)
5,000
6,410
(3,500)
2,250
7,800
6,920
8,770
6,500
4,100
(4,000)
2,840
(2,000)
2,110
8,900
14,000
8,100
(10,600)
(4,400)
776
18,920
1383
1407
37,060
38,840
1324
34,690
1327
30,850
932
2,700
−71
(3000)
296
147
15,340
3,800
39.1
677
717
833
638
305
525
3,700
4,400
4,130
2,990
1,340
217
1,220
10
1,010
1427
−67.6
−1
9,470
1,845
−33
−18.5
−138
−144
−185
−132.5
−117
−93.5
−93.8
−70.0
−126.5
−105.6
−144
1470
1700
3,400
2,100
960.5
430
455
350
557
209
842
657
2,700
2,180
3,155
2,750
2,250
2,755
3,360
(4,300)
97.7
966
630
8,660
3,900
280
417c
453c
74.2
−87.7
174
591
358c
105.1
508
12,520
25,600c
33,100
7,280
3,489 o
10,380
20,670
8,380
−61.8
4,010
362.4
18,060
679
1352
1381
1408
1304
753
736
−45.8c
317c
168
2290
56.8
139
211.4
135.6
−94.8c
−18.9c
−70.1
−31.5
−111.6
−14.3
53.1
100
2.4
70.5
31.8
48.7
−15.4
2230
2212
18,110
37,120
36,920
39,510
35,960
25,490
20,600
6,350c
20,900
6,860
12,340
8,820
6,130c
10,400c
4,460
5,080
2,960
5,110
6,780
8,890
5,650
6,840
6,360
6,850
5,350
60,720
1564
42,520
1506
34,450
914
23,120
(Continued )
LATEnT HEATS
2-117
TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued )
Substance
Sodium (Cont.)
NaBr
NaCl
NaClO3
NaCN
NaCNS
Na2CO3
NaF
NaI
Na2MoO4
NaNO3
NaOH
½Na2O⋅½Al2O3⋅3SiO2
NaPO3
Na4P2O7
Na2S
Na2SiO3
Na2Si2O5
Na2SO4
Na2WO4
Strontium
Sr
SrBr2
SrCl2
SrF2
Sr3(PO4)2
Sulfur
S (rhombic)
S (monoclinic)
S2Cl2
SF6
SO2
SO3(α)
SO3(β)
SO3(γ)
SOBr2
SOCl2
SO2Cl2
Tellurium
Te
TeCl4
TeF6
mp, °C
Heat of
fusion,a,b
cal/mol
747
800
255
562
323
854
992
662
687
310
322
1107
988
970
920
1087
884
884
702
6,140
7,220
5,290
(4,400)
4,450
7,000
7,000
5,240
3,600
3,760
2,000
13,150
(5,000)
(13,700)
(1,200)
10,300
8,460
5,830
5,800
757
643
872
1400
1770
2,190
4,780
4,100
4,260
18,500
112.8
119.2
−75.5
17
32.4
62.2
453
1,769p
2,060
2,890
6,310
3,230
bp at
1 atm, °C
Heat of
vaporization,a,b
cal/mol
1392
1465
37,950
40,810
1500
37,280
1704
53,260
1378
1384
33,610
444.6
2,200
138
−63.5c
−5.0
44.8
8,720
5,600c
5,960p
10,190
139.5
75.4
69.2
9,920
7,600
7,760
1090
392
−38.6c
16,830
6,700c
Values in parentheses are uncertain.
For the freezing point or the normal boiling point unless otherwise stated.
c
Sublimation.
d
Decomposes at about 75°C; value obtained by extrapolation.
e
Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York (1936).
f
Decomposes before the normal boiling point is reached.
g
Decomposes at about 40°C; value obtained by extrapolation.
h
See also pp. 2-304 through 2-307 on steam table.
i
Giauque and Ruehrwein, J. Am. Chem. Soc., 61 (1939): 2626.
j
Giauque and Egan, J. Chem. Phys., 5 (1937): 45.
Substance
Thallium
Tl
TlBr
TlCl
Tl2CO3
TlI
TlNO3
Tl2S
Tl2SO4
Tin
Sn4
SnBr2
SnBr4
SnCl2
SnCl4
Sn(CH3)4
SnH4
SnI4
Titanium
TiBr4
TiCl4
TiO2
Tungsten
W
WF6
Uranium
UF6
Xenon
Xe
Zinc
Zn
ZnCl2
Zn(C2H5)2
ZnO
ZnS
Zirconium
ZrBr4
Zr Cl4
ZrI4
Zr O2
mp, °C
Heat of
fusion,a,b
cal/mol
302.5
460
427
273
440
207
449
632
1,030
5,990
4,260
4,400
3,125
2,290
3,000
5,500
1457
819
807
38,810
23,800
24,420
823
25,030
231.8
232
30
247
−33.2
1,720
(1,700)
3,000
3,050
2,190
2270
68,000
−149.8
143.5
(4,300)
38.2
−23
1825
(2,060)
2,240
(11,400)
136
3390
−0.4
(8,400)
1,800
(5900)
17.3
(176,000)
6,350
55.1c
9,990c
−108.0
3,110
907
732
118
27,430
28,710
8,960
357c
311c
431c
25,800c
25,290c
29,030c
−111.5
419.5
283
1975
1645
2715
k
b
l
m
TABLE 2-67 Heats of Fusion of Miscellaneous Materials
Material
1,595
(5,500)
4,470
(9,000)
20,800
623
113
78.3
−52.3
Heat of
vaporization,a,b
cal/mol
20,740
8,330
7,320
4,420
8,350
Kemp and Giauque, J. Am. Chem. Soc., 59 (1937): 79.
Brown and Manov, J. Am. Chem. Soc., 59 (1937): 500.
Giauque and Powell, J. Am. Chem. Soc., 61 (1939): 1970.
n
Overstreet and Giauque, J. Am. Chem. Soc., 59 (1937): 254.
o
Stephenson and Giauque, J. Chem. Phys., 5 (1937): 149.
p
Giauque and Stephenson, J. Am. Chem. Soc., 60 (1938): 1389.
q
Osborne, Stimson, and Ginnings, Bur. Standards J. Research, 23, 197 (1939): 261.
r
Miles and Menzies, J. Am. Chem. Soc., 58 (1936): 1067.
s
Long and Kemp, J. Am. Chem. Soc., 58 (1936): 1829.
t
Giauque and Blue, J. Am. Chem. Soc., 58 (1936): 831.
u
Ruehrwein and Giauque, J. Am. Chem. Soc., 61 (1939): 2940.
a
Alloys
30.5 Pb + 69.5 Sn
36.9 Pb + 63.1 Sn
63.7 Pb + 36.3 Sn
77.8 Pb + 22.2 Sn
1 Pb + 9 Sn
24 Pb + 27.3 Sn + 48.7 Bi
25.8 Pb + 14.7 Sn + 52.4 Bi + 7 Cd
Silicates
Anorthite (CaAl2Si2O8)
Orthoclase (KAlSi2O8)
Microcline (KAlSi3O8)
Wollastonite (CaSiO8)
Malacolite (Ca8MgSi4O12)
Diopside (CaMgSi2O4)
Olivine (Mg2SiO4)
Fayalite (Fe2SiO4)
Spermaceti
Wax (bees’)
740
bp at
1 atm, °C
mp, °C
Heat of fusion, cal/g
183
179
177.5
176.5
236
98.8
75.5
17
15.5
11.6
9.54
28
6.85
8.4
43.9
61.8
100
100
83
100
94
100
130
85
37.0
42.3
2-118
PHYSICAL AnD CHEMICAL DATA
TABLE 2-68 Heats of Fusion of Organic Compounds
The values for the hydrocarbons are from the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards, with some from
Parks and Huffman, Ind. Eng. Chem., 23, 1138 (1931).
The values for the nonhydrocarbon compounds were recalculated from data in International Critical Tables, vol. 5.
Hydrocarbon compounds
Formula
mp, °C
Heat of fusion,
cal/g
Paraffins
Methane
Ethane
Propane
n-Butane
2-Methylpropane
n-Pentane
2-Methylbutane
2,2-Dimethylpropane
n-Hexane
2-Methylpentane
2,2-Dimethylbutane
2,3-Dimethylbutane
n-Heptane
2-Methylhexane
3-Ethylpentane
2,2-Dimethylpentane
2,4-Dimethylpentane
3,3-Dimethylpentane
2,2,3-Trimethylbutane
n-Octane
2-Methylheptane
3-Methylpentane
4-Methylheptane
2,2-Dimethylhexane
2,5-Dimethylhexane
3,3-Dimethylhexane
2-Methyl-3-ethylpentane
3-Methyl-3-ethylpentane
2,2,3-Trimethylpentane
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
2,3,4-Trimethylpentane
2,2,3,3-Tetramethylbutane
n-Nonane
n-Decane
n-Undecane
n-Dodecane
Eicosane
Pentacosane
Tritriacontane
Aromatics
Benzene
Methylbenzene (Toluene)
Ethylbenzene
o-Xylene
m-Xylene
p-Xylene
n-Propylbenzene
Isopropylbenzene
1-Methyl-2-ethylbenzene
CH4
C 2H 6
C 3H 8
C4H10
C4H10
C5H12
C5H12
C5H12
C6H14
C6H14
C6H14
C6H14
C7H16
C7H16
C7H16
C7H16
C7H16
C7H16
C7H16
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C8H18
C9H20
C10H22
C11H24
C12H26
C20H42
C25H52
C33H68
−182.48
−183.23
−187.65
−138.33
−159.60
−129.723
−159.890
−16.6
−95.320
−153.680
−99.73
−128.41
−90.595
−118.270
−118.593
−123.790
−119.230
−134.46
−24.96
−56.798
−109.04
−120.50
−120.955
−121.18
−91.200
−126.10
−114.960
−90.870
−112.27
−107.365
−100.70
−109.210
+100.69
−53.9
−30.0
−25.9
−9.6
+36.4
+53.3
+71.1
14.03
22.712
19.100
19.167
18.668
27.874
17.076
10.786
36.138
17.407
1.607
2.251
33.513
21.158
22.555
13.982
15.968
16.856
5.250
43.169
21.458
23.795
22.692
24.226
26.903
14.9
23.690
22.657
18.061
19.278
3.204
19.392
14.900
41.2
48.3
34.1
51.3
52.0
53.6
54.0
C 6H 6
C 7H 8
C8H10
C8H10
C8H10
C8H10
C9H12
C9H12
C9H12
+5.533
−94.991
−94.950
−25.187
−47.872
+13.263
−99.500
−96.028
−80.833
30.100
17.171
20.629
30.614
26.045
38.526
16.97
19.22
21.13
Nonhydrocarbon compounds
Formula
mp, °C
Acetic acid
Acetone
Acrylic acid
Allo-cinnamic acid
Aminobenzoic acid (o-)
(m-)
(p-)
Amyl alcohol
Anethole
Aniline
Anthraquinone
Apiol
Azobenzene
Azoxybenzene
C2H4O2
C3H6O
C3H4O2
C9H8O2
C7H7NO2
C7H7NO2
C7H7NO2
C5H12O
C10H12O
C6H5NH2
C14H8O2
C12H14O4
C12H10N2
C12H10N2O
16.7
−95.5
12.3
68
145
179.5
188.5
−78.9
22.5
−6.3
284.8
29.5
67.1
36
46.68
23.42
37.03
27.35
35.48
38.03
36.46
26.65
25.80
27.09
37.48
25.80
28.91
21.62
Benzil
Benzoic acid
Benzophenone
Benzylaniline
Bromocamphor
Bromochlorbenzene (o-)
(m-)
(p-)
Bromoiodobenzene (o-)
(m-)
(p-)
Bromol hydrate
Bromophenol (p-)
Bromotoluene (p-)
C14H10O2
C7H8O2
C13H10O
C13H13N
C10H15BrO
C6H4BrCl
C6H4BrCl
C6H4BrCl
C6H4BrI
C6H4BrI
C6H4BrI
C2H3Br3O2
C6H5BrO
C7H7Br
95.2
122.45
47.85
32.37
78
−12.6
−21.2
64.6
21
9.3
90.1
46
63.5
28
22.15
33.90
23.53
21.86
41.57
15.41
15.29
23.41
12.18
10.27
16.60
16.90
20.50
20.86
Heat of fusion,
cal/g
Hydrocarbon compounds
Aromatics—(Cont.)
1-Methyl-3-ethylbenzene
1-Methyl-4-ethylbenzene
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
1,3,5-Trimethylbenzene
Naphthalene
Camphene
Durene
Isodurene
Prehnitene
p-Cymene
n-Butyl benzene
tert-Butyl benzene
β-Methyl naphthalene
Diphenyl
Hexamethyl benzene
Diphenyl methane
Anthracene
Phenanthrene
Tolane
Stilbene
Dibenzil
Triphenyl methane
Alkyl cyclohexanes
Cyclohexane
Methylcyclohexane
Alkyl cyclopentanes
Cyclopentane
Methylcyclopentane
Ethylcyclopentane
1,1-Dimethylcyclopentane
cis-1,2-Dimethylcyclopentane
trans-1,2-Dimethylcyclopentane
trans-1,3-Dimethylcyclopentane
Monoolefins
Ethene (Ethylene)
Propene (Propylene)
1-Butene
cis-2-Butene
trans-2-Butene
2-Methylpropene (isobutene)
1-Pentene
cis-2-pentene
trans-2-pentene
2-Methyl-1-butene
3-Methyl-1-butene
2-Methyl-2-butene
Acetylenes
Acetylene
2-Butyne (dimethylacetylene)
mp, °C
Heat of fusion,
cal/g
C9H12
C9H12
C9H12
C9H12
C9H12
C10H8
C10H12
C10H14
C10H14
C10H14
C10H14
C10H14
C10H14
C11H10
C12H10
C12H18
C13H12
C14H10
C14H10
C14H10
C14H12
C14H14
C19H16
−95.55
−62.350
−25.375
−43.80
−44.720
+80.0
+51
+79.3
−24.0
−7.7
−68.9
−88.5
−58.1
+34.1
+68.6
+165.5
+25.2
+216.5
+96.3
+60
+124
+51.4
+92.1
15.14
25.29
16.64
24.54
18.97
36.0
57
37.4
23.0
20.0
17.1
19.5
14.9
20.1
28.8
30.4
26.4
38.7
25.0
28.7
40.0
30.7
21.1
C6H12
C7H14
+6.67
−126.58
7.569
16.429
C5H10
C6H12
C7H14
C7H14
C7H14
C7H14
C7H14
−93.80
−142.445
−138.435
−69.73
−53.85
−117.57
−133.680
2.068
19.68
11.10
3.36
3.87
15.68
17.93
C2H4
C3H6
C4H8
C4H8
C4H8
C4H8
C5H10
C5H10
C5H10
C5H10
C5H10
C5H10
−169.15
−185.25
−185.35
−138.91
−105.55
−140.35
−165.27
−151.363
−140.235
−137.560
−168.500
−133.780
28.547
17.054
16.393
31.135
41.564
25.265
16.82
24.239
26.536
26.879
18.009
25.738
C2H2
C4H6
−81.5
−132.23
23.04
40.808
Formula
Formula
mp, °C
Heat of fusion,
cal/g
Butyl alcohol (n-)
(t-)
Butyric acid (n-)
C4H10O
C4H10O
C4H8O2
−89.2
25.4
−5.7
29.93
21.88
30.04
Capric acid (n-)
Caprylic acid (n-)
Carbazole
Carbon tetrachloride
Carvoxime (d-)
(l-)
(dl-)
Cetyl alcohol
Chloracetic acid (α-)
(β-)
Chloral alcoholate
hydrate
Chloroaniline (p-)
Chlorobenzoic acid (o-)
(m-)
( p-)
Chloronitrobenzene (m-)
(p-)
Cinnamic acid
anhydride
Cresol (p-)
Crotonic acid (α-)
(cis-)
Cyanamide
Cyclohexanol
C10H20O2
C8H16O2
C12H9N
CCl4
C10H15NO
C10H15NO
C10H15NO
C16H34O
C2H3ClO2
C2H3ClO2
C4H7Cl3O2
C2H3Cl3O2
C6H6ClN
C7H5ClO2
C7H5ClO2
C7H5ClO2
C6H4ClNO2
C6H4ClNO2
C9H8O2
C18H14O3
C7H8O
C4H6O2
C4H6O2
CH2N2
C6H12O
31.99
16.3
243
−22.8
71.5
71
91
49.27
61.2
56
9
47.4
71
140.2
154.25
239.7
44.4
83.5
133
48
34.6
72
71.2
44
25.46
38.87
35.40
42.05
41.57
23.29
23.41
24.61
33.80
31.06
35.12
24.03
33.18
37.15
39.30
36.41
49.21
29.38
31.51
36.50
28.14
26.28
25.32
34.90
49.81
4.19
Nonhydrocarbon compounds
(Continued )
LATEnT HEATS
2-119
TABLE 2-68 Heats of Fusion of Organic Compounds (Continued )
Heat of fusion,
cal/g
Nonhydrocarbon compounds
Formula
mp, °C
Dibromobenzene (o-)
(m-)
(p-)
Dibromophenol (2, 4-)
Dichloroacetic acid
Dichlorobenzene (o-)
(m-)
(p-)
Dihydroxybenzene (o-)
(m-)
(p-)
Di-iodobenzene (o-)
(m-)
(p-)
Dimethyl tartrate (dl-)
(d-)
pyrone
Dinitrobenzene (o-)
(m-)
(p-)
Dinitrotoluene (2, 4-)
Dioxane
Diphenyl amine
C6H4Br2
C6H4Br2
C6H4Br2
C6H4Br2O
C2H2Cl2O2
C6H4Cl2
C6H4Cl2
C6H4Cl2
C6H6O2
C6H6O2
C6H6O2
C6H4I2
C6H4I2
C6H4I2
C6H10O6
C6H10O6
C7H8O2
C6H4N2O4
C6H4N2O4
C6H4N2O4
C7H6N2O4
C4H8O2
C12H11N
1.8
−6.9
86
12
−4(?)
−16.7
−24.8
53.13
104.3
109.65
172.3
23.4
34.2
129
87
49
132
116.93
89.7
173.5
70.14
11.0
52.98
12.78
13.38
20.55
13.97
14.21
21.02
20.55
29.67
49.40
46.20
58.77
10.15
11.54
16.20
35.12
21.50
56.14
32.25
24.70
39.99
26.40
34.85
25.23
Elaidic acid
Ethyl acetate
alcohol
Ethylene dibromide
Ethyl ether
C18H34O2
C4H8O2
C2H6O
C2H4Br2
C4H10O
44.4
83.8
−114.4
10.012
−116.3
52.08
28.43
25.76
13.52
23.54
Formic acid
CH2O2
8.40
58.89
Glutaric acid
Glycerol
Glycol, ethylene
C6H8O4
C3H8O3
C2H6O2
97.5
18.07
−11.5
37.39
47.49
43.26
Hydrazo benzene
Hydrocinnamic acid
Hydroxyacetanilide
C12H12N2
C9H10O2
C8H9NO2
134
48
91.3
22.89
28.14
33.59
Iodotoluene (p-)
Isopropyl alcohol
ether
C7H7I
C3H8O
C6H14O
34
−88.5
−86.8
18.75
21.08
25.79
Lauric acid (n-)
Levulinic acid
C12H24O2
C5H8O3
43.22
33
43.72
18.97
Menthol (l-) (α)
Methyl alcohol
Myristic acid
Methyl cinnamate
fumarate
oxalate
phenylpropiolate
succinate
C10H20O
CH4O
C14H28O2
C10H10O2
C6H8O4
C4H6O4
C10H8O2
C6H10O4
43.5
−97.8
53.86
36
102
54.35
18
19.5
18.63
23.7
47.49
26.53
57.93
42.64
22.86
35.72
Formula
mp, °C
Heat of fusion,
cal/g
Naphthol (α-)
(β-)
Naphthylamine (α-)
Nitroaniline (o-)
(m-)
(p-)
Nitrobenzene
Nitrobenzoic acid (o-)
(m-)
(p-)
Nitronaphthalene
Nitrophenol (o-)
C10H8O
C10H8O
C10H9N
C6H6N2O2
C6H6N2O2
C6H6N2O2
C6H5NO2
C7H5NO4
C7H5NO4
C7H5NO4
C10H7NO2
C6H5NO3
95.0
120.6
50
71.2
114.0
147.3
5.85
145.8
141.1
239.2
56.7
45.13
38.94
31.30
22.34
27.88
40.97
36.46
22.52
40.06
27.59
52.80
25.44
26.76
Palmitic acid
Paraldehyde
Pelargic acid (n-) (β-)
Pelargonic acid (n-) (α-)
Phenol
Phenylacetic acid
Phenylhydrazine
Propyl ether (n)
C16H32O2
C6H12O3
C9H18O2
C9H18O2
C6H6O
C8H8O2
C6H8N2
C6H14O
61.82
10.5
12.35
40.92
76.7
19.6
−126.1
39.18
25.02
39.04
30.63
29.03
25.44
36.31
20.66
Nonhydrocarbon compounds
Quinone
C6H4O2
115.7
40.85
Stearic acid
Succinic anhydride
Succinonitrile
C18H30O2
C4H4O3
C4H4N2
68.82
119
54.5
47.54
48.74
11.71
Tetrachloroxylene (o-)
(p-)
Thiophene
Thiosinamine
Thymol
Toluic acid (o-)
(m-)
(p-)
Toluidine (p-)
Tribromophenol (2, 4, 6-)
Trichloroacetic acid
Trinitroglycerol
Trinitrotoluene (2, 4, 6-)
Tristearin
C8H6Cl4
C8H6Cl4
C4H4S
C4H8N2S
C10H14O
C8H8O2
C8H8O2
C8H8O2
C7H9N
C6H3Br3O
C2HCl3O2
C3H5N3O9
C7H5N3O6
C57H110O6
86
95
−39.4
77
51.5
103.7
108.75
179.6
43.3
93
57.5
12.3
80.83
70.8, 54.5
21.02
22.10
14.11
33.45
27.47
35.40
27.59
39.90
39.90
13.38
8.60
23.02
22.34
45.63
Undecylic acid (α-) (n-)
(β-) (n-)
Urethane
C11H22O2
C11H22O2
C3H7NO2
28.25
48.7
32.20
42.91
40.85
Veratrol
C8H10O2
22.5
27.45
Xylene dibromide (o-)
(m-)
dichloride (o-)
(m-)
(p-)
C8H8Br2
C8H8Br2
C8H8Cl2
C8H8Cl2
C8H8Cl2
95
77
55
34
100
24.25
21.45
29.03
26.64
32.73
2-120
TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol)
Cmpd. no.*
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
Mol. wt.
C1 × 1E-07
C2
C3
C4
Tmin , K
ΔHv at
Tmin × 1E-07
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
3.4088
9.9475
6.127546
5.8564
4.9258
3.8345
1.7059
6.6599
4.3756
4.3052
0.74587
3.1523
7.6926
0.84215
8.7809
5.0007
6.081621
11.374
6.4966
10.523
8.4762
8.2051
11.544
7.6737
5.5242
5.0392
3.9247
3.1988
3.039582
3.8018
3.6238
9.4943
11.344
7.1274
7.5007
3.3774
4.3478
3.8671
8.8262
8.0911
5.0883
4.7563
4.3143
4.17
6.1947
5.1323
0.043317
0.94835
3.683421
0.33055
1.0809
0.033941
-0.52025
2.2443
2.2571
0.095188
0.47571
0.3914
1.4255
0.28333
0.1933
0.65393
0.2724357
1.4864
0.54598
0.87091
0.35251
1.4438
2.2311
0.28923
1.5015
-0.2027
0.28886
0.2896
0.2698591
0.90446
0.8337
0.64824
1.4414
0.0483
0.09616
0.5107
1.3196
1.0672
1.7772
1.2599
0.47166
0.49657
1.0149
0.23488
1.6524
0.32362
0.21502
-0.51011
-6.193052
-0.057073
-1.3684
0.34283
1.0982
-2.9192
-4.5116
0.47381
-0.71131
-0.2289
-1.6901
0.033281
0.30877
-0.27698
0.4430641
-2.3097
-0.42255
-0.45568
0.43853
-1.8053
-2.5186
0.34048
-1.7185
1.2207
0.38616
0.0344
-0.3789853
-0.74555
-0.82274
-0.24961
-1.9412
0.8966
1.1444
-0.17304
-1.5096
-1.2574
-1.926
-1.2911
-0.0078998
-0.13123
-0.99196
0.020947
-2.8505
0.16979
0.23791
0.015094
2.977694
0.083671
0.69723
-0.13415
-0.29832
1.1113
2.5738
-0.26294
0.60517
0.2309
0.72371
0.030551
-0.14162
0.029569
-0.3449689
1.4025
0.2597
149.780
353.150
289.810
200.150
178.450
229.315
192.400
185.450
286.150
189.630
59.150
195.410
235.650
83.780
403.000
278.680
258.270
395.450
260.280
321.350
257.850
275.650
243.950
342.200
265.850
242.430
154.250
179.440
136.950
164.250
134.860
220.000
196.150
183.850
158.450
87.800
134.260
167.620
199.650
185.300
157.460
133.020
147.430
176.800
250.000
161.300
3.23240
6.36890
2.44660
5.14960
3.66050
3.52490
1.62620
3.63950
2.79650
3.89890
0.63247
2.52980
5.10000
0.65440
7.12860
3.49320
5.06340
6.94850
5.33600
7.48950
6.88000
5.24700
6.26740
6.11280
3.28440
4.71870
3.42380
2.75620
2.82540
2.76410
2.86840
7.58750
8.14880
6.36430
6.59780
3.01970
3.10310
2.77200
5.32550
5.94710
4.37960
4.18430
3.20490
3.77230
4.16190
4.57590
-0.3026
0.79682
0.83063
-0.26011
0.6614
-0.70705
-0.35786
0.0114
0.5165115
0.24234
0.39613
0.058188
1.035
-0.5116
-0.78448
0.05181
0.63987
0.62539
0.63659
0.47381
-0.071247
0.027307
0.40891
0.086255
1.6285
-0.18921
Tmax , K
466.000
761.000
591.950
606.000
508.200
545.500
308.300
506.000
615.000
540.000
132.450
405.650
645.600
150.860
824.000
562.050
689.000
751.000
702.300
830.000
720.150
662.000
718.000
773.000
584.150
670.150
503.800
464.000
452.000
425.000
425.120
680.000
676.000
563.100
535.900
419.500
435.500
428.600
575.400
660.500
570.100
554.000
440.000
537.200
615.700
585.400
ΔHv
at Tmax
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
CO2
CS2
CO
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
44.0095
76.1407
28.0101
153.8227
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
2.173
4.0359
0.8585
4.6113
1.9311
3.068
4.6746
3.253
5.3032
2.442
3.93706
3.9033
6.87
13.355
8.0979
7.5255
2.3558
3.6762
5.193
5.5761
6.6898
4.698
3.4216
3.6524
2.7681
6.7798
9.0851
8.7515
12.531
7.9041
6.6985
8.4103
10.603
0.11867
4.7061
6.057225
6.1207
6.4978
5.3065
6.4394
7.0416
4.7631
5.6489
4.8739
5.6495
4.2593
12.931
2.595917
5.947
4.7806
0.382
1.0897
0.4921
0.55241
0.94983
0.8458
0.013055
0.321
1.0366
-0.298
0.14297
0.3867
-0.39158
2.3486
-0.33815
1.3714
-0.29499
0.76666
1.0019
-1.7498
1.0012
0.44894
-0.21723
0.17652
0.44645
1.1402
1.3026
1.3204
0.76281
-1.36
0.76944
0.40556
1.7758
-0.31087
0.098096
1.372193
1.2282
0.77464
0.20288
0.67955
0.96641
1.0048
1.0038
0.9583
1.0359
-0.0038971
1.2215
-1.334101
1.6416
0.39507
-0.4339
-1.6483
-0.326
-0.18725
-1.0615
-0.9001
0.51777
-0.252
-0.79572
0.87
0.55088
0.008595
1.7208
-2.5463
2.3495
-1.5024
0.34496
-0.74793
-1.0159
4.5168
-0.96028
0.070295
1.0245
0.2777
-0.28756
-1.1701
-1.6803
-1.2441
-0.32459
4.0854
-0.79975
0.34553
-1.6849
0.28353
0.20134
-2.053024
-1.1989
-0.67379
0.039962
-0.58058
-0.86362
-1.2457
-0.7936
-0.79374
-0.98747
0.58142
-1.3197
2.366723
-1.7394
-0.028657
0.42213
0.9779
0.2231
0.022973
0.51894
0.453
-0.18852
0.295
0.16746
-0.271
-0.3511
-0.016793
-0.97478
0.74218
-1.7015
0.59731
0.24271
0.35979
0.46332
-2.4034
0.37622
-0.14736
-0.49752
-0.10817
0.21791
0.45855
0.86441
0.38061
0.054808
-2.3871
0.42379
-0.4009
0.38281
0.34543
0.22064
1.161394
0.40137
0.31825
0.12466
0.36746
0.32976
0.67919
0.17013
0.28069
0.39006
-0.23734
0.50585
-0.7871881
0.5831
0.014929
216.580
161.110
68.130
250.330
89.560
172.120
227.950
136.750
209.630
175.430
150.350
155.970
285.390
304.190
307.930
177.140
245.250
182.480
279.690
296.600
242.000
169.670
179.280
138.130
145.590
189.640
285.000
243.510
304.550
280.050
206.890
247.560
229.150
18.730
210.150
282.850
220.600
175.300
248.390
256.150
326.140
176.190
237.490
178.010
192.500
172.710
301.150
223.350
156.850
169.200
1.52020
3.17860
0.65166
3.47600
1.42150
2.28780
4.32240
2.95540
3.65460
2.41470
3.56930
3.36320
6.37340
6.06020
6.57120
5.41880
2.33890
2.81720
3.38860
6.25790
4.84470
3.98460
3.30460
3.37950
2.33840
5.10540
6.02700
5.60450
8.84640
8.29590
5.35240
6.81720
6.07920
0.12605
4.35520
4.06410
4.18700
5.24340
4.77510
5.09850
4.68520
3.62860
3.84750
3.58500
4.13210
4.03570
8.64260
3.35400
3.75450
4.15460
304.210
552.000
132.920
556.350
227.510
417.150
632.350
460.350
536.400
416.250
503.150
489.000
705.850
697.550
704.650
631.000
400.150
459.930
553.800
650.100
653.000
560.400
511.700
507.000
398.000
664.000
674.000
617.700
722.100
688.000
616.600
696.000
619.850
38.350
628.000
650.150
611.000
584.100
683.950
705.000
684.750
523.000
561.600
510.000
560.000
572.000
736.600
496.600
466.700
557.150
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(Continued )
2-121
2-122
TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued )
Cmpd. no.*
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
Name
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Formula
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
CAS
Mol. wt.
C1 × 1E-07
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
3.663
4.2313
3.3907
2.8258
4.630224
5.2429
4.3872
4.7999
3.6881
3.4422
4.8054
5.5503
5.4479
5.8702
5.8328
2.6377
5.9186
5.3387
10.263
2.919
4.5493
7.0161
7.66109
5.0368
6.9745
7.993218
10.962
12.86
2.1091
6.5831
4.8272
4.275
7.4288
6.8245
8.7212
5.7624
6.0933
5.7997
2.0639
5.6091
8.9207
4.7462
4.4514
4.4151
11.08845
C2
0.93553
0.90591
1.1148
-1.5731
1.265631
0.80535
0.56226
0.30724
0.37958
-0.49774
1.0013
0.7692
0.56826
1.0022
0.99061
-0.072806
0.37731
0.9509
1.504
0.47315
0.81834
0.9938
0.36322
0.37438
0.43414
1.697066
1.5544
0.50351
0.60646
1.1905
0.2372
0.5857
1.6218
1.071
0.79255
0.46881
0.96339
1.0161
0.80153
0.077011
0.83021
0.37327
1.1569
0.51536
0.7029
C3
C4
Tmin , K
ΔHv at
Tmin × 1E-07
-0.9806
-0.59583
-1.2957
2.9709
-2.325122
-1.4147
-0.60662
-0.024545
-0.22063
1.8024
-1.0356
-0.56915
-0.29095
-1.0188
-0.9035
0.54324
0.0051489
-0.97007
-2.441
-0.19035
-0.47199
-1.4767
-0.28551
-0.0004344
-0.26069
-1.895364
-1.5358
0.32986
-0.55492
-1.7666
0.32434
-0.332
-2.0278
-1.943
-0.64882
-0.14511
-0.94933
-0.92313
-0.8128
0.66595
-0.88126
0.047488
-1.2336
-0.39281
-0.10529
0.46753
0.074323
0.58214
-1.1073
1.525306
1.0288
0.4202
0.091361
0.21968
-0.97741
0.4668
0.2328
0.15397
0.46949
0.34792
-0.13977
-0.0027682
0.44354
1.388
0.078322
0.047802
0.97462
0.23966
0.0050378
0.15024
0.6664379
0.46286
-0.42184
0.32799
1.0012
-0.19429
0.169
0.906
1.2788
0.28369
0.061942
0.44931
0.33212
0.4179
-0.43437
0.53255
0.045906
0.50875
0.28461
-0.17295
154.560
215.000
136.950
176.850
187.650
204.810
159.950
226.100
240.910
180.960
145.190
239.660
223.160
184.990
188.440
131.650
212.720
160.000
274.180
122.930
174.880
291.670
413.786
284.950
300.030
210.150
263.570
309.580
90.350
159.050
189.600
192.150
178.200
238.450
258.150
175.150
161.840
134.710
104.000
284.290
260.150
195.200
160.650
193.550
155.150
2.67130
2.78200
2.40150
3.76470
3.47860
4.33570
3.75280
4.05570
2.92830
3.29670
3.72820
4.11250
4.36640
4.47370
4.43890
2.54380
5.09300
4.16640
7.17430
2.50210
3.43160
5.27280
6.19680
3.92500
5.84730
4.77500
6.52590
9.59330
1.78790
5.00600
4.16260
3.29550
5.08620
5.40830
6.51870
4.92230
4.84420
4.65290
1.59660
4.62220
6.87400
3.96760
3.19090
3.63270
9.30840
Tmax , K
386.440
445.000
351.255
523.100
500.050
576.000
507.800
543.000
473.200
437.200
500.000
591.150
606.150
596.150
615.000
400.100
649.600
537.300
766.000
402.000
503.040
729.000
777.400
587.000
766.800
550.000
658.000
768.000
305.320
514.000
523.300
456.150
617.150
698.000
655.000
571.000
609.150
569.500
282.340
593.000
720.000
537.000
469.150
508.400
674.600
ΔHv
at Tmax
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
6.6828
4.2527
5.6735
4.292
5.033
5.438
5.0124
0.89107
3.7517
2.4749
1.9302
2.9575
5.8307
2.3195
4.4388
0.012504
15.97
4.7135
5.2516
12.916
7.0236
11.119
6.067
6.2857
4.9437
6.7011
4.8235
14.979
5.3802
4.3848
9.0746
7.035
9.591
5.5382
5.8213
4.249938
4.282053
5.9346
6.8856
6.0629
5.9794
0.10127
1.5513
3.4872
3.3907
13.451
2.6092
4.0385
5.6917
7.7143
0.6664
0.42014
0.85864
0.93726
-0.023028
0.60624
0.48381
0.48888
-0.33542
0.18492
-0.2029
0.098296
-0.62844
1.9091
0.82914
1.3038
1.977
-0.27964
0.51283
1.4923
-1.3652
1.3264
0.18619
0.3899
0.35428
0.38694
0.35765
1.89
0.52771
0.34057
0.8926
-0.9575
1.236
0.19854
0.44196
0.52336
0.5862582
0.41114
1.9737
1.1597
0.9424
0.698
-0.80615
2.1553
0.43574
13.36
0.47883
0.82698
1.2441
-1.0139
-0.4545
-0.17341
-1.1249
-1.0593
0.84791
0.20227
0.14204
0.69714
0.54636
-0.44199
-0.1946
-0.44035
1.0497
-0.21197
0.65339
0.28373
1.6751
-5.0003
-0.72757
-2.6954
-2.2318
0.89761
-0.10982
-1.3795
3.987
-1.1057
0.47762
0.17742
0.22149
0.24973
-0.060379
-2.0762
-0.4757
0.063282
-0.75172
3.1431
-1.359
0.47139
0.090968
-0.57323
-0.9710554
0.043753
-2.4886
-0.99686
-1.398
-1.817
1.1788
-2.9128
-0.56984
–23.383
-0.2233
-2.033
-1.0742
2.2898
0.12282
0.31792
-0.40021
0.36038
-0.16704
-0.77554
3.2641
0.33552
1.7098
0.78544
-0.33523
-0.01018
0.39603
-2.2545
0.36023
-0.26967
-0.19455
-0.2353
-0.26228
0.045749
0.71724
0.3242
-0.017037
0.34378
-1.8066
0.717
-0.31556
-0.15346
0.45101
0.8523437
-0.081964
0.99472
0.32547
0.8862
1.447
-0.070978
1.2442
0.36017
10.785
0.12903
1.4769
0.32331
-0.91517
180.000
140.000
204.150
125.260
199.250
145.650
167.550
53.480
230.940
129.950
131.350
155.150
275.700
250.000
196.290
2.200
295.130
229.800
182.570
265.830
239.150
220.000
234.150
238.150
154.120
229.920
192.220
291.310
214.930
177.830
269.250
228.550
223.000
217.350
217.500
133.390
170.050
192.620
141.250
183.650
274.690
13.950
185.150
158.970
259.830
277.560
187.680
227.150
177.950
409.150
5.46390
3.73840
4.45040
3.50010
4.53900
4.41400
4.29170
0.75083
3.69360
2.31740
1.89050
2.69310
6.17220
1.88650
3.27960
0.00966
8.59730
4.69820
4.31810
7.80040
7.64980
7.18220
5.16400
5.08510
4.32080
5.51330
4.15950
8.19340
4.49940
3.75320
6.47830
7.15090
6.46500
4.75590
4.70770
3.75440
3.73310
5.08670
4.44750
4.26690
4.52380
0.09131
1.81940
1.74720
2.79840
0.71043
1.97460
3.55340
3.74360
8.31300
583.000
489.000
567.000
499.150
546.000
500.230
559.950
144.120
560.090
375.310
317.420
420.000
771.000
588.000
490.150
5.200
736.000
620.000
540.200
677.300
632.300
608.300
606.600
611.400
537.400
645.000
547.000
723.000
594.000
507.600
660.200
611.300
585.300
587.610
582.820
504.000
544.000
623.000
516.200
549.000
653.150
33.190
363.150
324.650
456.650
461.150
373.530
605.000
471.850
834.000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(Continued )
2-123
2-124
TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued )
Cmpd. no.*
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
Name
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
Formula
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
CAS
Mol. wt.
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
C1 × 1E-07
176.7855
1.0194
3.2615
6.8795
4.329
3.0066
6.2689
4.2834
5.8474
4.2709
4.233
8.223
10.165
4.5217
4.897
4.5822
4.4918
6.8872
3.1821
5.1299
4.4696
5.3789
7.7573
9.4404
9.4625
5.1137
4.2603
4.2081
4.8242
3.7592
5.2256
4.9455
4.7691
4.266
8.1495
3.2575
3.8148
2.7567
4.0063
3.0851
5.6613
10.53
5.0351
5.0003
3.9654
C2
16.29674
0.26087
-1.0407
0.012343
0.18771
0.25873
1.6462
0.90615
-0.6042
0.70788
0.95448
0.80923
1.4422
1.0678
1.1838
1.3506
0.32576
1.2703
-0.89979
0.10033
1.1838
0.71218
0.56959
0.8722
0.88768
0.98237
0.34248
0.43515
1.3456
0.64544
0.9427
0.78235
0.98928
0.37791
1.8479
-0.58542
0.38959
-1.6298
-0.17489
-0.29985
0.3132
0.7454
1.1424
0.42203
1.274
C3
C4
Tmin , K
ΔHv at
Tmin × 1E-07
–28.8053
-0.14694
1.8695
0.77544
0.33528
0.033435
-2.2795
-0.93138
2.1528
-0.67299
-0.98289
-0.70838
-1.6123
-1.1735
-1.2079
-1.6049
0.1124
-1.2699
2.8579
0.64085
-0.87047
-0.28902
0.7221
-0.33173
-0.39167
-0.90553
-0.088074
-0.24963
-1.5783
-0.46384
-1.0868
-0.56637
-0.98574
0.0037827
-2.1328
1.4307
-0.15805
3.0001
0.94886
1.4733
0.57076
-0.39297
-1.3269
-0.14687
-1.4255
14.522
0.22154
-0.60801
-0.4379
-0.17125
0.087053
1.0975
0.4776
-1.2871
0.43009
0.45719
0.32497
0.75941
0.55525
0.43353
0.71575
-0.067377
0.44562
-1.7826
-0.38359
0.056694
-0.014989
-0.86278
-0.10938
-0.057899
0.34878
0.13072
0.20811
0.61746
0.21809
0.55491
0.22052
0.42695
-0.001928
0.76628
-0.54833
0.15228
-1.1865
-0.44746
-0.89559
-0.46309
0.047214
0.62481
0.11507
0.60708
288.150
90.690
175.470
301.150
175.150
170.450
196.320
179.690
260.750
159.530
113.250
193.000
155.950
135.580
139.390
160.150
157.480
175.300
183.450
187.350
139.050
146.580
299.150
280.150
269.150
130.730
146.620
168.540
182.550
160.000
186.480
167.230
174.150
188.000
189.150
256.150
127.930
180.150
171.640
150.180
224.950
240.000
119.550
176.000
113.540
4.28480
0.87235
3.97480
5.97080
3.83890
2.56480
4.04870
3.09550
5.78260
3.46030
3.43450
6.57690
7.27510
3.46420
3.61390
3.20970
3.94480
4.96500
3.25930
4.58370
3.16280
4.45440
5.13430
6.16980
6.31440
4.10400
3.84130
3.63850
3.24190
2.98760
3.98780
3.90650
3.51240
3.56270
4.98940
3.22260
3.39970
3.74640
3.89410
2.99210
4.46890
8.11060
3.97590
4.30250
2.93300
Tmax , K
662.000
190.564
512.500
718.000
506.550
402.400
536.000
430.050
693.000
490.000
460.400
643.000
577.200
465.000
470.000
492.000
512.740
593.000
463.200
554.500
442.000
572.100
686.000
614.000
617.000
532.700
542.000
526.000
483.000
437.800
535.500
533.000
487.200
497.000
574.600
488.000
464.480
553.400
553.100
469.950
566.000
694.000
497.700
546.490
407.800
ΔHv
at Tmax
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F 3N
CH3NO2
N 2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
2.2708
4.3172
4.9563
4.2364
5.7015
2.0613
5.3293
4.0052
3.2566
5.093
0.19063
3.8821
0.74905
1.8859
4.7494
2.2724
0.94287
17.161
4.5173
7.888
12.126
7.5429
14.251
5.9054
6.6716
8.7405
17.264
5.7746
6.7138
12.626
7.2468
12.581
11.048
6.6142
5.4859
7.3618
5.367
7.7236
0.9008
1.7289
10.052
5.2373
4.5087
7.3197
7.39
8.8703
5.3818
4.451
3.5027
5.0573
-3.8183
1.5334
0.22568
0.25325
1.0015
0.33885
0.15144
0.19309
0.10042
-0.44584
-0.048268
-1.2495
0.40406
1.0917
0.1535
0.22278
-2.0627
1.7444
-1.1627
1.3126
0.82704
-1.5966
1.418
0.61039
-0.70869
1.5599
2.167
0.16524
1.0769
1.1753
-1.2464
1.3269
2.5722
0.58562
0.26207
0.63204
0.31607
-0.55914
0.4542
0.12106
0.37778
1.0132
0.95886
1.2093
-0.1464
0.90566
0.35111
-0.5483
0.3481
0.45827
6.7137
-1.9
0.45949
0.58114
-0.95589
-0.63279
0.15411
0.20658
0.26926
1.0348
0.11183
3.2285
-0.317
-1.4143
0.49623
0.29352
3.2659
-1.6657
2.3227
-1.3571
-0.42449
4.6489
-0.53849
-0.54533
2.636
-1.7205
-2.6262
0.095968
-1.0124
-0.835
3.6797
-0.69134
-3.7155
-0.40512
0.50642
-0.29459
0.073613
1.8363
-0.4096
0.088716
0.50709
-1.6348
-0.92384
-1.9114
1.4751
-0.67627
0.40264
2.1051
-0.19672
-0.22568
-2.7247
0.83816
-0.31541
-0.4757
0.38421
0.6454
0.066538
-0.010244
-0.0003252
-0.19528
0.25512
-1.8283
0.27343
0.76165
-0.38464
-0.13493
-1.0186
0.43242
-0.89716
0.5034
0.08636
-2.7229
-0.33162
0.30683
-1.6685
0.64325
1.0161
0.10146
0.37075
0.1489
-2.0665
-0.08027
1.7307
0.22144
-0.43873
0.063444
-0.040895
-0.85806
0.3183
0.10749
-0.46599
1.0473
0.39393
1.1591
-0.9208
0.3485
-0.42577
-1.3486
0.22394
0.16393
298.970
132.810
185.650
133.970
160.170
116.340
249.950
164.550
151.150
353.430
24.560
183.630
63.150
66.460
244.600
182.300
109.500
305.040
267.300
219.660
285.550
268.150
238.150
191.910
253.050
223.150
301.310
251.650
216.380
289.650
257.650
241.550
252.850
255.550
171.450
223.950
193.550
462.650
54.360
80.150
283.070
191.590
143.420
239.150
195.560
200.000
196.290
234.180
108.016
160.750
4.65420
2.92920
4.26690
3.73780
4.42340
1.90240
4.79340
3.60720
2.99980
5.09530
0.17706
4.54440
0.60243
1.46720
4.05640
1.66660
1.44210
9.52160
5.47060
5.25710
8.59240
8.24110
8.32860
4.92180
6.54750
5.46000
8.94580
5.17550
4.69860
7.96680
7.67930
7.57060
5.50930
5.20760
4.79270
5.90250
4.67380
6.56310
0.77419
1.63130
7.76350
4.12150
3.47660
5.38130
6.70050
6.48970
4.45330
4.22720
3.22320
4.43430
506.200
417.900
530.600
476.250
565.000
352.500
654.000
497.100
437.000
748.400
44.400
593.000
126.200
234.000
588.150
309.570
180.150
758.000
658.500
594.600
710.700
670.900
649.500
593.100
681.000
598.050
747.000
638.900
568.700
694.260
652.300
629.800
632.700
627.700
566.900
667.300
574.000
828.000
154.580
261.000
708.000
566.100
469.700
639.160
588.100
561.000
561.080
560.950
464.800
584.300
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(Continued )
2-125
2-126
TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued )
Cmpd. no.*
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
Name
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Formula
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O 2S
F 6S
O 3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
CAS
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
Mol. wt.
C1 × 1E-07
C2
C3
C4
Tmin , K
ΔHv at
Tmin × 1E-07
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
5.4925
5.1346
5.4839
10.336
6.283
7.3079
18.461
2.8092
2.9209
6.8988
8.502
5.9068
3.3611
4
4.6242
6.4745
3.4054
7.2986
2.5216
5.7631
4.2077
4.4542
7.097812
6.2374
2.3637
8.6409
11.447
2.846
1.3661
0.8509
11.928
13.0705
12.007
4.0907
10.07
0.38608
1.3829
0.98943
1.0678
-0.64878
1.3522
3.6123
0.30398
0.78237
0.6458
1.474
0.44605
-0.27575
1.3936
0.12029
0.93113
-0.29885
1.2428
0.33721
0.70122
0.33823
0.31385
-0.5348227
0.73316
0.32997
1.8893
-0.04418
-0.24905
-1.1465
-7.1061
-0.063031
1.329955
1.445
0.12318
1.994
0.12415
-1.6264
-0.46159
-1.0693
2.4219
-1.6409
-5.1111
0.017572
-0.77319
-0.5384
-1.878
-0.18075
0.66467
-2.9465
0.62187
-0.65971
0.72173
-1.361
-0.18399
-0.15754
0.2503
0.30517
1.770112
-1.3874
0.055931
-2.1943
1.1282
0.62158
1.5442
11.558
0.89651
-1.300762
-1.3846
0.46123
-2.5052
-0.13245
0.67069
-0.064298
0.39121
-1.4972
0.66839
1.9668
0.10232
0.39246
0.3317
0.933
0.13426
197.450
167.450
163.830
372.380
314.060
243.150
404.150
136.870
85.470
146.950
185.258
199.000
165.000
252.450
180.370
178.150
188.360
173.550
87.890
180.250
142.610
159.950
213.150
388.850
186.350
242.540
460.850
197.670
223.150
289.950
700.150
329.350
279.010
164.650
237.380
4.65540
3.49690
3.99170
7.05940
5.77350
4.95580
6.24970
2.44810
2.47870
5.83560
5.61950
5.07850
3.43940
3.09220
4.16430
4.85340
3.46570
5.46050
2.31770
4.44670
3.70860
3.88960
7.23780
4.92650
1.48720
4.92460
8.50610
2.79080
1.62200
4.41460
7.16890
8.42870
7.33360
3.74660
6.02700
1.794
-0.48327
0.17587
-0.080173
0.56435
0.22377
-0.11477
-0.21085
-0.24568
-0.9904166
1.0391
-0.011041
0.81388
-0.67562
-0.020421
-0.15766
-4.483
-0.5152
0.5044183
0.42836
-0.23807
1.0593
Tmax , K
598.000
481.200
519.000
869.000
694.250
653.000
791.000
394.000
369.830
536.800
508.300
636.000
503.600
600.810
561.300
549.730
496.950
638.350
364.850
538.000
517.000
536.600
626.000
683.000
259.000
636.000
838.000
430.750
318.690
490.850
883.600
857.000
693.000
540.150
720.000
ΔHv
at Tmax
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
5.2918
3.8116
5.2472
5.4643
4.1283
11.72
4.6139
5.1056
7.0138
7.8955
5.935
6.0778
10.688
1.9497
10.136
8.7274
4.6643
3.649
4.2629
4.3817
5.66
6.493
6.5393
6.6475
0.57615
-0.60048
0.78829
0.76764
-0.34796
1.6004
0.41881
1.6568
1.0377
1.513
1.1967
1.207
0.38045
-8.4859
1.5084
-1.5834
0.50913
0.4
1.0111
0.26434
0.612041
1.0653
0.98813
1.1739
-0.32236
1.6501
-0.47503
-0.62056
1.0118
-1.6689
-0.23744
-1.6244
-1.1841
-1.9061
-1.2686
-1.3449
-0.00074017
17.865
-1.473
5.0913
-0.55117
0.043
-0.48757
0.034522
-0.625697
-1.1205
-0.91617
-1.2812
0.15218
-0.73052
0.098333
0.25935
-0.32712
0.56396
0.20257
0.41985
0.56211
0.85016
0.51652
0.58
0.0003222
–10.196
0.44521
-3.2171
0.45397
-0.045787
0.071549
0.398804
0.48226
0.35023
0.54229
176.990
373.960
234.940
178.180
236.500
267.760
158.450
156.080
247.790
229.330
165.780
172.220
398.400
354.000
247.570
288.450
180.350
173.150
119.360
178.350
273.160
225.300
247.980
286.410
4.49330
3.17800
3.81710
4.40060
4.13030
6.97470
4.05710
3.08740
5.12030
5.22830
4.34440
4.47800
8.39050
8.84860
6.19520
8.90070
3.97880
2.98760
3.21450
3.91430
4.49810
4.68030
4.65030
4.30350
631.950
568.000
579.350
591.750
602.000
675.000
535.150
433.250
664.500
649.100
543.800
573.500
846.000
828.000
639.000
703.900
519.130
454.000
432.000
543.150
647.096
617.000
630.300
616.200
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
The heat of vaporization ΔHv is calculated by
2
ΔHv = C1(1 - Tr)(C2+C3Tr+C4Tr )
where Tr = T/TC, TC is the critical temperature from Table 2-106, ΔHv is in J/kmol, and T is in K.
All substances are listed by chemical family in Table 2-6 and by formula.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced
with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure
Chemical Properties, Design Institute for Physical Properties, AIChE, New York NY (2016).
2-127
2-128
PHYSICAL AnD CHEMICAL DATA
SPECIFIC HEATS
SPECIFIC HEATS OF PURE COMPOUnDS
Unit Conversions For this subsection, the following unit conversions are
applicable: °F = 9⁄5°C + 32 and °R = 1.8 K. To convert calories per gram-kelvin
to British thermal units (Btu) per pound-degree Rankine, multiply by 1.0.
To convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Rankine, multiply by 0.2388.
Additional References Additional data are contained in the subsection “Thermodynamic Properties.” Data on water are also contained in that
subsection.
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds*
Substance
Aluminum1
Al
AlBr3
AlCl3
AlCl3⋅6H2O
AlF3
AlF3⋅3½H2O
AlF3⋅3NaF
AlI3
Al2O3
Al2O3⋅SiO2
3Al2O3⋅2SiO2
4Al2O3⋅3SiO2
Al2(SO4)3
Al2(SO4)3⋅18H2O
Antimony
Sb
SbBr3
SbCl3
Sb2O3
Sb2O4
Sb2S3
Argon2
A
Arsenic
As
AsCl3
As2O3
As2S3
Barium
BaCl2
BaCl2⋅H2O
BaCl2⋅2H2O
Ba(ClO3)2⋅H2O
BaCO3
State
†
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
273–931
931–1273
273–370
370–407
273–465
465–504
288–327
288–326
288–326
273–1273
1273–1373
273–464
464–480
273–1973
273–1573
273–1673
273–1573
273–576
273–575
273–373
288–325
1
5
3
5
3
3
?
?
?
2
?
3
5
3
3
2
3
5
3
?
?
c
l
c
l
c
l
c
c
c
c
l
c
l
c
c, sillimanite
c, disthene
c, andalusite
c, mullite
c
c
c
4.80 + 0.00322T
7.00
18.74 + 0.01866T
29.5
13.25 + 0.02800T
31.2
76
19.3
50.5
38.63 + 0.04760T - 449200/T 2
142
16.88 + 0.02266T
28.8
22.08 + 0.008971T - 522500/T 2
40.79 + 0.004763T - 992800/T 2
41.81 + 0.005283T - 1211000/T 2
43.96 + 0.001923T - 1086000/T 2
59.65 + 0.0670T
113.2 + 0.0652T
63.5
235
c
l
c
c
c
c
c
5.51 + 0.00178T
7.15
17.2 + 0.0293T
10.3 + 0.0511T
19.1 + 0.0171T
22.6 + 0.0162T
24.2 + 0.0132T
273–903
903–1273
273–370
273–346
273–929
273–1198
273–821
2
5
?
?
?
?
?
g
4.97
All
0
c
l
c
c
5.17 + 0.00234T
31.9
8.37 + 0.0486T
25.8
273–1168
286–371
273–548
293–373
5
?
?
?
c
c
c
c
c, α
c, β
c
c
c
17.0 + 0.00334T
28.2
37.3
51
17.26 + 0.0131T
30.0
34
39.8
21.35 + 0.0141T
273–1198
273–307
273–307
289–320
273–1083
1083–1255
273–297
285–371
273–1323
?
?
?
?
5
15
?
?
5
BaMoO4
Ba(NO3)2
BaSO4
Beryllium3,4
Be
c
4.698 + 0.001555T - 121000/T 2
273–1173
1
BeO
c
8.69 + 0.00365T - 313000/T 2
273–1175
5
BeO ⋅ Al2O3
c
25.4
273–373
?
BeSO4
c
20.8
273–373
?
*From Kelley, U.S. Bur. Mines Bull. 371, 1934. For a revision see Kelley, U.S. Bur. Mines Bull. 477, 1948. Data for many elements and compounds are given by Johnson (ed.), WADD-TR-60-56, 1960, for cryogenic temperatures. Tabulated data for gases can be obtained from many
of the references cited in the “Thermodynamic Properties” subsection and other tables in this section. Thinh, Duran, et al., Hydrocarbon
Process., 50, 98 (January 1971), review previous equation fits and give newer fits for 408 hydrocarbons and related compounds. Later publications include Duran, Thinh, et al., Hydrocarbon Process., 55, 153 (August 1976); Thompson, J. Chem. Eng. Data, 22(4), 431 (1977); and Passut
and Danner, Ind. Eng. Chem. Process Des. Dev., 11, 543 (1972); 13, 193 (1974).
†
The symbols in this column have the following meaning; c, crystal; l, liquid; g, gas; gls, glass.
SPECIFIC HEATS
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Bismuth4
Bi
Bi2O3
Bi2S3
Boron
B
B2O3
BN
Bromine
Br2
Cadmium
Cd
CdO
CdS
CdSO4⋅8/3H2O
Calcium
Ca
CaCl2
CaCO3
CaF2
CaMg(CO3)2
CaMoO4
CaO
Ca(OH)2
CaO⋅Al2O3⋅2SiO2
CaO⋅MgO⋅2SiO2
CaO⋅SiO2
CaP2O6
CaSO4
CaSO4⋅2H2O
CaWO4
Carbon5
C
CH4
CO6
CO2
CS2
Cerium
Ce
CeO2
Ce2(MoO4)3
Ce2(SO4)3
Ce2(SO4)3⋅5H2O
Cesium
Cs
CsBr
CsCl
CsF
CsI
Chlorine
Cl2
Chromium4
Cr
CrCl3
Cr2O3
CrSb
CrSb2
Cr2(SO4)3
Cobalt4
Co
CoAs2⋅CoS2
CoSb
Co2Sn
CoS
CoSO4⋅7H2O
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
c
l
c
c
5.38 + 0.00260T
7.60
23.27 + 0.01105T
30.4
273–544
544–1273
273–777
284–372
3
3
2
?
c
gls
gls
c
1.54 + 0.00440T
5.14 + 0.0320T
30.4
1.61 + 0.00400T
273–1174
273–513
513–623
273–1173
5
3
3
5
g
9.00
300–2000
5
c
l
c
c
c
5.46 + 0.002466T
7.13
9.65 + 0.00208T
12.9 + 0.00090T
51.3
273–594
594–973
273–2086
273–1273
293
1
5
?
?
?
c
c
c
c
c
c
c
c
c
c, anorthite
gls
c, diopside
gls
c, wollastonite
c, pseudowollastonite
gls
c
c
c
c
5.31 + 0.00333T
6.29 + 0.00140T
16.9 + 0.00386T
19.68 + 0.01189T - 307600/T 2
14.7 + 0.00380T
40.1
33
10.00 + 0.00484T - 108000/T 2
21.4
63.13 + 0.01500T - 1537000/T 2
67.41 + 0.01048T - 1874000/T 2
54.46 + 0.005746T - 1500000/T 2
51.68 + 0.009724T - 1308000/T 2
27.95 + 0.002056T - 745600/T 2
25.48 + 0.004132T - 488100/T 2
23.16 + 0.009672T - 487100/T 2
39.5
18.52 + 0.02197T - 156800/T 2
46.8
27.9
273–673
673–873
273–1055
273–1033
273–1651
299–372
273–297
273–1173
276–373
273–1673
273–973
273–1573
273–973
273–1573
273–1673
273–973
287–371
273–1373
282–373
292–322
2
2
?
3
?
?
?
2
?
1
1
1
1
1
1
1
?
5
?
?
c, graphite
c, diamond
g
g
g
l
2.673 + 0.002617T - 116900/T 2
2.162 + 0.003059T - 130300/T 2
5.34 + 0.0115T
6.60 + 0.00120T
10.34 + 0.00274T - 195500/T 2
18.4
273–1373
273–1313
273–1200
273–2500
273–1200
293
2
3
2
1½
1½
?
c
c
c
c
c
5.88 + 0.00123T
15.1
96
66.4
131.6
273–908
273–373
273–297
273–373
273–319
?
?
?
?
?
c
l
g
c
c
c
c
1.96 + 0.0182T
8.00
4.97
12.6 + 0.00259T
11.7 + 0.00309T
11.3 + 0.00285T
11.6 + 0.00268T
273–301
302
All
273–909
273–752
273–957
273–894
3
3
0
?
?
?
?
1½
g
8.28 + 0.00056T
273–2000
c
l
c
c
c
c
c
4.84 + 0.00295T
9.70
23
26.0 + 0.00400T
12.3 + 0.00120T
19.2 + 0.00184T
67.4
273–1823
1823–1923
286–319
273–2263
273–1383
273–949
273–373
5
10
?
?
?
?
?
c
l
c
c
c
c
c
5.12 + 0.00333T
8.40
32.9
11.7 + 0.00156T
15.83 + 0.00950T
10.6 + 0.00251T
96
273–1763
1763–1873
283–373
273–1464
273–903
273–1373
286–303
5
5
?
?
2
?
?
(Continued )
2-129
2-130
PHYSICAL AnD CHEMICAL DATA
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Copper7
Cu
CuAl
CuAl2
Cu3Al
CuI
CuI2
CuO
CuO⋅SiO2⋅H2O
CuS
Cu2S
CuS⋅FeS
Cu2Sb
Cu2Sb
Cu2Se
Cu3Si
CuSO4
CuSO4⋅H2O
CuSO4⋅3H2O
CuSO4⋅5H2O
Fluorine8
F2
Gallium
Ga2O3
Ga2(SO4)3
Germanium4
Ge
Gold
Au
AuSb2
Helium9
He
Hydrogen10
H
H2
HBr
HCl
HI
H2O
H2S
H2S2O7
Indium
In
Iodine
I2
Iridium
Ir
Iron4
Fe
FeAs2
Fe3C
FeCO3
FeO
Fe2O3
Fe3O4
Fe2O3⋅3H2O
FeS
FeS2
FeSi
Fe2SiO4
FeSO4
Fe2(SO4)3
FeSO4⋅4H2O
FeSO4⋅7H2O
Krypton
Kr
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
273–1357
1357–1573
273–733
273–773
273–775
273–675
274–328
273–810
293–323
273–1273
273–376
376–1173
292–321
273–573
273–693
273–383
383–488
273–1135
282
282
282
282
1
3
2
2
2
?
?
2
?
?
3
2
?
2
2
5
5
?
?
?
?
?
c
l
c
c
c
c
c
c
c
c
c, α
c, β
c
c
c
c, α
c, β
c
c
c
c
c
5.44 + 0.001462T
7.50
9.88 + 0.00500T
16.78 + 0.00366T
19.61 + 0.01054T
12.1 + 0.00286T
20.1
10.87 + 0.003576T - 150600/T 2
29
10.6 + 0.00264T
9.38 + 0.0312T
20.9
24
13.73 + 0.01350T
21.79 + 0.00900T
20.85
20.35
20.3 + 0.00587T
24.1
31.3
49.0
67.2
g
6.50 + 0.00100T
300–3000
5
c
c
18.2 + 0.0252T
62.4
273–923
273–373
?
?
273–1336
1336–1573
273–628
628–713
2
5
1
?
c
c
l
c, α
c, βγ
5.61 + 0.00144T
7.00
17.12 + 0.00465T
11.47 + 0.01756T
g
4.97
All
0
g
g
g
g
g
l
g
g
c
l
4.97
6.62 + 0.00081T
6.80 + 0.00084T
6.70 + 0.00084T
6.93 + 0.00083T
See Tables 2-72 and 2-136
8.22 + 0.00015T + 0.00000134T 2
7.20 + 0.00360T
27
58
All
273–2500
273–2000
273–2000
273–2000
0
2
2
1½
2
300–2500
300–600
281
308
?
8
?
?
g
9.00
300–2000
5
c
5.50 + 0.00148T
273–1873
1
c, α
c, β
c, γ
c, δ
l
c
c
c
c
c
c
c
c, α
c, β
c
c
c
c
c
c
c
4.13 + 0.00638T
6.12 + 0.00336T
8.40
10.0
8.15
17.8
25.17 + 0.00223T
22.7
12.62 + 0.001492T - 76200/T 2
24.72 + 0.01604T - 423400/T 2
41.17 + 0.01882T - 979500/T 2
47.8
2.03 + 0.0390T
12.05 + 0.00273T
10.7 + 0.01336T
10.54 + 0.00458T
33.57 + 0.01907T - 879700/T 2
22
66.2
63.6
96
273–1041
1041–1179
1179–1674
1674–1803
1803–1873
283–373
273–1173
293–368
273–1173
273–1097
273–1065
286–373
273–411
411–1468
273–773
273–903
273–1161
293–373
273–373
282
291–319
3
3
5
5
5
?
10
?
2
2
2
?
5
3
?
2
2
?
?
?
?
g
4.97
c
All
0
SPECIFIC HEATS
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Lanthanum
La
La2O3
La2(MoO4)3
La2(SO4)3
La2(SO4)3⋅9H2O
Lead4
Pb
Pb3(AsO4)2
PbB2O4
PbB4O7
PbBr2
PbCl2
2PbCl2⋅NH4Cl
PbCO3
PbCrO4
PbF2
PbI2
PbMoO4
Pb(NO3)2
PbO
PbO2
Pb2P2O7
PbS
PbSO4
PbS2O3
PbWO4
Lithium
Li
LiBr
LiBr⋅H2O
LiCl
LiCl⋅H2O
LiF
LiI
LiI⋅H2O
LiI⋅2H2O
LiI⋅3H2O
LiNO3
Magnesium4
Mg
MgAg
Mg4Al3
MgAu
Mg2Au
Mg3Au
MgCl2
MgCl2⋅6H2O
MgCO3
MgCu2
Mg2Cu
MgNi2
MgO
MgO⋅Al2O3
MgO⋅SiO2
6MgO⋅MgCl2⋅8B2O3
Mg(OH)2
Mg3Sb2
Mg2Si
MgSO4
MgSO4⋅H2O
MgSO4⋅6H2O
MgSO4⋅7H2O
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
c
c
c
c
c
5.91 + 0.00100T
22.6 + 0.00544T
86
66.9
152
273–1009
273–2273
273–307
273–373
273–319
?
?
?
?
?
c
l
c
c
c
c
l
c
l
c
c
c
c
c
l
c
c
c
c
c
c
c
c
c
5.77 + 0.00202T
6.8
65.5
26.5
41.4
18.13 + 0.00310T
27.4
15.88 + 0.00835T
27.2
53.1
21.1
29.1
16.5 + 0.00412T
18.66 + 0.00293T
32.3
30.4
36.4
10.33 + 0.00318T
12.7 + 0.00780T
48.3
10.63 + 0.00401T
26.4
29
35
273–600
600–1273
286–370
288–371
289–371
273–761
761–860
273–771
771–851
293
286–320
292–323
273–1091
273–648
648–776
292–322
286–320
273–544
273–?
284–371
273–873
293–372
293–373
273–297
2
5
?
?
?
2
10
2
10
?
?
?
?
2
20
?
?
2
?
?
3
?
?
?
c
g
c
c
c
c
c
c
c
c
c
c
l
0.68 + 0.0180T
4.97
11.5 + 0.00302T
22.6
11.0 + 0.00339T
23.6
8.20 + 0.00520T
12.5 + 0.00208T
23.6
32.9
43.2
9.17 + 0.0360T
26.8
273–459
All
273–825
278–318
273–887
279–360
273–1117
273–723
277–359
277–345
277–347
273–523
523–575
10
0
?
?
?
?
?
?
?
?
?
5
5
c
l
c
c
c
c
c
c
c
c
c
c
c
c
c
c, amphibole
c, pyroxene
gls
c, α
c, β
c
c
c
c
c
c
c
6.20 + 0.00133T - 67800/T 2
7.4
10.58 + 0.00412T
34.4 + 0.0198T
11.3 + 0.00189T
16.2 + 0.00451T
21.2 + 0.00614T
17.3 + 0.00377T
77.1
16.9
14.96 + 0.00776T
15.5 + 0.00652T
15.87 + 0.00692T
10.86 + 0.001197T - 208700/T 2
28
25.60 + 0.004380T - 674200/T 2
23.35 + 0.008062T - 558800/T 2
23.30 + 0.007734T - 542000/T 2
58.7 + 0.408T
107.2 + 0.2876T
18.2
28.2 + 0.00560T
15.4 + 0.00415T
26.7
33
80
89
273–923
923–1048
273–905
273–736
273–1433
273–1073
273–1103
273–991
292–342
290
273–903
273–843
273–903
273–2073
288–319
273–1373
273–773
273–973
273–538
538–623
292–323
273–1234
273–1343
296–372
282
282
291–319
1
10
2
?
?
?
?
?
?
?
3
?
2
2
?
1
1
1
5
5
?
?
?
?
?
?
?
(Continued )
2-131
2-132
PHYSICAL AnD CHEMICAL DATA
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
c, α
c, β
c, γ
l
c
c
c
c
c
c
c
c
c
c
3.76 + 0.00747T
5.06 + 0.00395T
4.80 + 0.00422T
11.0
16.2 + 0.00520T
7.79 + 0.0421T + 0.0000090T 2
7.43 + 0.01038T - 0.00000362T 2
10.33 + 0.0530T - 0.0000257T 2
19.25 + 0.0538T - 0.0000209T 2
1.92 + 0.0471T - 0.0000297T 2
31
10.21 + 0.00656T - 0.00000242T 2
27.5
78
273–1108
1108–1317
1317–1493
1493–1673
273–923
273–773
273–1923
273–1173
273–1773
273–773
291–322
273–1883
293–373
290–319
5
5
5
10
?
?
?
?
?
?
?
?
?
?
l
g
g
c
c
c
c
c, α
c, β
c
c
c
6.61
4.97
9.00
11.05 + 0.00370T
15.3 + 0.0103T
25
11.4 + 0.00461T
17.4 + 0.004001T
20.2
11.5
10.9 + 0.00365T
31.0
273–630
All
300–2000
273–798
273–553
285–319
273–563
273–403
403–523
278–371
273–853
273–307
1
0
5
?
?
?
?
3
3
?
?
?
c
c
c
5.69 + 0.00188T - 50300/T 2
15.1 + 0.0121T
19.7 + 0.00315T
273–1773
273–1068
273–729
5
?
?
g
4.97
All
0
c, α
c, β
l
c
c
c
c
c
c
c
c
4.26 + 0.00640T
6.99 + 0.000905T
8.55
11.3 + 0.00215T
9.25 + 0.00640T
15.8 + 0.00329T
10.0 + 0.00312T
20.78 + 0.0102T
33.4
82
11.00 + 0.00433T
g
g
c
c, α
c, β
c
c
c
g
6.50 + 0.00100T
6.70 + 0.00630T
22.8
9.80 + 0.0368T
5.0 + 0.0340T
17.8
31.8
51.6
8.05 + 0.000233T - 156300/T 2
300–3000
300–800
274–328
273–457
457–523
273–328
273–293
275–328
300–5000
3
1½
?
5
5
?
?
?
2
c
5.686 + 0.000875T
273–1877
1
300–5000
1
State†
Substance
Manganese
Mn
MnCl2
MnCO3
MnO
Mn2O3
Mn3O4
MnO2
Mn2O3⋅H2O
MnS
MnSO4
MnSO4⋅5H2O
Mercury11
Hg
Hg2
HgCl
HgCl2
Hg(CN)2
HgI
HgI2
HgO
HgS
Hg2SO4
Molybdenum
Mo
MoO3
MoS2
Neon12
Ne
Nickel4
Ni
NiO
NiS
Ni2Si
NiSi
Ni3Sn
NiSO4
NiSO4⋅6H2O
NiTe
Nitrogen13
N2
NH3
NH4Br
NH4Cl
NH4I
NH4NO3
(NH4)2SO4
NO
Osmium
Os
Oxygen14
O2
Palladium
Pd
Phosphorus
P
PCl3
P4O10
Platinum4
Pt
Potassium
K
273–626
626–1725
1725–1903
273–1273
273–597
273–1582
273–1273
273–904
293–373
291–325
273–700
2
2
5
10
?
3
?
?
2
?
?
2
g
8.27 + 0.000258T - 187700/T
c
5.41 + 0.00184T
273–1822
2
c, yellow
c, red
l
l
c
g
5.50
0.21 + 0.0180T
6.6
28.7
15.72 + 0.1092T
73.6
273–317
273–472
317–373
284–371
273–631
631–1371
5
10
10
?
2
3
c
5.92 + 0.00116T
273–1873
1
c
l
5.24 + 0.00555T
7.7
273–336
336–373
5
5
SPECIFIC HEATS
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Potassium—(Cont.)
K
K2
KAsO3
KBO2
K2B4O7
KBr
KCl
KClO3
KClO4
2KCl⋅CuCl2⋅2H2O
2KCl⋅PtCl4
2KCl⋅SnCl4
2KCl⋅ZnCl2
2KCN⋅Zn(CN)2
K2CO3
K2CrO4
K2Cr2O7
KF
K4Fe(CN)6
K4Fe(CN)6⋅3H2O
KH2AsO4
KH2PO4
KHSO4
KMnO4
KNO3
K2O⋅Al2O3⋅3SiO2
K4P2O7
K2SO4
K2S2O3
K2SO4⋅Al2(SO4)3⋅24H2O
K2SO4⋅Cr2(SO4)3⋅24H2O
K2SO4⋅MgSO4⋅6H2O
K2SO4⋅NiSO4⋅6H2O
K2SO4⋅ZnSO4⋅6H2O
Prometheum
Pr
Radon
Rn
Rhenium
Re
Rhodium
Rh
Rubidium
Rb
RbBr
RbCl
Rb2CO3
RbF
RbI
Scandium
Sc2O3
Sc2(SO4)3
Selenium
Se
Silicon
Si
SiC
SiCl4
SiO2
Silver4
Ag
g
g
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
l
c
c
c
c
c
c
c
c
c
l
c, orthoclase
gls, orthoclase
c, microcline
gls, microcline
c
c
c
c
c
c
c
c
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
4.97
9.00
25.3
12.6 + 0.0126T
51.3
11.49 + 0.00360T
10.93 + 0.00376T
25.7
26.3
63
55
54.5
43.4
57.4
29.9
35.9
42.80 + 0.0410T
96.9
10.8 + 0.00284T
80.1
114.5
32
28.3
30
28
6.42 + 0.0530T
28.8
29.5
69.26 + 0.00821T - 2331000/T 2
69.81 + 0.01053 - 2403000/T 2
65.65 + 0.01102T - 1748000/T 2
64.83 + 0.01438T - 1641000/T 2
63.1
33.1
37
352
324
106
107
120
Range of
temperature,
K
Uncertainty,
%
All
300–2000
290–372
273–1220
290–372
273–543
273–1043
289–371
287–318
292–323
286–319
292–323
279–319
277–319
296–372
289–371
273–671
671–757
273–1129
273–319
273–310
289–319
290–320
292–324
287–318
273–401
401–611
611–683
273–1373
273–1373
273–1373
273–1373
290–371
287–371
293–373
292–322
292–324
292–323
289–319
293–317
0
5
?
?
?
2
2
?
?
?
?
?
?
?
?
?
5
5
?
?
?
?
?
?
?
10
5
10
1½
1½
1½
1½
?
?
?
?
?
?
?
?
c
g
4.97
All
0
c
6.30 + 0.00053T
273–2273
?
c
5.40 + 0.00219T
273–1877
2
c
l
c
c
c
c
c
3.27 + 0.0131T
7.85
11.6 + 0.00255T
11.5 + 0.00249T
28.4
11.3 + 0.00256T
11.6 + 0.00263T
273–312
312–373
273–954
273–987
291–320
273–1048
273–913
2
5
?
?
?
?
?
c
c
21.1
62.0
273–373
273–373
?
?
c
l
4.53 + 0.00550T
8.35
273–490
490–570
2
3
c
c
l
c, quartz, α
c, quartz, β
c, cristobalite, α
c, cristobalite, β
gls
5.74 + 0.000617T - 101000/T 2
8.89 + 0.00291T - 284000/T 2
32.4
10.87 + 0.008712T - 241200/T 2
10.95 + 0.00550T
3.65 + 0.0240T
17.09 + 0.000454T - 897200/T 2
12.80 + 0.00447T - 302000/T 2
273–1174
273–1629
293–373
273–848
848–1873
273–523
523–1973
273–1973
2
2
?
1
3½
2½
2
3½
c
l
5.60 + 0.00150T
8.2
273–1234
1234–1573
1
3
(Continued )
2-133
2-134
PHYSICAL AnD CHEMICAL DATA
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Silver—(Cont.)
Ag3Al
Ag2Al
AgAl12
AgBr
AgCl
AgCNO
AgI
AgNO3
Ag3PO4
Ag2S
Ag3Sb
Ag2Se
Sodium15
Na
NaBO2
Na2B4O7
Na2B4O7⋅10H2O
NaBr
NaCl
NaClO3
NaCNO
Na2CO3
NaF
Na2HPO4⋅7H2O
Na2HPO4⋅12H2O
NaI
NaNO3
Na2O⋅Al2O3⋅3SiO2
NaPO3
Na4P2O7
Na2SO4
Na2S2O3
Na2S2O3⋅5H2O
Sodium-potassium alloys15
Strontium
SrBr2
SrBr2⋅H2O
SrBr2⋅6H2O
SrCl2
SrCl2⋅H2O
SrCl2⋅2H2O
SrCO3
SrI2
SrI2⋅H2O
SrI2⋅2H2O
SrI2⋅6H2O
SrMoO4
Sr(NO3)2
SrSO4
Sulfur16
S
S2
S2Cl2
SO2
Tantalum
Ta
Tellurium
Te
Thallium
Tl
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
273–902
273–903
273–768
273–703
703–836
273–728
728–806
273–353
273–423
273–433
433–482
482–541
293–325
273–448
448–597
273–694
273–406
406–460
2
2
5
6
5
2
5
?
6
2
5
5
?
5
5
5
5
5
273–371
371–451
All
273–1239
289–371
292–323
273–543
273–1074
1073–1205
273–528
528–572
273–353
288–371
273–1261
275–307
275–307
273–936
273–583
583–703
273–1373
273–1173
290–319
290–371
289–371
273–307
273–307
1½
2
0
?
?
?
2
2
3
3
5
?
?
?
?
?
?
5
10
1
1
?
?
?
?
?
c
c
c
c
l
c
l
c
c, α
c, α
c, β
l
c
c, α
c, β
c
c, α
c, β
22.56 + 0.00570T
16.85 + 0.00450T
58.62 + 0.0575T
8.58 + 0.0141T
14.9
9.60 + 0.00929T
14.05
18.7
8.58 + 0.0141T
18.83 + 0.0160T
25.7
30.2
37.5
18.8
21.8
19.53 + 0.0160T
20.2
20.4
c
l
g
c
c
c
c
c
l
c
l
c
c
c
c
c
c
c
l
c, albite
gls
c
c
c
c
c
l
5.01 + 0.00536T
7.50
4.97
10.4 + 0.0199T
47.9
147
11.74 + 0.00233T
10.79 + 0.00420T
15.9
9.48 + 0.0468T
31.8
13.1
28.9
10.4 + 0.00289T
86.6
133.4
12.5 + 0.00162T
4.56 + 0.0580T
37.2
63.78 + 0.01171T - 1678000/T 2
61.25 + 0.01768T - 1545000/T 2
22.1
60.7
32.8
34.9
86.2
c
c
c
c
c
c
c
c
c
c
c
c
c
c
18.1 + 0.00311T
28.9
82.1
18.2 + 0.00244T
28.7
38.3
21.8
18.6 + 0.00304T
28.5
39.1
84.9
37
38.3
26.2
273–923
277–370
276–327
273–1143
276–365
277–366
281–371
273–783
276–363
275–336
275–333
273–297
290–320
293–369
?
?
?
?
?
?
?
?
?
?
?
?
?
?
c, rhombic
c, monoclinic
g
l
g
3.63 + 0.00640T
4.38 + 0.00440T
8.58 + 0.00030T
27.5
7.70 + 0.00530T - 0.00000083T 2
273–368
368–392
300–2500
273–332
300–2500
3
3
5
?
2½
c
5.91 + 0.00099T
273–1173
2
c
5.19 + 0.00250T
273–600
3
c, α
c, β
5.32 + 0.00385T
8.12
273–500
500–576
1
1
SPECIFIC HEATS
TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued )
State†
Substance
Thallium—(Cont.)
Tl
TlBr
TlCl
Thorium
Th
ThO2
Th(SO4)2
Tin4
Sn
SnAu
SnCl2
SnCl4
SnO
SnO2
SnPt
SnS
SnS2
Titanium
Ti
TiCl4
TiO2
Tungsten
W
WO3
Uranium
U
U3O8
Vanadium
V
Xenon
Xe
Zinc4
Zn
ZnCl2
ZnO
ZnS
ZnSb
ZnSO4
ZnSO4⋅H2O
ZnSO4⋅6H2O
ZnSO4⋅7H2O
Zirconium
ZrO2
ZrO2⋅SiO2
1
Heat capacity at constant pressure
(T = K; 0°C = 273.1 K),
cal/(mol⋅K)
Range of
temperature,
K
Uncertainty,
%
l
c
l
c
l
7.12
12.53 + 0.00100T
16.0
12.56 + 0.00088T
14.2
576–773
273–733
733–800
273–700
700–803
3
10
10
5
10
c
c
c
6.40
14.6 + 0.00507T
41.2
273–373
273–1273
273–373
?
?
?
c
l
c
c
l
c
c
c
c
c
5.05 + 0.00480T
6.6
11.79 + 0.00233T
16.2 + 0.00926T
38.4
9.40 + 0.00362T
13.94 + 0.00565T - 252000/T 2
11.49 + 0.00190T
12.1 + 0.00165T
20.5 + 0.00400T
273–504
504–1273
273–581
273–520
286–371
273–1273
273–1373
273–1318
273–1153
273–873
2
10
1
?
?
?
?
1
?
?
c
l
c
8.91 + 0.00114T - 433000/T 2
35.7
11.81 + 0.00754T - 41900/T 2
273–713
285–372
273–713
3
?
3
c
c
5.65 + 0.00866
16.0 + 0.00774T
273–2073
273–1550
1
?
c
c
6.64
59.8
273–372
276–314
?
?
c
5.57 + 0.00097T
273–1993
?
g
4.97
All
0
c
l
c
c
c
c
c
c
c
c
5.25 + 0.00270T
7.59 + 0.00055T
15.9 + 0.00800T
11.40 + 0.00145T - 182400/T 2
12.81 + 0.00095T - 194600/T 2
11.5 + 0.00313T
28
34.7
80.8
100.2
273–692
692–1122
273–638
273–1573
273–1173
273–810
293–373
282
282
273–307
1
3
?
1
5
?
?
?
?
?
c
c
11.62 + 0.01046T - 177700/T 2
26.7
273–1673
297–372
5
?
See also Table 2-71. Data to 298 K are also given by Scott, Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959.
For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960.
Stalder, NACA Tech. Note 4141, 1957 (Fig. 5), gives data from 400 to 2600°R.
4
See also Table 2-71.
5
For data from 400 to 5500°R see Stalder, NACA Tech. Note 4141, 1975 (Fig. 4).
6
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960.
7
For data from 400 to 2350°R see Stalder, NACA Tech. Note 4141, 1957.
8
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960.
9
For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960.
10
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960.
11
See also Table 2-71. Douglas, Ball, et al., Bur. Stand. J. Res., 46 (1951): 334; Busey and Giaque, J. Am. Chem. Soc., 75 (1953): 806; Sheldon,
ASME Pap. 49-A-30, 1949.
12
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960.
13
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960.
14
For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. Ozone: For liquid see Brabets and Waterman, J. Chem. Phys.,
28 (1958): 1212.
15
For data on liquid Na-K alloys to 1500°F and for liquid Na to 1460°F, see Lubarsky and Kaufman, NACA Rep. 1270, 1956.
16
See also Evans and Wagman, Bur. Stand. J. Res. 49 (1952): 141; Gratch, OTS PB 124957, 1950; Guthrie, Scott et al., J. Am. Chem. Soc.,
76 (1954): 1488.
2
3
2-135
2-136
PHYSICAL AnD CHEMICAL DATA
TABLE 2-71 Specific Heat [kJ/(kg·K)] of Selected Elements
Temperature, K
Symbol
4
6
8
10
20
40
60
80
100
200
250
300
400
600
800
Al
Be
Bi
Cr
Co
0.00026
0.00008
0.00054
0.00016
0.00036
0.00050
0.00088
0.214
0.357
0.00541
0.00050
0.00085
0.0089
0.0014
0.0340
0.0021
0.0048
0.0775
0.00220
0.00029
0.00059
0.00140
0.00028
0.01040
0.00081
0.00121
0.0729
0.0107
0.0404
0.092
0.059
0.110
0.102
0.127
0.184
0.481
0.195
0.109
0.190
0.234
0.797
1.109
0.120
0.382
0.376
0.859
1.537
0.121
0.424
0.406
0.902
1.840
0.122
0.450
0.426
0.949
2.191
0.123
0.501
0.451
1.042
2.605
0.142
0.565
0.509
1.134
2.823
0.136
0.611
0.543
Cu
Ge
Au
Ir
Fe
0.00011
0.00024
0.00018
0.00047
0.00048
0.00037
0.00126
0.137
0.108
0.084
0.203
0.153
0.100
0.00061
0.00090
0.0076
0.0129
0.0163
0.0021
0.0039
0.059
0.0619
0.0569
0.00038
0.00086
0.00081
0.00255
0.00032
0.00127
0.0276
0.086
0.154
0.254
0.192
0.109
0.090
0.216
0.357
0.286
0.124
0.122
0.384
0.377
0.305
0.127
0.128
0.422
0.386
0.323
0.129
0.131
0.450
0.396
0.343
0.131
0.133
0.491
0.431
0.364
0.136
0.140
0.555
0.448
0.377
0.141
0.146
0.692
Pb
Mg
Hg
Mo
Ni
0.00075
0.00034
0.00417
0.00011
0.00054
0.00242
0.00080
0.01420
0.00019
0.00086
0.00747
0.00155
0.01820
0.00032
0.00121
0.01350
0.00172
0.02250
0.00050
0.00178
0.0531
0.0148
0.0515
0.0029
0.0058
0.0944
0.138
0.0895
0.0236
0.0380
0.108
0.336
0.107
0.061
0.103
0.114
0.513
0.116
0.105
0.173
0.118
0.648
0.121
0.140
0.232
0.125
0.929
0.136
0.223
0.383
0.127
0.985
0.141
0.241
0.416
1.129
1.005
0.139
0.248
0.444
0.132
1.082
0.136
0.261
0.490
0.142
1.177
0.135
0.280
0.590
1.263
0.104
0.292
0.530
Pt
Ag
Sn
Zn
0.00019
0.00016
0.00024
0.00011
0.00028
0.00035
0.00127
0.00029
0.00067
0.00093
0.00423
0.00096
0.00112
0.00186
0.00776
0.00250
0.0077
0.0159
0.0400
0.0269
0.0382
0.0778
0.108
0.123
0.069
0.133
0.149
0.205
0.088
0.166
0.173
0.258
0.101
0.187
0.189
0.295
0.127
0.225
0.214
0.366
0.132
0.232
0.220
0.380
0.134
0.236
0.222
0.389
0.136
0.240
0.245
0.404
0.140
0.251
0.257
0.435
0.146
0.264
0.257
0.479
TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)]
2-137
Eqn
Cmpd.
no.
100
100
100
100
100
100
100
100
100
100
100
114
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
114
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
C1
C2
C3
152.99
10,2300
13,9640
26,0050
13,5600
73,381
–122,020
103,090
55,300
109,750
–214,460
61.289
150,940
134,390
161,440
129,440
162,940
119,780
-5,480
66,950
156,130
–334,997
87,500
100,320
121,770
179,400
121,600
95,588
102,760
135,150
128,860
191,030
55.136
42.152
191,200
533,390
182,050
126,680
112,760
111,850
182,470
232,190
197,890
136,340
194,170
237,700
154,800
-8,304,300
85,600
65.429
598.64
128.7
-320.8
-565.43
-177
60.042
3082.7
-247.8
300
-108.61
9185.1
80925
93.455
-1989.4
260.66
-169.5
-344.94
180.34
647.12
333.33
454.49
3644.21
480
346.89
429.3
-667.11
-9.45
-110.94
-230.08
-311.14
-323.1
-1675
314200
324580
-730.4
-4986.2
-1611
-65.47
-104.7
384.52
-13.912
-804.35
-491.54
-300.4
-532.38
-746.4
-239.75
104370
-122
28723
-0.89481
0.8985
1.1035
0.2837
-15.895
1.0343
0.35246
-106.12
799.4
0.23602
11.043
C4
C5
0.000689
0.027732
0.41616
-2651
0.64781
0.85562
-7.77514
1.0701
0.358
0.41864
0.51796
0.97007
1.015
12.5
280.19
517.35
2.2998
18.908
11.963
-0.64
0.5214
0.72897
2.7063
1.7219
1.0216
1.4286
1.829
0.68616
-433.33
0.5605
-847.39
0.00591102
-0.0001523
0.000032
-0.03874
1413.9
1449.5
0.000046121
-0.02
-0.037454
0.002912
0.000045027
-0.0023017
-0.0012499
0.60052
-0.001452
1959.6
0.000002008
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
149.78
354.15
289.81
200.15
178.45
229.32
192.40
253.00
286.15
189.63
75.00
203.15
298.15
83.78
403.00
278.68
278.68
258.27
395.45
260.28
321.35
257.85
275.65
243.95
342.20
265.90
293.15
154.25
179.44
136.95
165.00
134.86
220.00
196.15
183.85
158.45
87.80
134.26
167.62
298.15
185.30
157.46
133.02
147.43
176.80
267.95
161.30
220.00
161.11
68.15
0.69743
1.47880
1.22130
1.91090
1.16960
0.87150
0.80208
1.06600
1.41150
1.01830
0.53065
0.75753
1.99780
0.45230
2.66490
1.32510
1.33260
1.66360
2.50420
1.53710
3.02180
1.89060
2.19810
1.84940
2.68680
0.77675
1.49600
0.88436
0.78152
1.10340
1.03330
1.12720
1.55900
0.62506
1.34650
1.38480
1.10150
1.13400
1.09860
2.26490
2.04920
1.63650
1.60030
1.14260
1.44700
1.69020
1.33980
0.78265
0.75774
0.59115
294.15
571.00
391.05
412.70
329.44
354.81
250.00
379.50
375.00
400.00
115.00
401.15
484.20
135.00
563.15
353.24
500.00
442.29
450.00
464.15
640.00
478.60
458.15
472.03
533.37
331.90
495.08
311.49
280.15
290.00
350.00
400.00
670.00
670.00
391.00
372.90
380.00
350.00
274.03
399.26
400.00
390.00
370.00
298.15
347.94
436.42
390.74
290.00
552.00
132.00
0.98820
1.75790
1.51590
2.14650
1.32710
0.94685
0.88530
1.58010
1.67800
1.22700
0.71317
4.18470
2.51530
0.67080
3.08230
1.50400
2.04380
1.99540
2.85720
2.21670
4.47000
2.76170
3.07410
2.64060
3.50750
0.75866
2.04670
1.01650
0.78955
1.22790
1.41480
2.22370
5.20450
5.24370
2.57210
2.66210
1.81030
1.50220
1.23220
2.65370
2.93540
1.93590
1.88440
1.37590
1.81880
2.60310
1.65880
1.66030
1.31250
6.47990
(Continued )
2-138
TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued )
Eqn
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
100
100
Cmpd.
no.
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
Name
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Formula
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
CAS
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
Mol. wt.
153.8227
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
C1
-752,700
104,600
63,936
-1,307,500
118,380
124,850
107,900
134,733
69,362
-246,700
-185,150
259,980
61,723
77,461
101,920
-220,600
-40,000
6,110.4
105,850
122,530
125,380
89,952
177,560
218,480
278,620
219,840
4,988,500
417,440
314,570
276,900
149,400
200,560
202,580
270,720
114,880
93,093
133,950
126,340
179,170
98,968
144,560
111,560
184,200
101,330
44,400
238,520
67.155
82,577
263,980
C2
C3
8966.1
-500.6
46.35
15338
-248.915
-166.34
-330.13
-176.332
215.01
3256.8
3148
-1112.3
494.81
111.51
-215.81
3118.3
853
600.94
-60
-403.8
-349.7
-196.63
-179.12
374.14
-197.91
140.41
-52898
-1616.5
-160.93
-371.23
-30.394
2.2851
-0.1623
-53.974
0.68074
0.43209
0.808
0.55966
0.034455
-7.4202
-8.0367
4.9427
0.0060467
0.007254
-0.0054367
0.8103
-9.4216
0.010687
-231.8
-491.44
-726.3
-259.83
187.25
183.97
-24.84
-94.63
-444.74
-62.941
-53.605
149.44
286
243.18
1301
-1038.4
105580
109.85
-1791.1
0.5946
0.9187
1.3377
0.95427
0.68
1.7344
1.143
0.65237
0.76723
0.11851
1.0737
0.9968
216.35
5.3948
0.95561
1.5774
C4
0.063483
-0.0010975
-0.37538
-0.004348
0.2314
0.48191
0.32
0.93009
0.23265
0.30617
-5.5
4.0587
310.21
4.3666
C5
0.008763
-0.0044691
-490.54
0.00023674
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
250.33
89.56
172.12
227.95
136.75
233.15
175.43
150.35
200.00
285.39
304.20
307.93
177.14
245.25
190.00
279.69
296.60
290.00
169.67
179.28
138.13
150.00
189.64
285.00
243.51
304.75
280.00
206.89
247.56
229.15
1.27630
0.78095
0.67106
1.36170
0.97071
1.09560
0.74852
1.20870
1.12360
2.18950
2.32970
2.27400
1.49370
1.04810
0.90168
1.48360
2.13000
1.80380
1.15250
0.99559
0.98884
0.75136
1.71180
3.34740
2.94090
3.55210
3.53690
2.75410
3.33300
2.74660
388.71
145.10
239.12
360.00
298.15
366.48
303.15
319.67
308.85
400.00
400.00
400.00
425.56
253.82
298.15
400.00
434.00
489.75
356.12
322.40
317.38
298.15
431.95
481.65
460.00
543.15
503.15
494.00
512.35
447.15
1.63740
0.80073
0.65739
1.81010
1.04680
1.21920
0.82076
1.35560
1.35770
2.55780
2.52430
2.57940
2.72290
1.05760
1.09610
2.03230
3.30200
3.00420
1.70720
1.35840
1.29530
0.89318
2.43340
4.26180
4.14780
5.90170
5.01740
4.11250
4.82970
4.26290
210.15
282.85
240.00
175.30
248.39
273.15
326.14
176.19
237.49
180.00
192.50
275.00
301.15
223.35
156.92
181.95
154.56
179.60
200.00
1.26950
1.35060
1.05320
2.54500
1.61390
1.60610
1.77110
1.19600
1.26010
0.95176
1.45590
1.52660
2.70330
1.55640
1.46980
1.57030
0.99146
1.02310
0.80424
381.15
410.00
370.10
450.00
400.00
528.75
513.56
330.45
356.59
320.00
361.25
369.52
541.54
328.60
460.00
322.08
359.98
283.65
250.00
1.47430
1.53500
1.17010
3.47040
1.89780
2.55060
2.48290
1.30010
1.38850
1.02650
1.65150
1.66780
3.39080
1.81240
3.32020
1.75790
1.68740
1.13740
0.89118
2-139
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
149
150
151
152
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
F2
C6H5F
C2H5F
CH3F
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
7782-41-4
462-06-6
353-36-6
593-53-3
101.19
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
37.9968064
96.1023032
48.0595
34.03292
98,434
163,000
179,270
187,790
199,930
88,153
-214,870
129,450
134,500
150,130
155,560
171,580
110,100
147,900
146,420
206,560
131,810
146,950
240,300
195,251
956,860
134,160
49,120
508,210
352,720
44.009
102,640
226,230
121,700
154,040
124,500
56,359
82,434
132,360
178,520
247,390
184,440
35,540
46,848
144,710
80,000
207,670
146,040
106,250
229,250
134,670
76,330
103,680
173,110
-94,585
1,724,400
148,640
65,106
141,790
429.04
-4.5
28.37
-313.41
-191.5
124.16
3787.2
18.5
8.765
-62.38
-145.26
-256.67
-157.47
-106
59.2
325.75
-380.06
-595
419.918
-5559.9
447.67
562.24
-1368.7
807.32
89718
-139.63
-624.8
38.993
-142.29
370.6
603.02
422.45
72.74
-518.35
-4428
-150.2
436.78
205.35
-758.87
223.6
-17.907
458.22
292.15
-404.54
-234.39
400.1
726.3
-697.18
7529.9
-59924
-202.58
103.44
-814.32
0.62
0.5375
1.1023
0.87664
-13.781
0.608
0.81151
0.8851
1.0932
0.5727
0.51853
0.384
0.604
0.016924
1.2035
1.013
-0.00084787
9.6124
3.1015
0.2122
918.77
-0.030341
1.472
–1886
0.0020386
0.80539
0.20992
0.64738
2.3255
40.936
0.37044
-0.18486
-0.0016818
-0.1697
2.8261
-0.003064
0.00026816
1.0493
1.1382
0.59656
-2.6047
3.7615
-139.6
537.85
0.66374
0.67161
2.2673
0.0040957
-0.005289
1.1301
-0.0074083
0
1.6179E-06
-0.0033241
0.000019119
275.00
187.65
204.81
159.95
226.10
240.91
180.96
145.19
239.66
223.16
184.99
188.44
131.65
273.82
90.00
274.16
298.15
174.88
291.67
413.79
284.95
300.03
277.90
263.57
309.58
92.00
159.05
189.60
192.15
178.20
238.45
258.15
285.50
161.84
134.71
104.00
284.29
260.15
250.00
160.65
254.20
155.15
298.15
298.15
204.15
125.26
298.15
145.65
167.55
58.00
53.48
230.94
129.95
131.35
2.16420
1.83990
2.07630
1.65860
2.01450
1.18060
1.19470
1.44950
1.83210
1.80290
1.66100
1.43550
0.98356
1.47670
1.56640
2.95870
1.31810
1.12760
1.52930
3.69010
1.53060
2.68470
2.05370
3.62920
6.22990
0.68554
0.87867
1.60680
1.29190
1.54260
2.12870
2.12030
2.20150
1.61090
1.46780
0.70123
1.71680
1.36660
0.98186
0.83031
1.36840
2.30150
2.82660
1.93350
1.94100
1.14670
1.95620
1.66860
1.38290
0.55414
0.57975
1.37260
0.79084
0.73946
357.05
341.45
410.00
337.45
366.15
300.13
298.15
331.13
392.70
402.94
396.58
360.00
250.00
466.44
380.00
360.00
298.15
310.48
422.15
559.20
374.47
570.00
407.90
433.15
616.93
290.00
390.00
350.21
289.73
409.35
486.55
466.95
428.25
404.95
301.82
252.70
390.41
493.15
329.00
283.85
374.20
510.10
417.15
326.15
386.55
315.25
410.00
320.00
371.05
98.00
56.00
504.08
337.78
285.70
2.51620
2.33750
2.81260
2.07550
2.47340
1.25420
1.37790
2.02240
2.63090
2.68700
2.69890
1.53400
1.03140
1.82000
2.56130
3.23830
1.31810
1.19590
1.69650
4.30070
2.22770
3.89330
2.78460
4.97260
9.31540
1.24440
1.64500
1.87960
1.33000
2.30750
3.04820
3.37940
3.01850
2.67980
1.87670
0.97582
1.82260
2.05980
1.14410
0.86932
1.63670
4.71570
3.37190
2.01530
2.42950
1.20070
2.40370
2.03580
1.92770
0.59663
0.55354
2.15180
1.40050
0.94206
(Continued )
2-140
TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued )
Eqn
Cmpd.
no.
100
100
100
100
100
100
100
100
114
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
100
100
100
100
114
100
100
100
100
114
100
100
100
100
100
100
100
100
153
154
155
156
157
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
Name
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
Formula
CH2O
CH3NO
CH2O2
C4H4O
He
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
CAS
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
Mol. wt.
30.02598
45.04062
46.0257
68.07396
4.0026
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
C1
70,077
63,400
78,060
114,370
387,220
410,430
376,970
176,120
61.26
194,570
2,416,800
1,070,000
270,730
265,040
267,950
236,870
46,798
370,350
157,820
172,120
161,980
1,638,600
1,409,400
208,250
235,960
164,640
82,795
303,320
93,000
94,860
79,815
66.653
57,720
47,300
95,398
62,520
64.666
127,540
-32,469
138,790
146,290
65.708
256,040
62,600
61,260
79,791
275,500
92,520
125,630
135,370
C2
-661.79
150.6
71.54
-215.69
-465570
-464890
347.82
242.92
314410
-23.206
-26105
-9470
-399.89
-375.68
-1315.9
-158.01
761.13
231.47
157.44
-183.78
44.116
-17261
-12553
-107.47
-345.94
-200.37
283.4
-1009
326
254.15
50.929
6765.9
9.9
90
-197.52
-223.02
49354
-65.35
1977.1
121.24
-58.59
38883
-2741.4
243.4
270.9
89.49
-1147
37.45
279.75
-133.34
C3
C4
C5
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
5.9749
-0.01813
0.00001983
155.15
292.00
281.45
187.55
2.20
1.80
295.13
229.80
182.57
265.83
239.15
220.00
234.15
238.15
154.12
229.92
200.00
291.31
214.93
177.83
269.25
228.55
223.00
217.35
217.50
133.39
300.00
192.62
200.00
300.00
274.69
13.95
185.15
165.00
259.83
189.79
187.68
270.00
177.95
409.15
288.15
90.69
175.47
359.00
253.40
200.00
196.32
179.69
260.75
159.53
0.55005
1.07380
0.98195
0.99486
0.10866
0.11352
5.30050
2.31940
1.99890
2.50870
2.35900
2.28350
2.35220
2.32420
1.81500
2.42290
1.73870
4.96020
1.91660
1.67500
2.25260
1.98210
2.04940
2.01850
2.05320
1.53540
1.67820
2.14950
1.58200
1.71110
0.97078
0.12622
0.59553
0.62150
0.70291
0.42875
0.67327
1.70310
1.46210
1.88400
1.59150
0.53605
0.71489
1.49980
1.29910
0.97689
1.49300
0.99249
1.98570
1.30350
253.85
493.00
380.00
304.50
4.60
2.10
575.30
426.15
520.00
496.15
448.60
432.90
480.00
490.00
430.00
460.00
372.93
560.01
401.15
460.00
478.85
460.00
412.40
460.00
460.00
404.00
354.35
430.00
344.48
357.67
653.15
32.00
206.45
185.00
298.85
292.67
370.00
427.65
320.00
580.00
434.15
190.00
503.15
538.50
373.40
249.94
353.35
266.82
472.65
314.56
0.72876
1.37650
1.05250
1.16090
0.29652
0.29952
7.68690
2.79640
4.06570
4.00650
3.87660
4.45840
3.23030
3.21630
2.75540
3.31310
2.43190
7.15210
2.20980
2.75340
3.45680
3.51970
3.98500
2.70870
2.76320
2.27060
1.83220
2.76390
2.05300
1.85760
1.31580
1.31220
0.59764
0.63950
0.71049
0.51186
4.91830
2.51140
1.66710
2.09110
1.88370
14.97800
2.46460
1.93670
1.62410
1.02160
1.90840
1.02510
2.57850
1.56620
0.72691
211800
135100
0.57895
1824.6
0.88395
110.03
33.004
1.0601
1.0024
6.5242
0.78982
-0.62882
0.68632
0.88734
0.709
71.721
40.991
0.2062
0.94278
0.8784
3.3885
0.043379
-123.63
0.3883
0.6297
22.493
0.82867
-7.0145
0.3582
-257.95
14.777
2.568
0.63868
-42494
3212.9
-2547.9
-0.19172
-0.0334
0.00011968
0
-0.011994
9.3808E-06
-0.12026
-0.04
0.00070293
0.000071087
-0.002762
478.27
-1623
0.0086913
614.07
-0.035078
0.000032719
2-141
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
CH3NO2
N2O
NO
C19H40
C9H18O
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
108,300
74,200
206,600
149,510
151,600
81,919
177,850
198,390
105,200
102,930
47,726
131,340
50,578
118,600
118,170
155,920
53,271
46,457
27,030
85,383
132,300
161,240
130,200
92,919
183,650
149,770
143,440
191,170
211,170
115,300
255,100
226,650
142,220
251,890
172,370
-925,460
87,680
71,140
144,110
179,850
113,470
76,822
134,580
73,600
29,800
1,034,100
187,740
281,970
101,400
116,270
67,556
–2,979,600
342,570
195,220
146
417.4
-761.14
-247.63
-266.72
181.01
-171.57
-220.35
191.1
129.1
338.4
-63.1
508.59
447.07
447.99
-490
327.92
346.93
413
199.08
200.87
-288.61
-396
324.43
-79.862
-529.82
-154.07
-331.04
-661.97
-263.23
-938.4
15.421
-47.83
-468.32
-1783.9
7894.9
217.1
335.5
-102.09
-264.1
421.6
90.833
184.7
527.5
-138770
-497.6
-12281
-682.11
-135.3
54.373
76602
762.08
378.71
-0.292
0.00151
2.5899
0.91849
0.90847
0.74379
0.76096
0.62516
0.8125
2.1383
-0.061547
-0.9597
0.78179
1.21
0.60769
1.3499
0.7255
0.98445
2.4216
0.60412
2.413
1.0578
0.739
1.2209
14.759
-17.661
-0.9153
-0.0015585
0.0019533
-0.0021383
-0.047909
0.013617
0.002266
0.00005805
0.58113
0.79202
0.011456
7154
1.0691
248
3.8912
0.345
-652.59
0.20481
0.029716
0.00095984
-162.55
-2.2182
1.8879
1.3841
0.0074902
113.25
321.50
155.95
135.58
139.39
298.15
157.48
175.30
200.00
277.25
250.00
146.58
300.00
300.00
300.00
130.73
200.00
200.00
250.00
160.00
186.48
167.23
174.15
298.15
189.15
256.15
127.93
180.15
171.64
150.18
224.95
240.00
119.55
176.00
113.54
298.96
132.81
300.00
133.97
160.17
298.15
249.95
164.55
151.15
353.43
24.56
183.63
63.15
117.00
244.60
182.30
109.50
305.04
267.30
1.23280
2.08390
1.50890
1.32820
1.32070
1.35890
1.69280
1.83150
1.43420
1.86780
1.32330
1.39550
2.03160
2.52720
2.52570
1.24920
1.18860
1.15840
1.30280
1.15660
1.49050
1.34840
0.97934
1.89650
1.90290
1.02630
1.35600
1.63480
1.58080
0.89393
1.66110
2.91280
1.47060
2.07280
0.99613
2.20160
1.05680
1.71790
1.40860
1.57870
1.13470
1.82200
1.54110
1.01520
2.16230
0.36664
1.32420
0.55925
0.74860
1.03820
0.77468
0.62287
5.94090
2.98570
310.00
481.50
404.15
304.31
311.71
305.40
343.31
510.00
299.49
415.87
325.00
320.00
441.15
438.15
440.15
366.48
348.64
338.05
350.00
280.50
373.15
339.80
304.90
350.00
389.15
366.00
310.00
440.00
357.91
298.15
373.45
518.15
333.41
372.00
380.00
460.00
343.15
390.00
312.20
368.69
298.15
438.65
328.20
278.65
491.14
40.00
387.22
112.00
175.50
473.15
200.00
150.00
603.05
465.52
1.70480
2.75180
3.22010
1.59210
1.56730
1.37200
2.06610
2.83940
1.62430
2.64740
1.57710
1.94350
2.74940
3.14480
3.15350
1.86820
1.67600
1.63740
1.71580
1.36380
1.75110
1.53440
1.21950
2.06470
2.44600
1.36680
1.65400
2.36100
1.86410
0.90520
2.41180
5.18640
2.08420
2.46630
2.07250
2.94550
1.45960
2.01990
1.68880
1.90140
1.13470
2.61760
1.99560
1.25070
2.88880
0.69796
1.55360
0.79596
1.01540
1.29490
0.78431
1.99090
8.76630
3.77960
(Continued )
2-142
TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued )
Eqn
Cmpd.
no.
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
114
100
100
100
100
100
100
100
100
100
100
100
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
Name
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
Formula
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
CAS
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
Mol. wt.
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
C1
383,080
224,336
10,483,000
1,510,000
254,490
265,350
253,580
399,430
171,960
224,830
205,260
571,370
1,115,100
300,400
289,980
509,420
240,040
42,642
63,131
175,430
60,046
346,910
102,000
159,080
145,050
201,200
883,630
194,590
193,020
156,100
188,200
213,760
86,200
68,671
103,370
101,720
60,834
145,400
66,230
62.983
158,760
471,710
201,400
55,679
213,660
121,750
83,400
139,530
174,380
114,140
75,700
C2
-1139.8
49.726
-115220
-12600
-298.06
-46.22
-366.3
374.64
383.28
-186.63
44.392
-4849
-9773.8
-426.2
-417.27
-4279.1
-33.198
886.67
199.92
-6152.3
281.16
219.54
389.95
-270.5
28.344
-651.3
-8220.5
-263.86
-176.43
-456.94
-140.84
-324.4
256.6
246.66
527.03
317.61
215.89
252.4
98.275
113630
-635
-4172.1
-450.6
406.13
-702.7
-149.56
384.1
78
-101.8
-343.72
326.1
C3
2.7101
0.9813
476.87
40.7
1.1707
0.79154
1.4881
0.58156
-0.059074
0.95891
0.8956
19.725
34.252
1.1172
1.2218
21.477
0.67889
-0.69315
113.92
0.65632
-0.32545
0.99537
0.6372
2.275
29.125
0.76808
0.5669
2.255
0.63581
0.9472
C4
-0.85381
-0.0386
0.79
1.0905
0.00056246
-0.021532
-0.03454
-0.044462
0.000035028
-0.92382
0.0027963
-0.02989
-0.003163
0.29552
633.21
1.969
14.745
1.7053
-0.50303
1.6605
0.47759
C5
-873.46
-0.014402
0.00000238
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
219.66
285.55
310.00
238.15
191.91
253.05
223.15
301.31
251.65
216.38
289.65
250.00
241.55
252.86
255.55
171.45
240.00
200.00
462.65
54.36
90.00
283.07
191.59
143.42
239.15
200.14
200.00
196.29
234.18
108.02
160.75
197.45
200.00
200.00
372.39
314.06
243.15
404.15
200.00
85.47
146.95
185.26
199.00
165.00
252.45
180.37
274.70
188.36
173.55
87.89
298.15
2.63480
3.18550
3.50590
2.96270
2.40410
3.04340
2.45940
5.65110
2.64670
2.29340
2.93260
2.55500
2.65930
2.64060
2.63140
2.13270
2.71180
1.92250
1.55620
0.53646
0.85350
4.61650
1.64760
1.40760
1.88270
1.61980
1.65410
1.72390
1.82790
1.29390
1.81990
1.86640
1.37520
1.18000
2.99630
2.01470
1.30800
2.47410
0.85885
0.84879
1.07970
1.13280
1.79260
1.09000
1.42090
1.10310
1.88910
1.54220
1.80510
0.92354
1.72930
325.00
528.75
460.00
471.70
475.00
492.95
423.85
589.86
445.15
460.00
512.85
467.10
452.90
500.00
440.65
454.00
472.19
399.35
516.00
142.00
150.00
543.84
375.15
390.00
458.95
389.15
392.20
375.46
375.14
372.00
385.15
399.79
313.33
329.27
500.00
425.00
489.75
557.65
238.65
360.00
400.00
463.00
431.65
322.15
414.32
370.25
404.70
340.00
432.39
298.15
398.15
2.98900
5.24980
4.64940
5.71150
3.77050
4.34910
3.65660
8.22760
3.30870
3.41890
4.63580
4.15660
5.05560
3.66600
3.43350
3.20980
3.75730
2.86190
1.66290
0.90662
1.02220
6.60420
2.02490
2.04980
2.92280
2.92270
3.36360
2.03800
2.06610
1.80920
2.28270
2.35460
1.66600
1.49890
3.66890
2.36700
2.37450
2.86150
0.89683
2.60790
2.19800
2.71460
3.24630
1.34310
2.07560
1.31850
2.38850
1.66050
2.78060
1.08600
2.05540
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
138,390
167,330
58,080
45,810
829,380
113,340
186,250
85,743
119,500
258,090
131,270
182,900
353,140
171,730
81,760
123,300
43,326
84,864
140,140
103,350
350,180
111,480
136,050
119,450
178,800
95,275
388,620
40,364
133,530
293,980
-1,360,200
136,300
68,720
-10,320
49,516
276,370
133,860
36,500
-35,500
-117.11
-319.1
445.2
368.33
-7331.5
290.2
247.8
5.7443
345.64
635.09
29.13
-800.47
455.38
-130.1
630.73
91.725
-152.3
159.3
-104.7
368.13
-288
324.54
-128.47
696.7
-1439.5
664.46
514.64
-114.98
10964
-106.17
135
322.8
420.35
-2090.1
7.8754
1017.5
1287.2
0.47059
0.8127
19.203
-0.6051
0.86116
2.8934
0.0013567
-0.0025015
0.6229
0.13243
0.695
1.0022
0.9913
0.83741
-1.3765
3.2187
0.0021734
0.96936
-20.86
0.75175
0.013055
8.125
0.52265
-2.63
-2.599
-0.014116
0.00302
0.002426
9.3701E-06
142.61
159.95
213.15
388.85
186.35
242.54
460.85
197.67
230.15
303.15
700.15
329.35
279.01
164.65
237.38
176.98
375.41
234.94
178.18
236.50
267.76
200.00
156.08
247.79
229.33
165.78
280.00
398.40
354.00
247.57
289.05
259.56
200.00
200.00
178.35
273.16
217.00
247.98
286.41
1.31260
1.37080
1.52970
1.89040
1.30000
1.67490
3.00450
0.86878
1.19500
2.58090
3.73270
3.92070
4.28310
1.07210
1.89860
1.19790
2.80110
1.13720
1.35070
1.41020
3.94000
1.85110
1.15250
1.99870
1.93380
1.82850
2.37910
3.05080
3.15710
3.24930
3.81370
1.59390
0.95720
0.54240
1.24490
0.76150
1.60180
1.73140
1.76970
350.00
340.87
460.75
683.00
253.15
418.31
591.00
350.00
230.15
303.15
795.28
609.15
526.73
339.12
480.77
394.27
426.00
357.31
500.00
300.00
508.62
361.92
276.02
449.27
350.00
520.00
320.00
475.47
475.00
433.42
523.15
389.35
278.25
400.00
363.85
533.15
540.15
417.58
600.00
1.55050
1.52990
2.63210
2.97380
2.04030
2.28160
3.32700
0.87754
1.19500
2.58090
4.06150
5.69770
6.07410
1.35460
3.00690
1.68830
3.12020
1.34550
2.37740
1.51140
5.56190
2.44710
1.32080
2.65260
2.36420
3.90950
2.57570
3.56290
3.77980
4.26240
5.35730
2.08920
1.06280
1.18800
2.02460
0.89394
2.90600
2.22690
3.25200
For the 11 substances: ammonia; 1,2-butanediol; 1,3-butanediol; carbon monoxide; 1,1-difluoroethane; ethane; heptane; hydrogen; hydrogen sulfide; methane; and propane; the liquid heat capacity CpL is calculated with Eq. (2-114):
CpL = C12/τ + C2 - 2C1C3τ - C1C4τ2 - C32τ3/3 - C3C4τ4/2 - C42τ5/5, where τ = 1 - Tr , Tr = T/TC, TC is the critical temperature from Table 2-106, CpL is in J/(kmol∙K) and T is in K.
For all other compounds, Eqn 100 is used. Eqn 100: CpL = C1 + C2T + C3T 2 + C4T 3 + C5T 4. For benzene, fluorine, and helium, two sets of constants are given for Eqn 100 that cover different temperature ranges, as shown in the table.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced
with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure
Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016).
2-143
2-144
PHYSICAL AnD CHEMICAL DATA
TABLE 2-73 Specific Heats of Organic Solids
Recalculated from International Critical Tables, vol. 5, pp. 101–105
Compound
Formula
Acetic acid
Acetone
Aminobenzoic acid (o-)
(m-)
(p-)
Aniline
Anthracene
C2H4O2
C3H6O
C7H7NO2
C7H7NO2
C7H7NO2
C6H7N
C14H10
Anthraquinone
Apiol
Azobenzene
C14H8O2
C12H14O4
C12H10N2
Benzene
C6H6
Benzoic acid
Benzophenone
C7H6O2
C13H10O
Betol
C17H12O3
Bromoiodobenzene (o-)
(m-)
(p-)
Bromonaphthalene (β-)
Bromophenol
C6H4BrI
C6H4BrI
C6H4BrI
C10H7Br
C6H5BrO
Camphene
Capric acid
Caprylic acid
Carbon tetrachloride
C10H16
C10H20O2
C8H16O2
CCl4
Cerotic acid
Chloral alcoholate
hydrate
Chloroacetic acid
Chlorobenzoic acid (o-)
(m-)
(p-)
Chlorobromobenzene (o-)
(m-)
(p-)
Crotonic acid
Cyamelide
Cyanamide
Cyanuric acid
C27H54O2
C4H7Cl3O2
C2H3Cl3O2
C2H3ClO2
C7H5ClO2
C7H5ClO2
C7H5ClO2
C6H4BrCl
C6H4BrCl
C6H4BrCl
C4H6O2
C3H3N3O3
CH2N2
C3H3N3O3
Dextrin
Dextrose
(C6H10O5)x
C6H12O6
Dibenzyl
Dibromobenzene (o-)
(m-)
(p-)
Dichloroacetic acid
Dichlorobenzene (o-)
(m-)
(p-)
Dicyandiamide
C14H14
C6H4Br2
C6H4Br2
C6H4Br2
C2H2Cl2O2
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4N4
Temperature, °C
-200 to +25
-210 to -80
85 to mp
120 to mp
128 to mp
sp ht, cal/(g⋅°C)
50
100
150
0 to 270
10
28
0.330 + 0.00080t
0.540 + 0.0156t
0.254 + 0.00136t
0.253 + 0.00122t
0.287 + 0.00088t
0.741
0.308
0.350
0.382
0.258 + 0.00069t
0.299
0.330
-250
-225
-200
-150
-100
-50
0
20 to mp
-150
-100
-50
0
+20
-150
-100
0
+50
-50 to 0
-75 to -15
-40 to 50
41
32
0.0399
0.0908
0.124
0.170
0.227
0.299
0.375
0.287 + 0.00050t
0.115
0.172
0.220
0.275
0.303
0.129
0.167
0.248
0.308
0.143 + 0.00025t
0.143
0.116 + 0.00032t
0.260
0.263
35
8
-2
-240
-200
-160
-120
-80
-40
15
78
32
60
80 to mp
94 to mp
180 to mp
-34
-52
-40
38 to 70
40
20
40
0.380
0.695
0.628
0.013
0.081
0.131
0.162
0.182
0.201
0.387
0.509
0.213
0.363
0.228 + 0.00084t
0.232 + 0.00073t
0.242 + 0.00055t
0.192
0.150
0.150
0.520 + 0.00020t
0.263
0.547
0.318
0 to 90
-250
-200
-100
0
20
28
-36
-25
-50 to +50
0.291 + 0.00096t
0.016
0.077
0.160
0.277
0.300
0.363
0.248
0.134
0.139 + 0.00038t
0.406
0.185
0.186
0.219 + 0.0021t
0.456
-48.5
-52
-50 to +53
0 to 204
SPECIFIC HEATS
TABLE 2-73 Specific Heats of Organic Solids (Continued )
Recalculated from International Critical Tables, vol. 5, pp. 101–105
Compound
Formula
Dihydroxybenzene (o-)
(m-)
(p-)
C6H6O2
C6H6O2
C6H6O2
Di-iodobenzene (o-)
(m-)
(p-)
Dimethyl oxalate
Dimethylpyrene
Dinitrobenzene (o-)
(m-)
(p-)
Diphenyl
Diphenylamine
Dulcitol
C6H4I2
C6H4I2
C6H4I2
C4H6O4
C7H8O2
C6H4N2O4
C6H4N2O4
C6H4N2O4
C12H10
C12H11N
C6H14O6
Erythritol
Ethyl alcohol
C4H10O4
C2H6O (crystalline)
(vitreous)
Temperature, °C
sp. ht., cal/(g⋅°C)
-163 to mp
-160 to mp
-250
-240
-220
-200
-150 to mp
-50 to +15
-52 to -42
-50 to +80
10 to 50
50
-160 to mp
-160 to mp
119 to mp
40
26
20
0.278 + 0.00098t
0.269 + 0.00118t
0.025
0.038
0.061
0.081
0.268 + 0.00093t
0.109 + 0.00026t
0.100 + 0.00026t
0.101 + 0.00026t
0.212 + 0.0044t
0.368
0.252 + 0.00083t
0.248 + 0.00077t
0.259 + 0.00057t
0.385
0.337
0.282
60
-190
-180
-160
-140
-130
-190
-180
-175
-170
-190 to -40
0.351
0.232
0.248
0.282
0.318
0.376
0.260
0.296
0.380
0.399
0.366 + 0.00110t
Ethylene glycol
C2H6O2
Formic acid
CH2O2
-22
0
0.387
0.430
Glutaric acid
Glycerol
C5H8O4
C3H8O3
20
-265
-260
-250
-220
-200
-100
0
0.299
0.009
0.022
0.047
0.085
0.115
0.217
0.330
Hexachloroethane
Hexadecane
Hydroxyacetanilide
C2Cl6
C16H34
C8H9NO2
Iodobenzene
Isopropyl alcohol
C6H5I
C3H8O
Lactose
Lauric acid
Levoglucosane
Levulose
C12H22O11
C12H22O11⋅H2O
C12H24O2
C6H10O5
C6H12O6
Malonic acid
Maltose
Mannitol
Melamine
Myristic acid
Naphthalene
Naphthol (α-)
(β-)
Naphthylamine (α-)
Nitroaniline (o-)
(m-)
(p-)
Nitrobenzoic acid (o-)
(m-)
(p-)
Nitronaphthalene
41 to mp
25
0.174
0.495
0.249 + 0.00154t
40
-200 to -160
0.191
0.051 + 0.00165t
20
20
-30 to +40
40
20
0.287
0.299
0.430 + 0.000027t
0.607
0.275
C3H4O4
C12H22O11
C6H14O6
C3H6N6
C14H28O2
20
20
0 to 100
40
0 to 35
0.275
0.320
0.313 + 0.00025t
0.351
0.381 + 0.00545t
C10H8
C10H8O
C10H8O
C10H9N
C6H6N2O2
C6H6N2O2
C6H6N2O2
C7H5NO4
C7H5NO4
C7H5NO4
C10H7NO2
-130 to mp
50 to mp
61 to mp
0 to 50
-160 to mp
-160 to mp
-160 to mp
-163 to mp
66 to mp
-160 to mp
0 to 55
0.281 + 0.00111t
0.240 + 0.00147t
0.252 + 0.00128t
0.270 + 0.0031t
0.269 + 0.000920t
0.275 + 0.000946t
0.276 + 0.001000t
0.256 + 0.00085t
0.258 + 0.00091t
0.247 + 0.00077t
0.236 + 0.00215t
(Continued)
2-145
2-146
PHYSICAL AnD CHEMICAL DATA
TABLE 2-73 Specific Heats of Organic Solids (Continued )
Recalculated from International Critical Tables, vol. 5, pp. 101–105
Compound
Formula
Temperature, °C
sp ht, cal/(g⋅°C)
Oxalic acid
C2H2O4
C2H2O4⋅2H2O
-200 to +50
-200
-100
0
+50
100
0.259 + 0.00076t
0.117
0.239
0.338
0.385
0.416
Palmitic acid
C16H32O2
Phenol
Phthalic acid
Picric acid
C6H6O
C8H6O4
C6H3N3O7
Propionic acid
Propyl alcohol (n-)
C3H6O2
C3H8O
Pyrotartaric acid
C6H8O4
-180
-140
-100
-50
0
+20
14 to 26
20
-100
0
+50
100
120
-33
-200
-175
-150
-130
20
0.167
0.208
0.251
0.306
0.382
0.430
0.561
0.232
0.165
0.240
0.263
0.297
0.332
0.726
0.170
0.363
0.471
0.497
0.301
Quinhydrone
C12H10O4
Quinone
C6H4O2
-250
-225
-200
-100
0
-250
-225
-200
-150 to mp
0.017
0.061
0.098
0.191
0.256
0.031
0.082
0.113
0.282 + 0.00083t
Salol
Stearic acid
Succinic acid
Sucrose
Sugar (cane)
C13H10O3
C18H36O2
C4H6O4
C12H22O11
C12H22O11
32
15
0 to 160
20
22 to 51
0.289
0.399
0.248 + 0.00153t
0.299
0.301
Tartaric acid
Tartaric acid
C4H6O6
C4H6O6⋅H2O
Tetrachloroethylene
Tetryl
C2Cl4
C7H5N5O8
1 Tetryl + 1 picric acid
1 Tetryl + 2 TNT
C13H8N8O15
C21H15N11O20
Thymol
Toluic acid (o-)
(m-)
(p-)
Toluidine (p-)
C10H14O
C8H8O2
C8H8O2
C8H8O2
C7H9N
Trichloroacetic acid
Trimethyl carbinol
Trinitrotoluene
C2HCl3O2
C4H10O
C7H5N3O6
Trinitroxylene
C8H7N3O6
Triphenylmethane
C19H16
36
-150
-100
-50
0
+50
-40 to 0
-100
-50
0
+100
-100 to +100
-100
0
+50
0 to 49
54 to mp
54 to mp
130 to mp
0
20
40
solid
-4
-100
-50
0
+100
-185 to +23
20 to 50
0 to 91
0.287
0.112
0.170
0.231
0.308
0.366
0.198 + 0.00018t
0.182
0.199
0.212
0.236
0.253 + 0.00072t
0.172
0.280
0.325
0.315 + 0.0031t
0.277 + 0.00120t
0.239 + 0.00195t
0.271 + 0.00106t
0.337
0.387
0.440
0.459
0.559
0.170
0.253
0.311
0.385
0.241
0.423
0.189 + 0.0027t
Urea
CH4N2O
20
0.320
TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)]
Cmpd. no.
1
7
8
14
16
27
29
31
34
37
38
43
59
60
61
64
67
81
88
95
97
98
99
112
120
125
126
134
145
151
156
157
182
183
190
194
197
217
221
231
236
237
238
243
246
247
248
251
Name
Acetaldehyde
Acetylene
Acrolein
Argon
Benzene
Bromoethane
1,2-Butadiene
Butane
1-Butanol
cis-2-Butene
trans-2-Butene
1-Butyne
m-Cresol
o-Cresol
p-Cresol
Cyclobutane
Cyclohexanone
1,1-Dibromoethane
1,1-Dichloroethane
Diethyl ether
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Dimethyl ether
1,4-Dioxane
Ethane
Ethanol
Ethylcyclopentane
Ethyl mercaptan
Fluoroethane
Furan
Helium-4
Hydrazine
Hydrogen
Isopropyl amine
Methanol
Methyl acetylene
Methylcyclopentane
Methylethyl ether
Methyl mercaptan
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
alpha-Methyl styrene
Naphthalene
Neon
Nitroethane
Nitromethane
Formula
C2H4O
C2H2
C3H4O
Ar
C6H6
C2H5Br
C4H6
C4H10
C4H10O
C4H8
C4H8
C4H6
C7H8O
C7H8O
C7H8O
C4H8
C6H10O
C2H4Br2
C2H4Cl2
C4H10O
C2H4F2
C2H4F2
CH2F2
C2H6O
C4H8O2
C2H6
C2H6O
C7H14
C2H6S
C2H5F
C4H4O
He
H4N2
H2
C3H9N
CH4O
C3H4
C6H12
C3H8O
CH4S
C4H10
C4H10O
C4H8
C9H10
C10H8
Ne
C2H5NO2
CH3NO2
CAS
75-07-0
74-86-2
107-02-8
7440-37-1
71-43-2
74-96-4
590-19-2
106-97-8
71-36-3
590-18-1
624-64-6
107-00-6
108-39-4
95-48-7
106-44-5
287-23-0
108-94-1
557-91-5
75-34-3
60-29-7
75-37-6
624-72-6
75-10-5
115-10-6
123-91-1
74-84-0
64-17-5
1640-89-7
75-08-1
353-36-6
110-00-9
7440-59-7
302-01-2
1333-74-0
75-31-0
67-56-1
74-99-7
96-37-7
540-67-0
74-93-1
75-28-5
75-65-0
115-11-7
98-83-9
91-20-3
7440-01-9
79-24-3
75-52-5
Mol. wt.
44.05256
26.03728
56.06326
39.948
78.11184
108.965
54.09044
58.1222
74.1216
56.10632
56.10632
54.09044
108.13782
108.13782
108.13782
56.10632
98.143
187.86116
98.95916
74.1216
66.04997
66.04997
52.02339
46.06844
88.10512
30.069
46.06844
98.18606
62.13404
48.0595
68.07396
4.0026
32.04516
2.01588
59.11026
32.04186
40.06386
84.15948
60.09502
48.10746
58.1222
74.1216
56.10632
118.1757
128.17052
20.1797
75.0666
61.04002
C1
29705
30800
30702
20786
35978
27112
27400
17330
25300
39760
20908
25300
29002
16192
29090
31863
32182
20560
19560
26040
29736
27581
33851
25940
28345
31742
32585
34710
23014
30358
40860
20786
32998
64979
23590
30270
30810
35465
23337
31520
21380
17080
24970
37735
29120
20786
33055
38782
C2
C3
127.43
-53.08
80.95
-0.21793
0.384
0.191
-101.69
117.99
177.6
458.16
371.2
108.8
324.73
183.2
158.79
469.81
166
37.226
116.87
285.2
249.01
388
72.364
169.88
-20.966
178.46
88.3
26.567
87.4
304.96
271.36
62.839
-160.3
0.939
-5.2147
-788.17
310.42
84.64
35.8
147.38
309.03
60.1
271.2
381.7
211.8
112.94
82.88
89.54
-48.39
C4
C5
-0.816
-0.461
-0.411
0.635
-0.479
0.616
0.23616
0.547
-0.332
-0.22187
-0.268
0.228
-0.1581
0.17584
-0.186
0.446
0.12927
0.05
-0.084
-0.4427
0.1067
0.87
0.21379
5.8287
-0.274
-0.188
0.27
0.242
-0.285
-0.092
-0.199
0.846
0.964
0.238
0.413
-0.018459
2.164E-05
Tmin, K
50
50
50
100
50
100
50
50
50
50
50
50
50
50
50
50
50
100
100
50
50
50
50
50
50
50
50
50
50
50
100
100
50
50
50
50
50
50
50
50
50
50
50
50
50
100
50
50
Cp at Tmin
3.553E+04
2.911E+04
3.523E+04
2.079E+04
3.324E+04
3.891E+04
3.628E+04
3.820E+04
4.271E+04
4.520E+04
3.612E+04
3.446E+04
3.853E+04
3.849E+04
3.893E+04
3.431E+04
3.939E+04
4.576E+04
4.224E+04
4.477E+04
3.392E+04
3.568E+04
3.324E+04
3.440E+04
3.388E+04
3.339E+04
3.708E+04
4.975E+04
3.548E+04
3.377E+04
3.353E+04
2.079E+04
3.327E+04
3.797E+04
3.843E+04
3.403E+04
3.328E+04
4.344E+04
3.808E+04
3.453E+04
3.471E+04
3.567E+04
3.556E+04
4.550E+04
3.567E+04
2.079E+04
3.813E+04
3.740E+04
Tmax, K
Cp at Tmax
200
200
200
1500
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
1500
200
250
200
200
200
200
200
200
200
200
200
200
200
1500
200
200
4.647E+04
3.554E+04
5.453E+04
2.079E+04
5.320E+04
5.071E+04
6.292E+04
7.632E+04
8.110E+04
6.152E+04
6.941E+04
6.194E+04
8.616E+04
9.099E+04
8.693E+04
4.875E+04
7.744E+04
6.432E+04
6.049E+04
9.292E+04
5.333E+04
5.523E+04
3.669E+04
5.419E+04
6.385E+04
4.223E+04
5.207E+04
9.234E+04
5.958E+04
4.719E+04
4.360E+04
2.079E+04
4.051E+04
2.834E+04
7.471E+04
3.968E+04
4.877E+04
7.462E+04
7.374E+04
4.354E+04
7.194E+04
8.546E+04
6.733E+04
9.416E+04
8.426E+04
2.079E+04
6.048E+04
4.562E+04
2-147
(Continued)
2-148
TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)] (Continued )
Cmpd. no.
Name
253
289
290
294
295
296
304
310
320
321
322
324
331
Nitric oxide
2-Pentyne
Phenanthrene
Propadiene
Propane
1-Propanol
Propylbenzene
Quinone
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
Thiophene
1,2,4-Trimethylbenzene
Formula
NO
C5H8
C14H10
C3H4
C3H8
C3H8O
C9H12
C6H4O2
C4H8O
C10H12
C4H8S
C4H4S
C9H12
CAS
10102-43-9
627-21-4
85-01-8
463-49-0
74-98-6
71-23-8
103-65-1
106-51-4
109-99-9
119-64-2
110-01-0
110-02-1
95-63-6
Mol. wt.
30.0061
68.11702
178.2292
40.06386
44.09562
60.09502
120.19158
108.09476
72.10572
132.20228
88.17132
84.13956
120.19158
C1
34980
24330
27700
31690
26675
28800
22880
29668
36970
28560
41195
36765
35652
C2
-35.32
335.7
210
17.1
147.04
257
538.46
129.07
-12.28
225.1
-88.3
-112.82
323.89
C3
0.07729
-0.37
1.24
0.282
-0.35
-0.546
0.53105
0.444
0.616
0.942
0.862
0.305
C4
C5
Tmin, K
-5.7357E-05
1.4526E-08
100
50
50
50
50
50
50
50
50
50
50
50
50
Cp at Tmin
3.216E+04
4.019E+04
4.130E+04
3.325E+04
3.403E+04
4.078E+04
4.844E+04
3.745E+04
3.747E+04
4.136E+04
3.914E+04
3.328E+04
5.261E+04
Tmax, K
Cp at Tmax
1500
200
200
200
200
200
200
200
200
200
200
200
200
3.586E+04
7.667E+04
1.193E+05
4.639E+04
5.608E+04
6.620E+04
1.087E+05
7.672E+04
5.227E+04
9.822E+04
6.122E+04
4.868E+04
1.126E+05
Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where C 0p is in J/(kmol∙K) and T is in K.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and
reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data
Compilation of Pure Chemical Properties, Design Institute for Physical Properties AIChE New York NY (2016)”.
TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)]
Cmpd.
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CAS
Mol. wt.
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
153.8227
C1 × 1E-05
C2 × 1E-05
0.48251
1.06650
0.34200
1.29400
0.40200
1.36750
0.87998
1.66350
0.57040
1.63200
0.44346
0.84650
0.36921
0.31793
0.57019
0.91830
0.60590
1.37030
0.56303
1.09720
0.28958
0.09390
0.33427
0.48980
0.76370
2.93770
See Table 2-155
1.95810
1.70190
0.55238
1.73380
0.68950
2.32750
0.77594
2.64550
0.76820
2.26350
1.00990
4.48980
0.84115
3.14280
0.95210
2.88680
0.99192
2.96330
1.07590
4.21050
0.30113
0.08009
0.72100
2.06400
0.52310
0.89110
0.36241
0.69248
0.66964
1.09950
0.50950
1.70500
0.80154
1.62420
1.04780
2.54900
1.06600
2.57500
0.74540
2.59070
0.90878
2.55080
0.64257
2.06180
0.65121
1.43250
0.74296
1.34760
1.16840
3.76900
1.13800
4.45400
0.92478
2.77950
0.92367
2.51660
0.66492
1.07260
0.89240
1.56750
1.48800
1.35220
0.82142
1.32340
0.29370
0.34540
0.30100
0.33380
0.29108
0.08773
0.37582
0.70540
C3 × 1E-03
C4 × 1E-05
1.99290
1.07500
1.26200
0.80153
1.60700
1.63980
0.67805
0.76747
1.64750
0.91248
3.01200
2.03600
1.60510
0.78851
0.64000
0.70030
0.76076
0.96800
0.49487
0.33430
0.38554
1.04460
-0.44070
0.07580
0.22560
2.17000
1.32570
0.76425
1.51200
1.79250
0.74786
1.31100
1.95390
0.70207
1.55830
1.90410
0.75140
1.65040
0.81205
1.74540
0.83737
1.53240
0.84149
1.87760
1.96700
1.60730
1.89300
1.67680
0.85796
0.87025
1.95600
1.55070
1.68370
1.61090
0.79390
0.90190
1.14600
0.84021
1.42800
0.89600
3.08510
0.51210
-37.41700
0.72545
1.75160
2.23820
-0.67585
2.83950
2.57430
1.63850
2.21160
4.17850
0.10780
1.68700
0.67540
0.44781
0.68373
1.33700
1.05750
1.87500
1.95100
1.73200
1.85200
1.33240
0.89648
0.89116
2.81800
3.04970
1.59740
1.56410
0.74240
1.09840
-678.00000
0.67932
0.26400
0.28930
0.08455
0.48500
C5
Tmin, K
Cp at
Tmin × 1E-05
912.78
502
569.7
2310.1
731.5
761.47
3036.6
2375.4
751.49
1178.4
1484
882
751.2
298.15
100
50
298.15
200
298.15
298.15
298.15
250
298.15
50
100
300
0.54732
0.34481
0.40200
1.10440
0.60487
0.52233
0.44032
0.71326
0.69837
0.64356
0.28958
0.33427
1.13020
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1.29930
1.49970
1.57560
2.69700
1.88200
1.11990
0.75868
1.56240
1.74240
1.37940
0.34956
0.66465
3.02260
41.232
2445.7
697.9
835.9
896
627.4
850.06
2002.6
719.16
828.81
314.6
765.3
2809
793.32
2441.1
685.6
2476.1
833
860.5
712.4
832.13
757.06
2477.2
2463.4
811.2
708.86
758.68
739.2
-2458.4
2566
6.98
2313.7
588
374.7
1538.2
236.1
298.15
298.15
200
200
298
300
298.15
300
300
200
100
200
298.15
298.15
298.15
200
298.15
298.15
298.15
298.15
298.15
250
298.15
298.15
298.15
200
200
200
298.15
298.15
298.15
298.15
50
100
60
100
1.27450
0.82616
0.76894
0.81258
1.09070
1.80010
1.11980
1.55010
1.41560
1.14810
0.30901
0.76789
0.63800
0.42454
0.79668
0.57563
0.98586
1.26670
1.26790
1.07860
1.12570
0.75708
0.80241
0.87766
1.52810
1.26590
0.97140
0.97633
0.81441
1.02830
1.15330
0.97246
0.29370
0.31003
0.29108
0.47299
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500.1
1500.15
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
5000
1500
1500
1500
3.25010
2.41800
2.67390
2.97120
2.68100
4.93110
3.28800
4.34450
3.29570
4.55570
0.37938
2.46280
1.54570
0.90758
1.92080
1.95550
2.66050
3.02890
3.03110
2.85090
2.87300
2.28980
2.27180
2.28360
3.67240
4.84350
3.10080
2.96150
1.92210
2.67780
2.59050
2.28510
0.63346
0.61475
0.35208
1.06620
Tmax, K
Cp at
Tmax × 1E-05
2-149
(Continued)
2-150
TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued )
Cmpd.
no.
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
Name
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
Formula
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
CAS
Mol. wt.
C1 × 1E-05
C2 × 1E-05
C3 × 1E-03
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
0.92004
0.29142
0.80110
0.52590
0.39420
0.36220
0.64710
0.61809
0.90974
0.79880
0.92021
1.08100
0.45894
0.50835
0.43200
0.90430
0.85860
0.58171
0.41600
0.48074
0.33800
0.54305
1.94250
1.67200
0.24457
1.69840
1.71010
1.93100
1.50450
0.30290
0.66622
0.74906
0.39100
1.61220
0.70000
0.69480
0.69780
0.63412
0.65271
0.36280
0.71450
0.78658
1.20800
0.91020
0.99953
0.91273
0.55477
0.57793
0.37540
1.13840
1.09300
1.08690
0.16446
0.09176
2.31000
1.40200
0.65730
0.69810
1.79800
1.80230
2.13210
2.85300
2.11060
3.79320
0.41286
1.64870
3.73500
2.57710
2.57770
3.17170
3.01400
2.51590
1.68940
3.99620
5.14030
5.35300
6.54600
5.39200
5.20890
5.48150
4.37940
0.09750
0.81703
1.27250
0.64800
4.47770
2.07460
2.08040
2.07800
0.83862
1.12540
0.68040
1.73440
1.74290
3.06600
2.67400
1.70380
2.41000
1.23610
0.89811
0.53510
2.57470
3.68300
4.05400
1.07640
0.94900
2.15700
2.03700
0.92800
1.80500
1.67600
1.54380
0.76324
1.47650
0.76622
1.75050
1.38120
0.82849
1.19200
0.78820
0.84895
1.54350
1.46170
1.58030
1.61350
1.35750
1.89780
1.61410
1.08990
1.56800
1.72650
1.60850
1.32910
2.51500
0.76285
1.98100
1.19400
1.68310
1.36640
1.36320
1.36350
0.76898
1.73760
1.25600
1.52400
1.71570
2.08900
1.71900
0.87072
1.66860
0.83501
0.84727
0.86687
0.73840
1.60570
1.78020
C4 × 1E-05
-5083.80000
0.10030
2.04600
0.99820
0.49300
0.44470
1.23300
1.18930
0.93355
2.04200
0.95073
3.00270
0.33023
0.86658
1.63500
1.30680
0.77780
2.12730
1.80950
1.74540
1.17680
2.56230
4.17520
3.78200
4.86420
3.93800
3.59350
3.74000
2.55570
-0.02750
0.40941
0.94370
0.42000
2.91800
1.59830
1.59400
1.59650
0.44030
0.87800
0.42750
1.22300
1.26270
2.34300
1.79260
1.07460
1.65200
-0.40972
0.43249
0.22998
1.62000
2.34200
2.97860
C5
2.3486
425
897.6
861.18
399.6
844.27
755.78
685.93
2474.5
664.7
2464.6
794.8
559.94
2472.4
530.1
1952.2
2401.5
701.62
668.8
718.37
722.8
618.54
859.95
742
424
720.5
782.92
754.75
632.01
368
2488.3
845.2
501
781.6
620.16
619.2
619.37
2533.2
795.45
548
674.2
765.1
891
794.94
2471.3
771.08
1033.4
2424.2
2437.2
2143
699
791.6
Tmin, K
Cp at
Tmin × 1E-05
298
50
200
298.15
100
298.15
298.15
200
298.15
200
298.15
200
273.15
298.15
100
200
298.15
150
100
150
100
300
298.15
200
298.15
298.15
298.15
200
298
100
298.15
200
100
200
200
200
200
298.15
200
100
150
200
298.15
200
298.15
200
298.15
298.15
298.15
300
298.15
300
0.61055
0.29142
0.82193
0.62879
0.40484
0.41193
0.84674
0.67679
1.24780
0.91584
1.25080
1.14800
0.54968
0.70636
0.43657
0.96478
1.14170
0.59782
0.41650
0.49182
0.33813
1.26440
2.37630
1.79670
2.52320
2.43540
2.23040
2.04340
2.19380
0.30195
0.79599
0.76345
0.39288
1.68410
0.82450
0.81978
0.82283
0.76395
0.67221
0.36369
0.72683
0.82172
1.41970
0.95017
1.16950
0.95673
0.67988
0.67730
0.42969
1.59950
1.56690
1.51020
Tmax, K
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500.1
1500
1500
1500
1500
1500
1500
1500
1500
1500
Cp at
Tmax × 1E-05
1.04650
0.37930
2.53270
1.55080
1.00630
0.90655
2.09750
2.10230
3.21580
3.21630
3.21320
4.18080
0.81268
2.32330
3.65160
3.82510
3.47740
3.21320
2.92980
2.56190
1.72130
3.72360
6.04070
6.09320
6.10990
6.21860
5.87450
6.46130
5.27940
0.34251
1.56840
1.70410
0.95987
5.21450
2.51610
2.51610
2.51750
1.56330
1.57430
0.95430
2.16090
2.18940
3.46740
3.05190
2.92630
2.87240
1.54560
1.55140
0.94201
4.19410
4.05350
4.30930
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
1.15560
1.01130
0.65340
0.55650
0.77720
1.07760
1.10390
1.09910
0.78430
0.57431
0.72200
0.85438
1.39600
0.61453
0.60370
0.69490
1.14025
0.68444
1.09850
1.21140
2.12950
3.24810
0.44256
0.49200
0.99810
0.59400
0.78440
1.09440
1.04550
1.11500
1.10590
0.93177
0.33380
0.72860
0.63012
0.34300
0.33460
0.53700
1.57770
1.63400
1.09530
1.24000
0.60436
0.93700
1.13200
0.96993
0.29122
0.73393
0.49090
0.35193
0.33503
0.38220
0.33810
0.43673
See Table 2-155
1.83050
3.23930
1.61790
1.63840
4.03200
4.67180
4.64450
4.64010
1.43640
0.94494
1.78300
4.57720
4.78000
1.74380
1.37470
1.52400
5.36801
1.98020
4.34120
2.61270
6.63300
11.09000
0.84737
1.45770
2.09310
1.61800
3.39900
4.17940
2.31480
3.39100
4.63060
2.79330
0.94790
1.84360
1.45840
1.42700
1.21160
1.88600
4.40170
4.51190
3.00320
3.20000
0.87524
2.82900
2.94000
1.08780
0.10132
2.37390
0.88880
0.65344
0.49394
0.93000
0.75930
1.28390
0.95919
1.56110
1.78370
1.73410
1.54400
1.65400
1.69430
1.66790
1.58360
0.89551
1.53200
1.51810
2.19000
1.34180
1.64100
1.65140
2.08860
0.82793
1.62220
0.78956
1.71550
1.63600
0.87224
1.66280
2.02260
1.81200
1.55900
0.88375
0.71000
1.67050
1.66280
0.78650
1.59600
1.68800
1.67300
1.63800
1.60840
1.20700
1.74940
1.75320
1.79880
1.96700
0.78662
1.64800
1.82700
0.70467
1.45300
2.30860
0.83107
1.13330
1.92800
1.84500
1.19250
0.74699
0.99605
2.15010
1.02420
1.08990
2.50800
3.33970
3.39490
3.37360
0.87100
0.65065
1.31000
2.97400
3.97050
1.01020
0.79880
1.06580
4.13440
0.90830
3.64550
1.69030
4.51610
7.45000
0.67130
0.93900
1.80300
1.07800
2.42600
-1.60900
1.47100
2.51800
3.29900
1.64590
0.55100
1.19900
0.97296
1.03700
0.82410
0.86400
3.23780
3.10320
2.13110
2.34600
0.62622
2.15500
2.05500
0.55556
0.09410
2.45890
0.54120
0.15240
0.29728
0.69000
0.31800
0.47541
2826.3
689.3
821.4
793.04
649.95
792.5
798.35
781.97
730.65
2467.4
762
641.01
900.6
592.09
743.5
722.2
809.837
2447.1
743.62
2394.4
777.5
726.27
2430.4
744.7
928.05
820
702
1183.1
2061.6
733.6
781.1
2303.3
740.8
767.3
773.65
744.7
737.3
496
792.34
809.75
817.35
896
–2190
724.7
852
2089.7
662.91
906.45
2446
5316.2
965.04
850
550
2500.6
298.15
298.15
200
200
200
200
200
200
200
298.15
200
200
300
200
200
200
298.15
298.15
300
300
200
200
298.15
273.15
200
200
200
300
300
298
200
298.15
60
300
300
150
50
100
298.15
298.15
298.15
298.15
298.15
300
298.15
298.15
50
200
298.15
100
298.15
150
50
298.15
1.27770
1.46380
0.67211
0.58115
0.93628
1.15350
1.17770
1.18200
0.81551
0.65866
0.75937
1.05500
1.74810
0.70950
0.62976
0.73547
1.67000
0.92284
1.72980
1.59000
2.24420
3.52350
0.52652
0.61172
1.01260
0.61390
0.89121
1.45980
1.51020
1.55830
1.18750
1.33350
0.33380
0.91775
0.77997
0.34798
0.33460
0.54118
2.02790
2.03600
1.36200
1.44790
0.73021
1.33770
1.35380
1.18910
0.29122
0.75730
0.59646
0.35193
0.35440
0.38326
0.33810
0.65450
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200.15
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1200
1200
1500
1200
1500
1500
1500
1500
1500
6000
1500
1500
1500
1500
3.06780
3.66690
1.91480
1.85850
4.03530
4.95430
4.92430
4.92750
1.95230
1.65840
2.25960
4.59830
4.47400
2.09440
1.69490
1.92550
4.97220
2.81860
4.51430
4.24840
7.43250
12.21100
1.45610
1.65760
2.65940
1.85280
3.61470
4.25400
3.63300
3.62130
4.91840
4.14000
1.09870
2.20160
1.80950
1.51780
1.32970
2.14850
5.12010
4.87440
3.22890
3.42340
1.66280
3.05690
3.45350
2.21700
0.38122
2.50800
1.49880
1.05710
0.71121
1.12030
0.99328
1.79520
2-151
(Continued)
2-152
TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued )
Cmpd.
no.
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
Name
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
Formula
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
CAS
Mol. wt.
C1 × 1E-05
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
2.78780
1.30930
1.20150
1.31350
1.22150
1.41060
1.27680
1.25070
1.18510
1.44200
1.07120
2.62830
1.18400
1.04400
1.16220
1.06250
1.26150
1.09400
1.12370
1.04340
0.93760
1.26620
0.91290
1.03600
0.41729
0.27617
0.29120
0.29157
0.30125
0.29134
0.33288
0.74694
0.79534
0.49522
0.72510
0.33298
0.39252
0.61160
0.55500
0.51734
0.12060
0.41000
0.93960
0.67100
0.74600
1.84580
0.92139
0.87026
0.81924
0.79060
0.82051
1.07850
C2 × 1E-05
9.52470
3.53810
4.00100
2.33170
3.99100
2.88580
3.38100
2.14800
3.63620
4.16030
3.02580
8.97330
3.07260
3.52300
2.07080
3.52100
3.59640
1.80700
2.93600
3.07490
3.01500
3.72940
2.55770
3.00900
0.54686
0.09560
0.09530
0.09048
0.31710
0.09325
0.26086
2.43560
1.44250
1.87180
2.08900
0.79933
0.87900
2.02900
1.78200
0.68157
2.37660
1.05780
2.55900
2.22200
3.26500
1.74300
3.33710
2.55560
2.60380
1.65600
3.08690
2.73880
C3 × 1E-03
C4 × 1E-05
C5
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
1.69350
1.52500
1.67660
0.67567
1.58000
0.80394
1.38310
0.69120
1.73590
1.66030
1.52730
1.69120
1.70770
1.69460
0.68661
1.58350
1.84450
0.68900
1.40100
1.74590
1.90570
1.65740
1.52900
2.11600
0.81130
2.46600
2.14200
2.09380
1.61020
2.90500
0.91340
1.71500
0.81831
1.29580
1.85160
2.08690
1.91650
1.76830
1.26000
0.80525
1.05430
1.70800
0.82500
1.42100
1.54500
1.22000
1.83610
1.77570
1.75930
1.69260
1.38640
1.58850
6.66510
2.23950
2.74000
1.82400
2.83500
1.49680
1.88800
1.61900
2.50480
2.65720
2.09750
6.26400
2.11740
2.36900
1.53550
2.46200
2.59400
1.47400
1.60100
2.07280
1.98600
2.30800
1.73700
2.10600
0.41755
0.03760
0.01570
-0.00107
0.21790
0.00195
-0.17979
1.84840
0.95493
1.48520
1.64830
0.41602
0.53654
1.33020
0.85300
0.51402
1.81860
0.68360
1.36000
1.19400
1.92300
-56.11000
2.46440
1.76360
1.71950
1.21670
1.78860
1.90670
744.57
740.37
756.4
1846
717.7
2456.1
650.3
1759.3
785.73
759.39
689.62
744.41
790.64
761.6
1932.5
715.75
819.17
1772
650.5
793.53
817
757.8
683
902.4
2639.2
567.6
1400
120
626
1326
949.4
757.75
2499.9
569.96
798.43
991.96
896.7
835.5
562
2463.8
418.8
735
3000
614.7
666.7
31.2
757.83
807.82
800.93
788.4
613.87
749.6
200
298.15
200
300
298.15
298.15
200
150
298.15
200
200
200
298.15
200
298.15
298.15
298.15
200
150
298
300
200
200
300
298.15
250
50
50
100
50
100
298.15
298.15
300
298.15
50
273.15
300
298
298.15
298.15
150
300
150
200
300
298.15
200
200
298.15
300
273.15
3.00340
1.70230
1.28280
1.84970
1.75720
1.79590
1.39680
1.26880
1.54340
1.51910
1.17210
2.83120
1.48160
1.11170
1.61070
1.53110
1.58290
1.18150
1.14430
1.33010
1.19090
1.33400
1.00040
1.22150
0.48803
0.28426
0.29120
0.29137
0.30137
0.29134
0.33288
1.04270
0.97640
0.97903
0.94749
0.33298
0.42513
0.76980
0.84891
0.60784
0.99083
0.41364
1.25860
0.69311
0.85462
1.27930
1.31350
0.90596
0.85589
0.96319
1.33000
1.31730
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1200.1
1500
1500
1500
1500
1500
1200.1
1500
1200
1500
1500
1500
1500
1500
1500
1500.15
1200
1200
10.41600
4.27590
4.42830
4.29410
4.53460
4.59900
4.13860
3.84460
4.08360
4.78310
3.59850
9.81820
3.66440
3.86200
3.76360
3.97260
4.06720
3.32070
3.58740
3.48190
3.18890
4.24830
3.03710
3.18940
1.05830
0.32248
0.34786
0.34063
0.55224
0.32243
0.51432
2.53830
2.45580
2.14970
2.20570
0.88904
1.05330
2.22090
2.07540
1.33000
2.16630
1.23880
3.35690
2.50280
3.37920
3.22620
3.48560
2.89230
2.87090
2.15020
3.19940
3.16870
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F 3N
CH3NO2
N 2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
0.82740
0.89400
0.59895
0.92270
0.79590
0.92279
0.92279
0.78439
0.69411
0.64220
0.72830
0.79188
0.78400
0.75083
0.50600
0.72840
1.22700
0.47400
0.89232
1.59140
0.99247
0.43697
0.86400
1.74830
0.90300
0.94326
0.76394
0.90658
0.73226
0.77650
0.92151
0.93775
0.46149
1.00010
0.98059
0.60865
0.89232
See Table 2-155
0.64084
0.29105
0.33284
0.47876
0.29338
See Table 2-155
3.10620
1.71190
1.51750
0.12660
1.54000
1.81180
1.53520
1.76460
1.62890
2.95020
2.13770
2.91000
1.16360
4.11500
2.59600
2.67090
2.67090
2.50070
3.02090
3.07110
1.03070
1.31660
2.10320
1.95770
1.21900
3.17130
2.19500
1.22600
2.47650
1.76400
2.72750
0.50387
1.81100
4.92880
3.80100
3.59650
1.68020
1.71370
1.36060
2.44200
2.39430
2.61780
1.27810
2.65370
3.08940
1.59650
2.67720
1.75500
1.57000
1.56500
1.65040
0.62130
0.68784
0.68784
0.81937
1.69030
1.63870
1.54290
0.87136
1.54880
1.64240
1.63700
1.35200
0.84200
2.18800
1.69600
1.20760
2.00300
0.80924
0.75430
1.73840
1.60200
1.35330
0.82654
0.80201
0.84872
1.71400
1.69360
1.72910
1.45650
0.77176
1.64560
1.61900
0.76122
1.51490
2.07300
0.81581
2.90060
2.28800
1.98470
1.98470
1.30010
2.12090
2.12980
0.78110
0.86597
1.18550
1.19490
0.89400
1.89480
1.19100
0.85983
1.55980
-407.40000
1.89740
0.42223
0.80000
3.58970
2.45300
2.05690
1.02850
1.04240
0.88667
1.81800
1.48960
1.62360
0.79115
1.11620
2.09850
0.93783
1.02010
782
678.3
690.39
779.48
1698.6
1732.4
1732.4
2416.4
781.56
750.25
668.94
2468
693
749.19
743
585.14
2460
1008.2
791.4
10.503
849.64
2192.4
2160
788.01
691.6
599.92
2483.1
2489.7
2499.8
716
797.79
783.23
643.23
2405.2
732.6
739.55
2435.5
200
298
200
200
300
300
300
298.15
200
200
200
298.15
200
273.16
250
300
298.15
298.15
200
300
273
298.15
298.15
298.15
200
300
298.15
298.15
298.15
300
298
298.15
200
298.15
298.15
300
298.15
0.86459
1.34610
0.63795
0.99530
1.53020
1.50990
1.50990
1.09680
0.74637
0.70833
0.77172
0.92283
0.83967
0.90040
0.58880
1.32000
1.47550
0.51946
0.92804
1.12910
1.13770
0.50277
1.16210
2.25670
1.01920
1.56000
0.96745
1.13730
0.88184
1.12420
1.12510
1.17280
0.51411
1.40620
1.35330
0.77480
1.32040
1500
1200
1500
1500
1200
1200
1200
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500.15
1500
1500
1500
1500
1500
1500
1500
1500
1200
1500
1500
1500
1200
1200
1500
1500
1500
1500
1500
1500
2.52550
3.07660
1.55930
4.31800
4.13590
4.14670
4.14670
3.54830
3.14960
3.15490
1.58930
2.29440
2.48160
2.31780
1.51090
3.19870
3.65320
1.35950
2.86960
2.99910
2.99520
1.06940
2.86370
5.71770
3.96170
3.74090
2.66680
2.85290
2.28420
2.52760
2.63910
2.99040
1.52530
3.86080
3.47810
1.88710
3.73860
1.16310
0.08615
0.49837
0.78357
0.32360
0.80970
1.70160
0.70930
0.82960
1.12380
0.59591
0.00103
0.23264
0.37215
0.21770
2425.6
909.79
372.91
2433.8
479.4
298.15
50
100
298.15
100
0.79235
0.29105
0.34036
0.57242
0.29475
1500
1500
1500
1500
1500
1.92450
0.34838
0.80919
1.32860
0.58278
10.57500
4.50580
4.91500
6.01100
4.93600
3.59270
4.68440
5.04400
3.97080
10.03400
0.76791
1.71000
1.64480
1.08150
1.57800
0.81841
1.72880
1.61820
1.89280
0.77107
-4.56610
3.36580
3.47000
4.59460
3.58800
2.17920
3.23040
3.38570
3.21360
-4.30120
912.03
807.38
749.6
418.2
721.11
2550.1
783.67
755.48
855.52
916.73
200
298.15
200
298.15
298.15
298.15
298.15
200
298.15
200
3.35330
2.15310
1.62570
2.29530
2.20920
2.26250
2.00140
1.86580
1.96930
3.18000
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
11.61300
5.42420
5.54070
5.52670
5.66060
5.85550
5.27760
5.90820
4.79240
11.01600
2-153
(Continued)
2-154
TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued )
Cmpd.
no.
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
Name
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Formula
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
CAS
Mol. wt.
C1 × 1E-05
C2 × 1E-05
C3 × 1E-03
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
1.59550
1.35540
1.40820
1.38050
1.58030
1.39010
1.49520
1.35990
1.59810
1.23070
0.56777
0.29103
0.33483
2.46790
1.06000
0.88050
2.83600
0.90600
1.08530
0.90053
0.96896
0.82523
1.13270
1.09740
0.75300
0.82096
1.27200
0.43400
0.59683
0.73640
0.48308
0.59474
0.61900
0.73145
1.05630
0.71306
0.69590
0.52525
1.79940
0.76078
1.13460
0.43852
3.14670
4.43100
4.34360
4.45900
3.23480
3.80600
4.41030
4.16050
4.60630
3.49420
1.11940
0.10040
0.29577
8.42120
2.85000
3.01100
1.08000
3.06200
3.07470
2.70850
2.49070
2.59430
2.94700
3.29590
2.09050
1.46770
3.56890
2.44500
2.55330
2.54400
0.73665
1.26610
2.02130
2.03130
4.33970
1.16890
1.77780
1.46630
1.75300
2.10490
2.80980
1.50600
0.85788
1.63560
1.46620
1.57510
0.79814
1.37170
0.80211
1.73170
1.62950
1.52800
0.62070
2.52650
1.52170
1.68650
1.93000
1.65020
2.10700
1.60540
1.86720
1.65920
1.41770
1.72910
1.74180
1.67610
1.53070
0.84463
0.75021
1.15200
1.23970
1.08520
0.78152
0.84431
1.62930
1.93750
1.60980
0.92731
1.70980
1.54760
1.19600
1.72560
0.79504
1.39880
C4 × 1E-05
1.47130
3.05400
2.76870
3.20160
1.78820
2.25730
-2.09580
2.86750
3.03010
2.46170
-0.38079
0.09356
0.27151
5.85370
2.01000
1.89200
-3.56000
2.11500
2.22710
1.80120
1.30100
1.76800
2.09870
1.94860
1.37800
0.96258
1.32990
1.51200
1.55190
0.80800
0.48698
0.86165
1.29560
1.48150
3.18100
1.02100
1.26540
0.93033
-4.12000
1.39360
1.23760
0.74754
C5
Tmin, K
Cp at
Tmin × 1E-05
Tmax, K
Cp at
Tmax × 1E-05
2679.4
746.4
659.38
718.8
2434.3
660.96
981.95
784.47
756.28
694.81
676.72
1153.8
680.35
743.6
879.23
747.6
283
717.97
825.4
743.96
646.7
778.7
795.78
757.67
672.8
2452.3
2409.4
507
576.78
573
2480
2482.7
727.4
843.37
729.66
2512.8
763.78
674.15
108.2
789.03
2449.5
616.46
298.15
200
298.15
298.15
298.15
150
200
298.15
200
200
298.15
50
100
200
298.15
200
298.15
298.15
298.15
200
200
298.15
298
200
200
298.15
298.15
100
298.15
298.15
298.15
298.15
298.15
298.15
300
298.15
298.15
298.15
298.15
200
298.15
130
1.92770
1.45290
2.06520
1.98320
2.02310
1.41620
1.57750
1.77230
1.68810
1.34480
0.79711
0.29103
0.33489
2.65860
1.25200
0.94039
1.38240
1.30440
1.35390
0.95908
1.05360
1.08560
1.42020
1.15470
0.82759
0.98524
1.86940
0.44014
1.10540
1.07450
0.59127
0.73665
0.85428
0.89664
1.63920
0.80337
0.89382
0.73244
1.35940
0.79326
1.52430
0.44363
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1000.15
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
4.91940
4.97640
5.04110
5.09650
5.20600
4.65470
4.90670
4.68070
5.35490
4.16040
1.56180
0.36533
0.59282
9.22090
3.24590
3.29270
3.29520
3.41330
3.47010
3.07970
3.03580
2.88970
3.49940
3.69560
2.47540
2.50600
5.06820
2.60450
2.83900
2.67370
1.33810
2.05600
2.24580
2.27600
4.65270
2.11890
2.12480
1.72030
3.20240
2.43530
4.16280
1.68170
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O 2S
F 6S
O 3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
0.87100
0.73815
0.74740
2.01140
0.80992
0.36810
0.89300
0.71806
0.33375
0.35256
0.33408
1.00130
2.07190
2.30820
0.54850
1.05550
0.65341
1.13520
0.48694
0.58140
0.66554
2.14960
1.27660
0.71070
1.05200
1.22100
1.13900
0.98200
2.03670
2.15400
1.95290
1.85900
0.53600
0.55978
0.42364
0.84894
0.33363
0.75680
0.85210
0.75120
2.44700
1.95290
1.95230
0.80820
1.57510
0.71245
2.15030
2.26690
0.25864
1.22700
0.49677
2.61780
6.26680
7.86780
1.84910
3.21010
1.71150
5.63310
1.23760
2.86300
1.12570
7.30450
2.55590
1.50510
3.79000
2.68650
5.28600
5.40200
1.81810
2.44320
6.09980
5.86900
2.11900
1.21410
0.87350
1.14710
0.26790
3.39240
3.29540
3.39700
1.92540
1.59540
1.63100
1.86560
0.74707
0.65201
0.77200
1.27390
0.93280
0.67938
0.87322
0.87239
2.40440
1.68230
0.83310
0.78248
0.77705
1.62110
0.71271
1.44060
1.54540
1.66950
0.80937
0.79662
1.48140
0.82886
1.59400
1.53100
1.20890
1.11260
1.70870
1.57180
1.19800
1.61020
1.64920
1.38000
2.61050
1.49600
1.49440
1.49280
1.88800
1.23560
1.21120
-2.44040
0.60196
0.46721
0.99900
1.73420
0.10880
0.78407
0.28563
1.28310
6.34500
5.44860
0.89089
1.43950
0.91824
3.38290
0.47248
1.89800
0.97196
4.99980
1.48290
0.84537
2.33100
1.42030
3.35100
3.49300
0.79777
0.58651
4.13020
4.32600
1.14700
0.89079
0.65560
0.90000
0.08896
2.24700
2.11500
2.24700
821.3
730.5
750.92
279.98
2344.9
286.03
2442
537.65
423.7
351.27
393.74
3521.5
967.71
743.1
2458.5
2433
2432.6
681.9
2484.2
650.43
717.04
741.02
2231.7
2187.6
667.3
2443
677.94
639.9
1060.8
950.59
775.4
722.7
510
710.4
739.07
644.61
1169
675.9
675.8
675.1
298.15
200
200
298.15
298.15
100
100
300
100
100
100
298.15
298.15
200
298.15
298.15
298.15
200
298.15
200
298.15
200
200
200
200
298.15
200
200
298.15
298.15
200
298.15
100
200
200
298.15
100
200
200
200
1.10220
0.78247
0.78483
1.02180
1.07700
0.41815
0.89310
1.33700
0.33538
0.38719
0.34081
1.26040
2.47630
2.48640
0.76617
1.52510
0.90956
1.30690
0.72827
0.70157
0.84963
2.31560
1.32780
0.74387
1.18320
1.54310
1.31390
1.21940
2.10540
2.27260
2.05940
2.66140
0.54044
0.59670
0.44572
1.07540
0.33363
0.87588
0.96428
0.87096
1500
1500
1500
1000.15
1500
1500
1500
1200
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
1500
2273.15
1500
1500
1500
2.74840
2.32870
2.32160
2.11750
2.49790
1.05370
3.24160
2.58230
0.56950
1.53970
0.79673
3.59670
6.69470
8.62250
2.55380
4.53700
2.56890
5.57840
1.81130
3.00290
1.64330
8.02510
4.20460
2.43220
4.19830
4.18780
5.37690
5.37540
3.75850
4.35600
6.83420
6.78340
2.37500
1.55900
1.14230
1.85950
0.52760
3.59200
3.59650
3.59230
Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2[C3/T/sinh(C3/T)]2 + C4[C5/T/cosh(C5/T)]2 where C0p is in J/(kmol∙K) and T is in K.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced
with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
2-155
2-156
PHYSICAL AnD CHEMICAL DATA
TABLE 2-76 Cp/Cv: Ratios of Specific Heats of Gases at 1 atm Pressure*
Compound
Formula
Acetaldehyde
Acetic acid
Acetylene
C2H4O
C2H4O2
C2H2
Air
Ammonia
Argon
NH3
Ar
Temperature, °C
Ratio of specific
heats,
(γ) = Cp /Cv
30
136
15
-71
925
17
-78
-118
15
15
-180
0–100
1.14
1.15
1.26
1.31
1.36
1.403
1.408
1.415
1.320
1.670
1.715
1.67
Benzene
Bromine
C6H6
Br2
90
20–350
1.10
1.32
Carbon dioxide
CO2
disulfide
monoxide
CS2
CO
1.299
1.37
1.21
1.402
1.433
1.355
1.15
1.256
1.315
Chlorine
Chloroform
Cyanogen
Cyclohexane
Cl2
CHCl3
(CN)2
C6H12
15
-75
100
15
-180
15
100
15
80
Dichlorodifluormethane
CCl2F2
25
1.139
Ethane
C2H6
Ethyl alcohol
ether
C2H6O
C4H10O
Ethylene
C2H4
100
15
-82
90
35
80
100
15
-91
1.157
1.200
1.28
1.13
1.08
1.086
1.201
1.253
1.345
Helium
Hexane (n-)
Hydrogen
He
C6H14
H2
-180
80
15
-76
-181
20
15
100
65
140
210
1.667
1.066
1.407
1.441
1.607
1.42
1.41
1.40
1.31
1.28
1.24
bromide
chloride
HBr
HCl
cyanide
HCN
Compound
Formula
Hydrogen (Cont.)
iodide
sulfide
HI
H 2S
Iodine
Isobutane
I2
C4H10
Krypton
Kr
Mercury
Methane
Hg
CH4
Methyl acetate
alcohol
ether
Methylal
C3H6O2
CH4O
C2H6O
C3H8O2
Neon
Nitric oxide
Ne
NO
Nitrogen
N2
Nitrous oxide
N2O
Oxygen
O2
Pentane (n-)
Phosphorus
Potassium
C5H12
P
K
Sodium
Sulfur dioxide
Na
SO2
Xenon
Xe
Temperature, °C
Ratio of specific
heats,
(γ) = Cp /Cv
20–100
15
-45
-57
1.40
1.332
1.350
1.356
185
15
1.30
1.110
19
1.672
360
600
300
15
-80
-115
15
77
6–30
13
40
1.67
1.113
1.196
1.310
1.339
1.347
1.14
1.237
1.11
1.06
1.09
19
15
-45
-80
15
-181
100
15
-30
-70
1.667
1.400
1.39
1.38
1.402
1.433
1.28
1.303
1.31
1.34
15
-76
-181
1.398
1.405
1.439
86
300
850
1.071
1.17
1.77
750–920
15
1.68
1.290
19
1.678
*For compounds that appear in Tables 2-109 to 2-122, values are from E. W. Lemmon, M. O. McLinden, and D. G. Friend, “Thermophysical Properties of Fluid Systems”
in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P. J. Linstrom and W. G. Mallard, June 2005, National Institute of Standards and
Technology, Gaithersburg, Md. (http://webbook.nist.gov). Values for other compounds are from International Critical Tables, vol. 5, pp. 80–82.
SPECIFIC HEATS OF AQUEOUS SOLUTIOnS
TABLE 2-79 Ethyl Alcohol
Additional References Most of the tables below are from International Critical Tables, vol. 5, pp. 115–116, 122–125. Specific heats for other
compounds in aqueous solution can also be found in the same reference.
TABLE 2-77 Acetic Acid (at 38çC)
Mole % acetic acid
Cal/(g⋅°C)
0
1.0
6.98
0.911
30.9
0.73
54.5
0.631
100
0.535
Specific heat, cal/(g⋅°C)
Mole % C2H5OH
3°C
23°C
41°C
4.16
11.5
37.0
61.0
100.0
1.05
1.02
0.805
0.67
0.54
1.02
1.03
0.86
0.727
0.577
1.02
1.03
0.875
0.748
0.621
TABLE 2-80
TABLE 2-78 Ammonia
Glycerol
Specific heat, cal/(g⋅°C)
Specific heat, cal/(g⋅°C)
Mole % NH3
2.4°C
20.6°C
41°C
61°C
0
10.5
20.9
31.2
41.4
1.01
0.98
0.96
0.956
0.985
1.0
0.995
0.99
1.0
0.995
1.06
1.03
1.0
1.02
Mole % C3H5(OH)3
15°C
32°C
2.12
4.66
11.5
22.7
43.9
100.0
0.961
0.929
0.851
0.765
0.67
0.555
0.960
0.924
0.841
0.758
0.672
0.576
SPECIFIC HEATS
TABLE 2-81 Hydrochloric Acid
TABLE 2-86 Potassium Hydroxide (at 19çC)
Specific heat, cal/(g⋅°C)
Mole % HCl
0.0
9.09
16.7
20.0
25.9
2-157
0°C
10°C
20°C
40°C
60°C
1.00
0.72
0.61
0.58
0.55
0.72
0.605
0.575
0.74
0.631
0.591
0.75
0.645
0.615
0.78
0.67
0.638
0.61
TABLE 2-82 Methyl Alcohol
Specific heat, cal/(g⋅°C)
Mole % CH3OH
5°C
20°C
40°C
5.88
12.3
27.3
45.8
69.6
100
1.02
0.975
0.877
0.776
0.681
0.576
1.0
0.982
0.917
0.811
0.708
0.60
0.995
0.98
0.92
0.83
0.726
0.617
Specific heat at 20°C,
cal/(g⋅°C)
0
10
20
30
40
50
60
70
80
90
1.000
0.900
0.810
0.730
0.675
0.650
0.640
0.615
0.575
0.515
0
1.0
0.497
0.975
1.64
0.93
4.76
0.814
9.09
0.75
TABLE 2-87 normal Propyl Alcohol
Specific heat, cal/(g⋅°C)
Mole % C3H7OH
5°C
20°C
40°C
1.55
5.03
11.4
23.1
41.2
73.0
100.0
1.03
1.07
1.035
0.877
0.75
0.612
0.534
1.02
1.06
1.032
0.90
0.78
0.645
0.57
1.01
1.03
0.99
0.91
0.815
0.708
0.621
TABLE 2-88 Sodium Carbonate*
Temperature, °C
% Na2CO3
by weight
0.000
1.498
2.000
2.901
4.000
5.000
6.000
8.000
10.000
13.790
13.840
20.000
25.000
TABLE 2-83 nitric Acid
% HNO3
by Weight
Mole % KOH
Cal/(g⋅°C)
17.6
30.0
76.6
98.0
0.9992
0.9807
0.9986
1.0098
1.0084
0.9786
0.9597
0.9594
0.9428
0.9761
0.9392
0.9183
0.9086
0.8924
0.9452
0.8881
0.8631
0.8936
0.8615
0.8911
*J. Chem. Soc. 3062–3079 (1931).
TABLE 2-89 Sodium Chloride
Specific heat, cal/(g⋅°C)
TABLE 2-84 Phosphoric Acid*
Mole % NaCl
%H2PO4
Cp at 21.3°C
cal/(g⋅°C)
%H3PO4
Cp at 21.3°C
cal/(g⋅°C)
2.50
3.80
5.33
8.81
10.27
14.39
16.23
19.99
22.10
24.56
25.98
28.15
29.96
32.09
33.95
36.26
38.10
40.10
42.08
44.11
46.22
48.16
49.79
0.9903
0.9970
0.9669
0.9389
0.9293
0.8958
0.8796
0.8489
0.8300
0.8125
0.8004
0.7856
0.7735
0.7590
0.7432
0.7270
0.7160
0.7024
0.6877
0.6748
0.6607
0.6475
0.6370
50.00
52.19
53.72
56.04
58.06
60.23
62.10
64.14
66.13
68.14
69.97
69.50
71.88
73.71
75.79
77.69
79.54
80.00
82.00
84.00
85.98
88.01
89.72
0.6350
0.6220
0.6113
0.5972
0.5831
0.5704
0.5603
0.5460
0.5349
0.5242
0.5157
0.5160
0.5046
0.4940
0.4847
0.4786
0.4680
0.4686
0.4593
0.4500
0.4419
0.4359
0.4206
*Z. Physik. Chem., A167, 42 (1933).
TABLE 2-85 Potassium Chloride
Specific heat, cal/(g⋅°C)
Mole % KCl
6°C
20°C
33°C
40°C
0.99
3.85
5.66
7.41
0.945
0.828
0.77
0.947
0.831
0.775
0.727
0.947
0.835
0.778
0.947
0.837
0.775
0.249
0.99
2.44
9.09
6°C
20°C
33°C
57°C
0.96
0.91
0.805
0.99
0.97
0.915
0.81
0.97
0.915
0.81
0.923
0.82
TABLE 2-90 Sodium Hydroxide (at 20çC)
Mole % NaOH
Cal/(g . °C)
0
1.0
0.5
0.985
1.0
0.97
9.09
0.835
16.7
0.80
28.6
0.784
37.5
0.782
TABLE 2-91 Sulfuric Acid*
%H2SO4
Cp at 20°C,
cal/(g⋅°C)
%H2SO4
Cp at 20°C,
cal/(g⋅°C)
0.34
0.68
1.34
2.65
3.50
5.16
9.82
15.36
21.40
22.27
23.22
24.25
25.39
26.63
28.00
29.52
30.34
31.20
33.11
0.9968
0.9937
0.9877
0.9762
0.9688
0.9549
0.9177
0.8767
0.8339
0.8275
0.8205
0.8127
0.8041
0.7945
0.7837
0.7717
0.7647
0.7579
0.7422
35.25
37.69
40.49
43.75
47.57
52.13
57.65
64.47
73.13
77.91
81.33
82.49
84.48
85.48
89.36
91.81
94.82
97.44
100.00
0.7238
.7023
.6770
.6476
.6153
.5801
.5420
.5012
.4628
.4518
.4481
.4467
.4408
.4346
.4016
.3787
.3554
.3404
.3352
*Vinal and Craig, Bur. Standards J. Research, 24, 475 (1940).
2-158
PHYSICAL AnD CHEMICAL DATA
SPECIFIC HEATS OF MISCELLAnEOUS MATERIALS
TABLE 2-92 Specific Heats of Miscellaneous Liquids
and Solids
Material
Alumina
Alundum
Asbestos
Asphalt
Bakelite
Brickwork
Carbon
(gas retort)
(see under Graphite)
Cellulose
Cement, Portland Clinker
Charcoal (wood)
Chrome brick
Clay
Coal
tar oils
Coal tars
Coke
Concrete
Cryolite
Diamond
Fireclay brick
Fluorspar
Gasoline
Glass (crown)
( flint)
(pyrex)
(silicate)
wool
Granite
Graphite
Gypsum
Kerosene
Limestone
Litharge
Magnesia
Magnesite brick
Marble
Porcelain, fired Berlin
Porcelain, green Berlin
Porcelain, fired earthenware
Porcelain, green earthenware
Specific heat, cal/(g⋅°C)
0.2 (100°C); 0.274 (1500°C)
0.186 (100°C)
0.25
0.22
0.3 to 0.4
About 0.2
0.168 (26 to 76°C)
0.314 (40 to 892°C)
0.387 (56 to 1450°C)
0.204
0.32
0.186
0.242
0.17
0.224
0.26 to 0.37
0.34 (15 to 90°C)
0.35 (40°C); 0.45 (200°C)
0.265 (21 to 400°C)
0.359 (21 to 800°C)
0.403 (21 to 1300°C)
0.156 (70 to 312°F); 0.219 (72 to 1472°F)
0.253 (16 to 55°C)
0.147
0.198 (100°C); 0.298 (1500°C)
0.21 (30°C)
0.53
0.16 to 0.20
0.117
0.20
0.188 to 0.204 (0 to 100°C)
0.24 to 0.26 (0 to 700°C)
0.157
0.20 (20 to 100°C)
0.165 (26 to 76°C); 0.390 (56 to 1450°C)
0.259 (16 to 46°C)
0.47
0.217
0.055
0.234 (100°C); 0.188 (1500°C)
0.222 (100°C); 0.195 (1500°C)
0.21 (18°C)
0.189 (60°C)
0.185 (60°C)
0.186 (60°C)
0.181 (60°C)
TABLE 2-92 Specific Heats of Miscellaneous Liquids
and Solids (Continued )
Material
Specific heat, cal/(g⋅°C)
Pyrex glass
Pyrites (copper)
Pyrites (iron)
Pyroxylin plastics
Quartz
Rubber (vulcanized)
Sand
Silica
Silica brick
Silicon carbide brick
Silk
Steel
Stone
Stoneware (common)
Turpentine
Wood (Oak)
Woods, miscellaneous
Wool
Zirconium oxide
0.20
0.131 (30°C)
0.136 (30°C)
0.34 to 0.38
0.17 (0°C); 0.28 (350°C)
0.415
0.191
0.316
0.202 (100°C); 0.195 (1500°C)
0.202 (100°C)
0.33
0.12
about 0.2
0.188 (60°C)
0.42 (18°C)
0.570
0.45 to 0.65
0.325
0.11 (100°C); 0.179 (1500°C)
TABLE 2-93 Oils (Animal, Vegetable, Mineral Oils)
Cp[cal/(g⋅°C)] = A / d 415 + B(t - 15)
where d = density, g/cm3.
°F = 9⁄5°C + 32; to convert calories per gram-degree Celsius to British thermal units per pound-degree Fahrenheit, multiply by 1.0; to convert grams
per cubic centimeter to pounds per cubic foot, multiply by 62.43.
Oils
A
Castor
Citron
Fatty drying
nondrying
semidrying
oils (except castor)
Naphthene base
Olive
Paraffin base
Petroleum oils
0.500
0.440
0.450
0.445
0.450
0.405
0.425
0.415
B
0.0007
(0.438 at 54°C)
0.0007
0.0007
0.0007
0.0007
0.0009
(0.47 at 7°C)
0.0009
0.0009
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
Unit Conversions °F = 9⁄5°C + 32; to convert kilocalories per gram-mole
to British thermal units per pound-mole, multiply by 1.799 × 10-3.
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
2-159
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds*
The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from (a) Bichowsky and Rossini, “Thermochemistry of the Chemical Substances,” Reinhold, New York, 1936; (b) Latimer, “Oxidation States of the Elements and Their Potentials in Aqueous Solution,” Prentice-Hall,
New York, 1938; (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards; and (d) the tables of Selected Values of
Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods
of calculation, standard states, and so on.
State†
Compound
Aluminum
Al
AlBr3
Al4C3
AlCl3
AlF3
AlI3
AlN
Al(NH4)(SO4)2
Al(NH4)(SO4)2⋅12H2O
Al(NO3)3⋅6H2O
Al(NO3)3⋅9H2O
Al2O3
Al(OH)3
Al2O3⋅SiO2
Al2O3⋅SiO2
Al2O3⋅SiO2
3Al2O3⋅2SiO2
Al2S3
Al2(SO4)3
Al2(SO4)3⋅6H2O
Al2(SO4)3⋅18H2O
Antimony
Sb
SbBr3
SbCl3
SbCl5
SbF3
SbI3
Sb2O3
Sb2O4
Sb2O5
Sb2S3
Arsenic
As
AsBr3
AsCl3
AsF3
AsH3
AsI3
As2O3
As2O5
As2S3
Barium
Ba
BaBr2
BaCl2
Ba(ClO3)2
Ba(ClO4)2
Ba(CN)2
Ba(CNO)2
BaCN2
BaCO3
BaCrO4
BaF2
BaH2
Ba(HCO3)2
BaI2
c
c
aq
c
c
aq, 600
c
aq
c
aq
c
c
c
c
c
c, corundum
c
c, sillimanite
c, disthene
c, andalusite
c, mullite
c
c
aq
c
c
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
0.00
-123.4
-209.5
-30.8
-163.8
-243.9
-329
-360.8
-72.8
-163.4
-57.7
-561.19
-1419.36
-680.89
-897.59
-399.09
-304.8
-648.7
-642.4
-642.0
-1874
-121.6
-820.99
-893.9
-1268.15
-2120
c
c
c
l
c
c
c, I, orthorhombic
c, II, octahedral
c
c
c, black
0.00
-59.9
-91.3
-104.8
-216.6
-22.8
-165.4
-166.6
-213.0
-230.0
-38.2
c
c
l
l
g
c
c
c
c
amorphous
0.00
-45.9
-80.2
-223.76
43.6
-13.6
-154.1
-217.9
-20
-34.76
c
c
aq, 400
c
aq, 300
c
aq, 1600
c
aq, 800
c
c
aq
c
c, witherite
c
c
aq, 1600
c
aq
c
aq, 400
0.00
-180.38
-185.67
-205.25
-207.92
-176.6
-170.0
-210.2
*For footnotes see end of table.
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
0.00
-189.2
-29.0
-209.5
-312.6
-152.5
-50.4
-486.17
-1179.26
-526.32
-376.87
-272.9
-739.53
-759.3
-1103.39
0.00
-77.8
-146.0
-186.6
-196.1
-36.9
0.00
-70.5
-212.27
37.7
-134.8
-183.9
-20
0.00
-183.0
-196.5
-134.4
-155.3
-63.6
-284.2
-342.2
-287.9
-284.6
-40.8
-459
-144.6
-155.17
BaMoO4
Ba3N2
Ba(NO2)2
Ba(NO3)2
BaO
Ba(OH)2
BaO⋅SiO2
Ba3(PO4)2
BaPtCl6
BaS
BaSO3
BaSO4
BaWO4
Beryllium
Be
BeBr2
BeCl2
BeI2
Be3N2
BeO
Be(OH)2
BeS
BeSO4
Bismuth
Bi
BiCl3
BiI3
BiO
Bi2O3
Bi(OH)3
Bi2S3
Bi2(SO4)3
Boron
B
BBr3
BCl3
BF3
B2H6
BN
B2O3
B(OH)3
B2S3
Bromine
Br2
-180.7
BrCl
Cadmium
Cd
CdBr2
-271.4
CdCl2
-48
-212.1
-265.3
-31.5
-414.4
-158.52
State†
Compound
Barium (Cont.)
Ba(IO3)2
Cd(CN)2
CdCO3
CdI2
Cd3N2
Cd(NO3)2
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
c
aq
c
c
c
aq
c
aq, 600
c
c
aq, 400
c
c
c
c
c
c
c
-264.5
-237.50
-370
-90.7
-184.5
-179.05
-236.99
-227.74
-133.0
-225.9
-237.76
-363
-992
-284.9
-111.2
-282.5
-340.2
-402
c
c
aq
c
aq
c
aq
c
c
c
c
c
aq
0.00
-79.4
-142
-112.6
-163.9
-39.4
-112
-134.5
-145.3
-215.6
-56.1
-281
c
c
aq
c
aq
c
c
c
c
c
0.00
-90.5
-101.6
-24
-27
-49.5
-137.1
-171.1
-43.9
-607.1
c
l
g
g
g
g
c
c
gls
c
c
0.00
-52.7
-44.6
-94.5
-265.2
7.5
-32.1
-302.0
-297.6
-260.0
-56.6
l
g
g
c
c
aq, 400
c
aq, 400
c
c
c
aq, 400
c
aq, 400
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-198.35
-150.75
-189.94
-209.02
-313.4
0.00
-127.9
-141.4
-103.4
-122.4
-138.3
-254.8
0.00
7.47
3.06
0.00
-75.8
-76.6
-92.149
-96.44
36.2
-178.2
-48.40
-47.46
39.8
-115.67
0.00
-76.4
-43.2
-117.9
-39.1
0.00
-50.9
-90.8
-261.0
19.9
-27.2
-282.9
-280.3
-229.4
0.00
0.931
-0.63
0.00
-70.7
-67.6
-81.889
-81.2
-163.2
-43.22
-71.05
(Continued)
2-160
PHYSICAL AnD CHEMICAL DATA
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
State†
Compound
Cadmium (Cont.)
CdO
Cd(OH)2
CdS
CdSO4
Calcium
Ca
CaBr2
CaC2
CaCl2
CaCN2
Ca(CN)2
CaCO3
CaCO3⋅MgCO3
CaC2O4
Ca(C2H3O2)2
CaF2
CaH2
CaI2
Ca3N2
Ca(NO3)2
Ca(NO3)2⋅2H2O
Ca(NO3)2⋅3H2O
Ca(NO3)2⋅4H2O
CaO
Ca(OH)2
CaO⋅SiO2
CaS
CaSO4
CaSO4⋅½H2O
CaSO4⋅2H2O
CaWO4
Carbon
C
CO
CO2
Cerium
Ce
CeN
Cesium
Cs
CsBr
CsCl
Cs2CO3
CsF
CsH
CsHCO3
CsI
CsNH2
CsNO3
Cs2O
CsOH
Cs2S
Cs2SO4
c
c
c
c
aq, 400
c
c
aq, 400
c
c
aq
c
c
aq
c, calcite
c, aragonite
c
c
c
aq
c
aq
c
c
aq, 400
c
c
aq, 400
c
c
c
c
c
aq, 800
c, II, wollastonite
c, I, pseudowollastonite
c
c, insoluble form
c, soluble form α
c, soluble form β
c
c
c
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
-62.35
-135.0
-34.5
-222.23
-232.635
0.00
-162.20
-187.19
-14.8
-190.6
-209.15
-85
-43.3
-289.5
-289.54
-558.8
-332.2
-356.3
-364.1
-290.2
-286.5
-46
-128.49
-156.63
-103.2
-224.05
-228.29
-367.95
-439.05
-509.43
-151.7
-235.58
-239.2
-377.9
-376.6
-114.3
-338.73
-336.58
-335.52
-376.13
-479.33
-387
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-55.28
-113.7
-33.6
-194.65
0.00
-181.86
-16.0
-179.8
-195.36
-54.0
-270.8
-270.57
-311.3
-264.1
-35.7
-157.37
-88.2
-177.38
-293.57
-351.58
-409.32
-144.3
-213.9
-207.9
-357.5
-356.6
-113.1
-311.9
-309.8
-308.8
-425.47
c, graphite
c, diamond
g
g
0.00
0.453
-26.416
-94.052
0.00
0.685
-32.808
-94.260
c
c
0.00
-78.2
0.00
-70.8
c
c
aq, 500
c
aq, 400
c
c
aq, 400
c
c
aq, 2000
c
aq, 400
c
c
aq, 400
c
c
aq, 200
c
c
aq
0.00
-97.64
-91.39
-106.31
-102.01
-271.88
-131.67
-140.48
-12
-230.6
-226.6
-83.91
-75.74
-28.2
-121.14
-111.54
-82.1
-100.2
-117.0
-87
-344.86
-340.12
0.00
-94.86
Chlorine
Cl2
ClF
ClO
ClO2
ClO3
Cl2O
Cl2O7
Chromium
Cr
CrBr3
Cr3C2
Cr4C
CrCl2
CrF2
CrF3
CrI2
CrO3
Cr2O3
Cr2(SO4)3
Cobalt
Co
CoBr2
Co3C
CoCl2
CoCO3
CoF2
CoI2
Co(NO3)2
CoO
Co3O4
Co(OH)2
Co(OH)3
CoS
Co2S3
CoSO4
Columbium
Cb
Cb2O5
Copper
Cu
CuBr
CuBr2
CuCl
CuCl2
CuClO4
Cu(ClO3)2
Cu(ClO4)2
CuI
CuI2
-101.61
Cu3N
Cu(NO3)2
-135.98
-7.30
CuO
Cu2O
Cu(OH)2
CuS
Cu2S
CuSO4
-210.56
-82.61
-96.53
-107.87
-316.66
State†
Compound
Cu2SO4
Erbium
Er
Er(OH)3
Fluorine
F2
F2O
g
g
g
g
g
g
g
c
aq
c
c
c
aq
c
c
c
aq
c
c
aq
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
0.00
-25.7
33
24.7
37
18.20
63
0.00
-21.008
-16.378
-103.1
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
0.00
29.5
22.40
0.00
-122.7
-21.20
-16.74
-93.8
-102.1
-152
-231
-63.7
-64.1
-139.3
-268.8
-249.3
-626.3
c
c
aq
c
c
aq, 400
c
aq
c
aq
c
aq
c
c
c
c
c
c
c
aq, 400
0.00
-55.0
-73.61
9.49
-76.9
-95.58
-172.39
-172.98
-24.2
-43.15
-102.8
-114.9
-57.5
-196.5
-131.5
-177.0
-22.3
-40.0
-216.6
c
c
0.00
-462.96
0.00
0.00
-26.7
-34.0
-42.4
-31.4
-48.83
-64.7
-28.3
0.00
-23.8
c
c
c
aq
c
c
aq, 400
aq
aq, 400
aq
c
c
aq
c
c
aq, 200
c
c
c
c
c
c
aq, 800
c
aq
0.00
-61.96
7.08
-66.6
-75.46
-155.36
-144.2
-37.4
-65.3
-108.9
-142.0
-19.8
-188.9
-17.8
-4.8
-11.9
17.78
-73.1
-83.6
-38.5
-43.00
-108.9
-11.6
-18.97
-184.7
-200.78
-179.6
-33.25
-24.13
1.34
15.4
-5.5
-16.66
-8.76
-36.6
-31.9
-38.13
-85.5
-11.69
-20.56
-158.3
-160.19
-152.0
c
c
0.00
-326.8
0.00
g
g
0.00
5.5
0.00
9.7
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
2-161
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
State†
Compound
Gallium
Ga
GaBr3
GaCl3
GaN
Ga2O
Ga2O3
Germanium
Ge
Ge3N4
GeO2
Gold
Au
AuBr
AuBr3
AuCl
AuCl3
AuI
Au2O3
Au(OH)3
Hafnium
Hf
HfO2
Hydrogen
H3AsO3
H3AsO4
HBr
HBrO
HBrO3
HCl
HCN
HClO
HClO3
HClO4
HC2H3O2
H2C2O4
HCOOH
H2CO3
HF
HI
HIO
HIO3
HN3
HNO3
HNO3⋅H2O
HNO3⋅3H2O
H2O
H2O2
H3PO2
H3PO3
H3PO4
H2S
H2S2
H2SO3
H2SO4
H2Se
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
c
c
c
c
c
c
0.00
-92.4
-125.4
-26.2
-84.3
-259.9
0.00
c
c
c
0.00
-15.7
-128.6
0.00
c
c
c
aq
c
c
aq
c
c
c
0.00
-3.4
-14.5
-11.0
-8.3
-28.3
-32.96
0.2
11.0
-100.6
0.00
c
c
0.00
-271.1
0.00
-258.2
aq
c
aq
g
aq, 400
aq
aq
g
aq, 400
g
aq, 100
aq, 400
aq
aq, 660
l
aq, 400
c
aq, 300
l
aq, 200
aq
g
aq, 200
g
aq, 400
aq
c
aq
g
g
l
aq, 400
l
l
g
l
l
aq, 200
c
aq
c
aq
c
aq, 400
g
aq, 2000
l
aq, 200
l
aq, 400
g
aq
-175.6
-214.9
-214.8
-8.66
-28.80
-25.4
-11.51
-22.063
-39.85
31.1
24.2
-28.18
-23.4
-31.4
-116.2
-116.74
-196.7
-194.6
-97.8
-98.0
-167.19
-64.2
-75.75
6.27
-13.47
-38
-56.77
-54.8
70.3
-31.99
-41.35
-49.210
-112.91
-252.15
-57.7979
-68.3174
-45.16
-45.80
-145.5
-145.6
-232.2
-232.2
-306.2
-309.32
-4.77
-9.38
-3.6
-146.88
-193.69
-212.03
20.5
18.1
-153.04
Hydrogen (Cont.)
H2SeO3
H2SeO4
24.47
H2SiO3
H4SiO4
H2Te
H2TeO3
H2TeO4
Indium
In
InBr3
InCl3
InI3
4.21
-0.76
18.71
-183.93
-12.72
-24.58
-19.90
5.00
-22.778
-31.330
27.94
26.55
-19.11
-0.25
-10.70
-93.56
-96.8
-165.64
-82.7
-85.1
-149.0
-64.7
0.365
-12.35
-23.33
-32.25
78.50
-17.57
-19.05
-78.36
-193.70
-54.6351
-56.6899
-28.23
-31.47
-120.0
-204.0
-270.0
-7.85
-128.54
17.0
18.4
State†
Compound
InN
In2O3
Iodine
I2
IBr
ICl
ICl3
I 2 O5
Iridium
Ir
IrCl
IrCl2
IrCl3
IrF6
IrO2
Iron
Fe
FeBr2
FeBr3
Fe3C
Fe(CO)5
FeCO3
FeCl2
FeCl3
FeF2
FeI2
FeI3
Fe4N
Fe(NO3)2
Fe(NO3)3
FeO
Fe2O3
Fe3O4
Fe(OH)2
Fe(OH)3
FeO⋅SiO2
Fe2P
FeSi
FeS
FeS2
FeSO4
Fe2(SO4)3
FeTiO3
Lanthanum
La
LaCl3
La3H8
LaN
La2O3
LaS2
La2S3
La2(SO4)3
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
c
aq
c
aq, 400
c
c
g
c
aq
aq
-126.5
-122.4
-130.23
-143.4
-267.8
-340.6
36.9
-145.0
-145.0
-165.6
c
c
aq
c
aq
c
aq
c
c
0.00
-97.2
-112.9
-128.5
-145.6
-56.5
-67.2
-4.8
-222.47
c
g
g
g
c
c
0.00
14.88
10.05
4.20
-21.8
-42.5
0.00
4.63
1.24
-1.32
-6.05
c
c
c
c
l
c
0.00
-20.5
-40.6
-60.5
-130
-40.14
0.00
-16.9
-32.0
-46.5
c, α
c
aq, 540
aq
c
l
c, siderite
c
aq
c
aq, 2000
aq, 1200
c
aq
aq
c
aq
aq, 800
c
c
c
c
c
c
c
c
c
c, pyrites
c, marcasite
c
aq, 400
aq, 400
c, ilmenite
0.00
-57.15
-78.7
-95.5
5.69
-187.6
-172.4
-81.9
-100.0
-96.4
-128.5
-177.2
-24.2
-47.7
-49.7
-2.55
-118.9
-156.5
-64.62
-198.5
-266.9
-135.9
-197.3
-273.5
-13
-19.0
-22.64
-38.62
-33.0
-221.3
-236.2
-653.3
-295.51
0.00
c
c
aq
c
c
c
c
c
aq
0.00
-253.1
-284.7
-160
-72.0
-539
-148.3
-351.4
-972
-101.36
-247.9
33.1
-115.7
0.00
-97.2
-117.5
-60.5
-69.47
-76.26
4.24
-154.8
-72.6
-83.0
-96.5
-151.7
-45
-39.5
0.862
-72.8
-81.3
-59.38
-179.1
-242.3
-115.7
-166.3
-23.23
-35.93
-195.5
-196.4
-533.4
-277.06
0.00
-64.6
(Continued)
2-162
PHYSICAL AnD CHEMICAL DATA
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
Compound
Lead
Pb
PbBr2
PbCO3
Pb(C2H3O2)2
PbC2O4
PbCl2
PbF2
PbI2
Pb(NO3)2
PbO
PbO2
Pb3O4
Pb(OH)2
PbS
PbSO4
Lithium
Li
LiBr
LiBrO3
Li2C2
LiCN
LiCNO
LiC2H3O2
Li2CO3
LiCl
LiClO3
LiClO4
LiF
LiH
LiHCO3
LiI
LiIO3
Li3N
LiNO3
Li2O
Li2O2
LiOH
LiOH⋅H2O
Li2O⋅SiO2
Li2Se
Li2SO4
Li2SO4⋅H2O
Magnesium
Mg
Mg(AsO4)2
MgBr2
Mg(CN)2
MgCN2
Mg(C2H3O2)2
MgCO3
MgCl2
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
c
c
aq
c, cerussite
c
aq, 400
c
c
aq
c
c
c
aq, 400
c, red
c, yellow
c
c
c
c
c
0.00
-66.24
-56.4
-167.6
-232.6
-234.2
-205.3
-85.68
-82.5
-159.5
-41.77
-106.88
-99.46
-51.72
-50.86
-65.0
-172.4
-123.0
-22.38
-218.5
0.00
-62.06
-54.97
-150.0
c
c
aq, 400
aq
c
aq
aq
aq
c
aq, 1900
c
aq, 278
aq
aq
c
aq, 400
c
aq, 2000
c
aq, 400
aq
c
c
aq, 400
c
c
aq
c
aq, 400
c
gls
c
aq
c
aq, 400
c
0.00
-83.75
-95.40
-77.9
-13.0
-31.4
-101.2
-183.9
-289.7
-293.1
-97.63
-106.45
-87.5
-106.3
-145.57
-144.85
-22.9
-231.1
-65.07
-80.09
-121.3
-47.45
-115.350
-115.88
-142.3
-151.9
-159
-116.58
-121.47
-188.92
-374
-84.9
-95.5
-340.23
-347.02
-411.57
c
c
aq
c
aq, 400
aq
c
aq
c
c
aq, 400
0.00
-731.3
-749
-123.9
-167.33
-39.7
-61
-344.6
-261.7
-153.220
-189.76
State†
-184.40
-75.04
-68.47
-148.1
-41.47
-58.3
-45.53
-43.88
-52.0
-142.2
-102.2
-21.98
-192.9
0.00
-95.28
-65.70
-31.35
-94.12
-160.00
-269.8
-267.58
-102.03
-70.95
-81.4
Compound
Magnesium (Cont.)
MgCl2⋅H2O
MgCl2⋅2H2O
MgCl2⋅4H2O
MgCl2⋅6H2O
MgF2
MgI2
MgMoO4
Mg3N2
Mg(NO3)2
Mg(NO3)2⋅2H2O
Mg(NO3)2⋅6H2O
MgO
MgO⋅SiO2
Mg(OH)2
MgS
MgSO4
MgTe
MgWO4
Manganese
Mn
MnBr2
Mn3C
Mn(C2H3O2)2
MnCO3
MnC2O4
MnCl2
MnF2
MnI2
-136.40
-210.98
-83.03
-102.95
-37.33
-96.95
-138.0
-106.44
-108.29
-105.64
-314.66
-375.07
0.00
Mn5N2
Mn(NO3)2
Mn(NO3)2.6H2O
MnO
MnO2
Mn2O3
Mn3O4
MnO.SiO2
Mn(OH)2
Mn(OH)3
Mn3(PO4)2
MnSe
MnS
MnSO4
Mn2(SO4)3
Mercury
Hg
HgBr
HgBr2
-630.14
Hg(C2H3O2)2
-156.94
-29.08
HgCl2
-286.38
-241.7
-143.77
HgCl
Hg2Cl2
Hg(CN)2
HgC2O4
State†
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
c
c
c
c
c
c
aq, 400
c
c
c
aq, 400
c
c
c
c
c, ppt.
c, brucite
c
aq
c
aq, 400
c
c
-230.970
-305.810
-453.820
-597.240
-263.8
-86.8
-136.79
-329.9
-115.2
-188.770
-209.927
-336.625
-624.48
-143.84
-347.5
-221.90
-223.9
-84.2
-108
-304.94
-325.4
-25
-345.2
c, α
c
aq
c
c
aq
c
c
c
aq, 400
aq, 1200
c
aq
c
c
aq, 400
c
c
c
c
c
c
c
c
c
c
c, green
c
aq, 400
c
aq
0.00
-91
-106
1.1
-270.3
-282.7
-211
-240.9
-112.0
-128.9
-206.1
-49.8
-76.2
-57.77
-134.9
-148.0
-557.07
-92.04
-124.58
-229.5
-331.65
-301.3
-163.4
-221
-736
-26.3
-47.0
-254.18
-265.2
-635
-657
l
g
c
aq
c
aq
c
aq
g
c
c
aq, 1110
c
0.00
23
-40.68
-38.4
-196.3
-192.5
-53.4
-50.3
19
-63.13
62.8
66.25
-159.3
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-205.93
-267.20
-387.98
-505.45
-132.45
-100.8
-140.66
-160.28
-496.03
-136.17
-326.7
-200.17
-193.3
-277.7
-283.88
0.00
-97.8
1.26
-227.2
-192.5
-102.2
-180.0
-73.3
-46.49
-101.1
-441.2
-86.77
-111.49
-209.9
-306.22
-282.1
-143.1
-190
-27.5
-48.0
-228.41
0.00
18
-38.8
-9.74
-139.2
-42.2
-23.25
14
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
2-163
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
g
c, red
g
c
aq
aq
c, red
c, yellow ppt.
c
c, black
c
c
57.1
-25.3
33
-28.88
-56.8
-58.5
-21.6
-20.8
-21.6
-10.7
-166.6
-177.34
52.25
-24.0
23
-26.53
-13.09
-15.65
-13.94
c
c
c
c
c
c
c
0.00
4.36
-8.3
-130
-180.39
-56.27
-61.48
c
c
aq
c
aq
aq
c
aq, 400
c
aq
c
aq
c
aq, 200
c
c
c
c
c
aq, 200
0.00
-53.4
-72.6
9.2
-249.6
230.9
-75.0
-94.34
-157.5
-171.6
-22.4
-42.0
-101.5
-113.5
-58.4
-129.8
-163.2
-20.4
-216
-231.3
g
g
g
aq, 200
c
aq
c
aq, 400
c
aq
c
aq
aq
c
aq
c
aq, 400
c
aq
c
aq
c
aq
c
aq
c
aq, 500
0.00
-27
-10.96
-19.27
-64.57
-60.27
-148.1
-148.58
-0.7
3.6
-17.8
-12.3
-223.4
-266.3
-260.6
-75.23
-71.20
-69.4
-63.2
-276.9
-271.3
-111.6
-110.2
-48.43
-44.97
-87.40
-80.89
State†
Compound
Mercury (Cont.)
HgH
HgI2
HgI
Hg2I2
Hg(NO3)2
Hg2(NO3)2
HgO
Hg2O
HgS
HgSO4
Hg2SO4
Molybdenum
Mo
Mo2C
Mo2N
MoO2
MoO3
MoS2
MoS3
Nickel
Ni
NiBr2
Ni3C
Ni(C2H3O2)2
Ni(CN)2
NiCl2
NiF2
NiI2
Ni(NO3)2
NiO
Ni(OH)2
Ni(OH)3
NiS
NiSO4
Nitrogen
N2
NF3
NH3
NH4Br
NH4C2H3O2
NH4CN
NH4CNS
(NH4)2CO3
(NH4)2C2O4
NH4Cl
NH4ClO4
(NH4)2CrO4
NH4F
NH4I
NH4NO3
-12.80
-8.80
-149.12
0.00
2.91
-118.0
-162.01
-54.19
-57.38
0.00
-60.7
8.88
-190.1
66.3
-74.19
-142.9
-36.2
-64.0
-51.7
-105.6
-187.6
Nitrogen (Cont.)
NH4OH
(NH4)2S
(NH4)2SO4
N2H4
N2H4⋅H2O
N2H4⋅H2SO4
N2O
NO
NO2
N2O4
N2O5
NOBr
NOCl
Osmium
Os
OsO4
Oxygen
O2
O3
Palladium
Pd
PdO
Phosphorus
P
P
P2
P4
PBr3
PBr5
PCl3
PCl5
PH3
PI3
P2O5
POCl3
Platinum
Pt
PtBr4
0.00
-3.903
-43.54
-108.26
20.4
4.4
-164.1
-196.2
-48.59
-21.1
PtCl2
PtCl4
PtI4
Pt(OH)2
PtS
PtS2
Potassium
K
K3AsO3
K3AsO4
KH2AsO4
KBr
KBrO3
KC2H3O2
KCl
-209.3
-84.7
-31.3
State†
Compound
KClO3
KClO4
KCN
aq
aq, 400
c
aq, 400
l
l
c
g
g
g
g
c
l
g
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
-87.59
-55.21
-281.74
-279.33
12.06
-57.96
-232.2
19.55
21.600
7.96
2.23
-10.0
11.6
12.8
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-14.50
-215.06
-214.02
24.82
20.719
12.26
23.41
19.26
16.1
c
c
g
0.00
-93.6
-80.1
0.00
-70.9
-68.1
g
g
0.00
33.88
0.00
38.86
c
c
0.00
-20.40
0.00
0.00
-4.22
150.35
33.82
13.2
-45
-60.6
-70.0
-76.8
-91.0
2.21
-10.9
-360.0
-138.4
0.00
-1.80
141.88
24.60
5.89
c, white (“yellow”)
c, red (“violet”)
g
g
g
l
c
g
l
g
g
c
c
g
c
c
aq
c
c
aq
c
c
c
c
c
aq
aq
c
c
aq, 400
c
aq, 1667
c
aq, 400
c
aq, 400
c
aq, 400
c
aq, 400
c
aq, 400
0.00
-40.6
-50.7
-34
-62.6
-82.3
-18
-87.5
-20.18
-26.64
0.00
-323.0
-390.3
-271.2
-94.06
-89.19
-81.58
-71.68
-173.80
-177.38
-104.348
-100.164
-93.5
-81.34
-103.8
-101.14
-28.1
-25.3
-65.2
-63.3
-73.2
-1.45
-127.2
0.00
-67.9
-18.55
-24.28
0.00
-355.7
-236.7
-90.8
-92.0
-60.30
-156.73
-97.76
-98.76
-69.30
-72.86
-28.08
(Continued)
2-164
PHYSICAL AnD CHEMICAL DATA
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
State†
Compound
Potassium (Cont.)
KCNO
KCNS
K2CO3
K2C2O4
K2CrO4
K2Cr2O7
KF
K3Fe(CN)6
K4Fe(CN)6
KH
KHCO3
KI
KIO3
KIO4
KMnO4
K2MoO4
KNH2
KNO2
KNO3
K2O
K2O⋅Al2O3⋅SiO2
K2O⋅Al2O3⋅SiO2
KOH
K3PO3
K3PO4
KH2PO4
K2PtCl4
K2PtCl6
K2Se
K2SeO4
K2S
K2SO3
K2SO4
K2SO4⋅Al2(SO4)3
K2SO4⋅Al2(SO4)3·
24H2O
K2S2O6
Rhenium
Re
ReF6
Rhodium
Rh
RhO
Rh2O
Rh2O3
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
c
aq
c
aq, 400
c
aq, 400
c
aq, 400
c
aq, 400
c
aq, 400
c
aq, 180
c
aq
c
aq
c
c
aq, 2000
c
aq, 500
c
aq, 400
aq
c
aq, 400
aq, 880
c
aq
c
aq, 400
c
c, leucite
gls
c, adularia
c, microcline
gls
c
aq, 400
aq
aq
c
c
aq
c
aq, 9400
c
aq
aq
c
aq, 400
c
aq
c
aq, 400
c
-99.6
-94.5
-47.0
-41.07
-274.01
-280.90
-319.9
-315.5
-333.4
-328.2
-488.5
-472.1
-134.50
-138.36
-48.4
-34.5
-131.8
-119.9
-10
-229.8
-224.85
-78.88
-73.95
-121.69
-115.18
-98.1
-192.9
-182.5
-364.2
-28.25
-86.0
-118.08
-109.79
-86.2
-1379.6
-1368.2
-1784.5
-1784.5
-1747
-102.02
-114.96
-397.5
-478.7
-362.7
-254.7
-242.6
-299.5
-286.1
-74.4
-83.4
-267.1
-121.5
-110.75
-267.7
-269.7
-342.65
-336.48
-1178.38
c
c
-2895.44
-418.62
-2455.68
c
g
0.00
-274
0.00
c
c
c
c
0.00
-21.7
-22.7
-68.3
0.00
-90.85
Rubidium
Rb
RbBr
-44.08
-264.04
RbCN
Rb2CO3
-293.1
RbCl
-306.3
RbF
-440.9
-133.13
RbHCO3
RbI
-5.3
-207.71
-77.37
-79.76
-101.87
-99.68
-169.1
-168.0
-342.9
-75.9
-94.29
-93.68
-105.0
-443.3
-326.1
-226.5
-263.6
-99.10
-240.0
-111.44
-251.3
-314.62
-310.96
-1068.48
State†
Compound
RbNH2
RbNO3
Rb2O
Rb2O2
RbOH
Ruthenium
Ru
RuS2
Selenium
Se
Se2Cl2
SeF6
SeO2
Silicon
Si
SiBr4
SiC
SiCl4
SiF4
SiH4
SiI4
Si3N4
SiO2
Silver
Ag
AgBr
Ag2C2
AgC2H3O2
AgCN
Ag2CO3
Ag2C2O4
AgCl
AgF
AgI
AgIO3
AgNO2
AgNO3
Ag2O
c
c
g
aq, 500
aq
c
aq, 220
c
g
aq, ∞
c
aq, 400
c
aq, 2000
c
g
aq, 400
c
c
aq, 400
c
c
c
aq, 200
c
c
c, I, hexagonal
c, II, red, monoclinic
l
g
c
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
0.00
-95.82
-45.0
-90.54
-25.9
-273.22
-282.61
-105.06
-53.6
-101.06
-133.23
-139.31
-230.01
-225.59
-81.04
-31.2
-74.57
-27.74
-119.22
-110.52
-82.9
-107
-101.3
-115.8
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
0.00
-52.50
-93.38
-263.78
-98.48
-57.9
-100.13
-134.5
-209.07
-40.5
-81.13
-95.05
-106.39
0.00
-46.99
0.00
-44.11
0.00
0.2
0.00
-22.06
-246
-56.33
-13.73
-222
0.00
-93.0
-28
-150.0
-142.5
-370
-14.8
-29.8
-179.25
-202.62
0.00
c
l
c
l
g
g
g
c
c
c, cristobalite,
1600° form
c, cristobalite,
1100° form
c, quartz
c, tridymite
-203.35
-203.23
c
c
c
c
aq
c
c
c
c
c
aq, 400
c
c
c
aq
c
aq, 6500
c
0.00
-23.90
84.5
-95.9
-91.7
33.8
-119.5
-158.7
-30.11
-48.7
-53.1
-15.14
-42.02
-11.6
-2.9
-29.4
-24.02
-6.95
-27.4
-133.9
-133.0
-360
-9.4
-154.74
-202.46
-190.4
0.00
-23.02
-70.86
38.70
-103.0
-25.98
-47.26
-16.17
-24.08
3.76
9.99
-7.66
-7.81
-2.23
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
2-165
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
State†
Compound
Silver (Cont.)
Ag2S
Ag2SO4
Sodium
Na
Na3AsO3
Na3AsO4
NaBr
NaBrO
NaBrO3
NaC2H3O2
NaCN
NaCNO
NaCNS
Na2CO3
NaCO2NH2
Na2C2O4
NaCl
NaClO3
NaClO4
Na2CrO4
Na2Cr2O7
NaF
NaH
NaHCO3
NaI
NaIO3
Na2MoO4
NaNO2
NaNO3
Na2O
Na2O2
Na2O⋅SiO2
Na2O⋅Al2O3⋅3SiO2
Na2O⋅Al2O3⋅4SiO2
NaOH
Na3PO3
Na3PO4
Na2PtCl4
Na2PtCl6
Na2Se
Na2SeO4
Na2S
Na2SO3
Na2SO4
c
c
aq
c
aq, 500
c
aq, 500
c
aq, 400
aq
aq, 400
c
aq, 400
c
aq, 200
c
aq
c
aq, 400
c
aq, 1000
c
c
aq, 600
c
aq, 400
c
aq, 400
c
aq, 476
c
aq, 800
aq, 1200
c
aq, 400
c
c
aq
c
aq, ∞
aq, 400
c
aq
c
aq
c
aq, 400
c
c
c
c, natrolite
c
c
aq, 400
aq, 1000
c
aq, 400
aq
c
aq
c
aq, 440
c
aq, 800
c
aq, 400
c
aq, 800
c
aq, 1100
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-5.5
-170.1
-165.8
-7.6
-146.8
-139.22
0.00
-314.61
-366
-381.97
-86.72
-86.33
-78.9
-68.89
-170.45
-175.450
-22.47
-22.29
-96.3
-91.7
-39.94
-38.23
-269.46
-275.13
-142.17
-313.8
-309.92
-98.321
-97.324
-83.59
-78.42
-101.12
-97.66
-319.8
-323.0
-465.9
-135.94
-135.711
-14
-226.0
-222.1
-69.28
-71.10
-112.300
-364
-358.7
-86.6
-83.1
-111.71
-106.880
-99.45
-119.2
-383.91
-1180
-1366
-101.96
-112.193
-389.1
-457
-471.9
-237.2
-272.1
-280.9
-59.1
-78.1
-254
-261.5
-89.8
-105.17
-261.2
-264.1
-330.50
-330.82
0.00
-341.17
-87.17
-57.59
-152.31
-23.24
-86.00
-39.24
-249.55
-251.36
-283.42
-91.894
-93.92
Sodium (Cont.)
Na2SO4⋅10H2O
Na2WO4
Strontium
Sr
SrBr2
Sr(C2H3O2)2
Sr(CN)2
SrCO3
SrCl2
SrF2
Sr(HCO3)2
SrI2
Sr3N2
Sr(NO3)2
SrO
SrO⋅SiO2
SrO2
Sr2O
Sr(OH)2
Sr3(PO4)2
-62.84
SrS
-73.29
SrSO4
-296.58
-431.18
-129.0
-128.29
-9.30
-202.66
-202.87
SrWO4
Sulfur
S
-74.92
-94.84
-333.18
-71.04
-87.62
-88.84
-90.06
-105.0
-361.49
-90.60
-100.18
-428.74
-216.78
-89.42
-230.30
-101.76
-240.14
-241.58
-302.38
-301.28
State†
Compound
S2
S6
S8
S2Br2
SCl4
S2Cl2
S2Cl4
SF6
SO
SO2
SO3
SO2Cl2
Tantalum
Ta
TaN
Ta2O5
Tellurium
Te
TeBr4
TeCl4
TeF6
TeO2
Thallium
Tl
TlBr
TlCl
c
c
aq
c
c
aq, 400
c
aq
aq
c
c
aq, 400
c
aq
c
aq, 400
c
c
aq, 400
c
gls
c
c
c
aq, 800
c
aq
c
aq
c
aq, 400
c
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-1033.85
-391
-381.5
-870.52
0.00
-171.0
-187.24
-358.0
-364.4
-59.5
-290.9
-197.84
-209.20
-289.0
-459.1
-136.1
-156.70
-91.4
-233.2
-228.73
-140.8
-364
-153.3
-153.6
-228.7
-239.4
-980
-985
-113.1
-120.4
-345.3
-345.0
-393
0.00
-0.071
0.257
-345.18
0.00
-182.36
-311.80
-54.50
-271.9
-195.86
-413.76
-157.87
-76.5
-185.70
-133.7
-139.0
-208.27
-881.54
-109.78
-309.30
c, rhombic
c, monoclinic
l, λ
l, λµ equilibrium
g
g
g
g
l
l
l
l
g
g
g
g
l
c, α
c, β
c, γ
g
l
0.00
0.023
0.072
0.071
43.57
19.36
13.97
12.770
53.25
31.02
27.78
27.090
-4
-13.7
-14.2
-24.1
-262
19.02
-70.94
-94.39
-103.03
-105.09
-105.92
-109.34
-82.04
-89.80
-237
12.75
-71.68
-88.59
-88.28
-88.22
-88.34
-88.98
-74.06
-75.06
c
c
c
0.00
-51.2
-486.0
0.00
-45.11
-453.7
c
c
c
g
c
0.00
-49.3
-77.4
-315
-77.56
0.00
-57.4
-292
-64.66
c
c
aq
c
aq
0.00
-41.5
-28.0
-49.37
-38.4
0.00
-39.43
-32.34
-44.46
-39.09
-5.90
(Continued)
2-166
PHYSICAL AnD CHEMICAL DATA
TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued )
Compound
Thallium (Cont.)
TlCl3
TlF
TlI
TlNO3
Tl2O
Tl2O3
TlOH
Tl2S
Tl2SO4
Thorium
Th
ThBr4
ThC2
ThCl4
ThI4
Th3N4
ThO2
Th(OH)4
Th(SO4)2
Tin
Sn
SnBr2
SnBr4
SnCl2
SnCl4
SnI2
SnO
SnO2
Sn(OH)2
Sn(OH)4
SnS
Titanium
Ti
TiC
TiCl4
TiN
TiO2
†
State†
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
c
aq
aq
c
aq
c
aq
c
c
c
aq
c
c
aq, 800
-82.4
-91.0
-77.6
-31.1
-12.7
-58.2
-48.4
-43.18
-120
-57.44
-53.9
-22
-222.8
-214.1
c
c
aq
c
c
aq
aq
c
c
c, “soluble”
c
aq
0.00
-281.5
-352.0
-45.1
-335
-392
-292.0
-309.0
-291.6
-336.1
-632
-668.1
c, II, tetragonal
c, III, “gray,” cubic
c
aq
c
aq
c
aq
l
aq
c
aq
c
c
c
c
c
0.00
0.6
-61.4
-60.0
-94.8
-110.6
-83.6
-81.7
-127.3
-157.6
-38.9
-33.3
-67.7
-138.1
-136.2
-268.9
-18.61
c
c
l
c
c, III, rutil
amorphous
0.00
-110
-181.4
-80.0
-225.0
-214.1
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
-44.25
-73.46
-31.3
-20.09
-36.32
-34.01
-45.54
-45.35
-197.79
-191.62
0.00
-295.31
-322.32
-246.33
-282.3
-280.1
-549.2
0.00
1.1
-55.43
-97.66
-68.94
-110.4
-124.67
-30.95
-60.75
-123.6
-115.95
-226.00
0.00
-109.2
-165.5
-73.17
-211.9
-201.4
Heat of
formation‡§
ΔH ( formation) at
25°C,
kcal/mol
Free energy
of formation∙¶ ΔF
( formation)
at 25°C,
kcal/mol
c
c
c
c
0.00
-130.5
-195.7
-84
0.00
-118.3
-177.3
c
c
c
c
c
c
c
c
c
0.00
-29
-213
-251
-274
-256.6
-756.8
-291.6
-845.1
0.00
c
c
l
l
c
c
c
c
c
0.00
-147
-187
-165
-41.43
-195
-296
-342
-373
c
c
c
aq, 400
c
aq, 400
c
c
c
aq, 400
aq
c
aq
aq, 400
c, hexagonal
c
c, rhombic
c, wurtzite
c
aq, 400
0.00
-3.6
-77.0
-93.6
-259.4
-269.4
17.06
-192.9
-99.9
-115.44
-192.9
-50.50
-61.6
-134.9
-83.36
-282.6
-153.66
-45.3
-233.4
-252.12
c
c
c
c
c, monoclinic
c
c
0.00
-29.8
-268.9
-82.5
-258.5
-411.0
-337
State†
Compound
Tungsten
W
WO2
WO3
WS2
Uranium
U
UC2
UCl3
UCl4
U3N4
UO2
UO2(NO3)2⋅6H2O
UO3
U3O8
Vanadium
V
VCl2
VCl3
VCl4
VN
V2O2
V2O3
V2O4
V2O5
Zinc
Zn
ZnSb
ZnBr2
Zn(C2H3O2)2
Zn(CN)2
ZnCO3
ZnCl2
ZnF2
ZnI2
Zn(NO3)2
ZnO
ZnO⋅SiO2
Zn(OH)2
ZnS
ZnSO4
Zirconium
Zr
ZrC
ZrCl4
ZrN
ZrO2
Zr(OH)4
ZrO(OH)2
-249.6
-242.2
-617.8
0.00
-35.08
-277
-316
-342
0.00
-3.88
-72.9
-214.4
-173.5
-88.8
-166.6
-49.93
-87.7
-76.19
-44.2
-211.28
0.00
-34.6
-75.9
-244.6
-307.6
The physical state is indicated as follows: c, crystal (solid); l, liquid; g, gas; gls, glass or solid supercooled liquid; aq, in aqueous solution. A number following the
symbol aq applies only to the values of the heats of formation (not to those of free energies of formation); and indicates the number of moles of water per mole of solute;
when no number is given, the solution is understood to be dilute. For the free energy of formation of a substance in aqueous solution, the concentration is always that
of the hypothetical solution of unit molality.
‡
The increment in heat content, ΔH, is the reaction of forming the given substance from its elements in their standard states. When ΔH is negative, heat is evolved in
the process, and, when positive, heat is absorbed.
§
The heat of solution in water of a given solid, liquid, or gaseous compound is given by the difference in the value for the heat of formation of the given compound in
the solid, liquid, or gaseous state and its heat of formation in aqueous solution. The following two examples serve as an illustration of the procedure: (1) For NaCl(c) and
NaCl(aq, 400H2O), the values of ΔH( formation) are, respectively, -98.321 and -97.324 kcal/mol. Subtraction of the first value from the second gives
ΔH = 0.998 kcal/mol for the reaction of dissolving crystalline sodium chloride in 400 mol of water. When this process occurs at a constant pressure of 1 atm, 0.998 kg-cal
of energy are absorbed. (2) For HCl(g) and HCl(aq, 400H2O), the values for ΔH( formation) are, respectively, -22.06 and -39.85 kcal/mol. Subtraction of the first from the
second gives ΔH = -17.79 kcal/mol for the reaction of dissolving gaseous hydrogen chloride in 400 mol of water. At a constant pressure of 1 atm, 17.79 kcal of energy are
evolved in this process.
∙The increment in the free energy, ΔF, is the reaction of forming the given substance in its standard state from its elements in their standard states. The standard
states are: for a gas, fugacity (approximately equal to the pressure) of 1 atm; for a pure liquid or solid, the substance at a pressure of 1 atm; for a substance in aqueous
solution, the hypothetical solution of unit molality, which has all the properties of the infinitely dilute solution except the property of concentration.
¶ The free energy of solution of a given substance from its normal standard state as a solid, liquid, or gas to the hypothetical one molal state in aqueous solution may
be calculated in a manner similar to that described in footnote § for calculating the heat of solution.
TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K
Cmpd. no.
2-167
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
Ideal gas enthalpy of
formation, J/kmol × 1E-07
-17.1
-23.83
-43.28
-57.55
-21.57
6.467
22.82
-8.18
-35.591
17.97
0
-4.5898
-6.79
0
-10.09
8.288
11.15
-29.41
21.57
5.68
-9.025
-11.5
9.33
17.849
3.091
10.5018
-6.36
-3.77
16.23
10.924
-12.579
-44.58
-43.32
-27.51
-29.29
-0.05
-0.74
-1.1
-48.56
-1.314
-8.78
-9.66
16.52
-20.62
-47.58
3.342
-39.351
11.69
-11.053
Ideal gas Gibbs energy of
formation, J/kmol × 1E-07
-13.78
-15.96
-37.45
-47.6
-15.13
8.241
21.068
-5.68
-30.6
18.92
0
-1.64
2.27
0
-0.211
12.96
14.76
-21.42
25.8
17.3
-0.254
3.37
16.3
27.63
0.314
13.8532
-2.574
-2.7037
19.86
14.972
-1.67
-30.44
-29.18
-15.07
-16.7
7.041
6.536
6.32
-31.26
14.54
1.139
0.512
20.225
-11.48
-36
10.57
-39.437
6.68
-13.715
Ideal gas entropy,
J/(kmol∙K) × 1E-05
Standard net enthalpy of
combustion, J/kmol × 1E-09
2.6384
2.722
2.825
3.899
2.954
2.438
2.0081
2.97
3.15
2.77267
1.94452
1.9266
3.61
1.54845
3.641
2.693
3.369
3.69
3.21
4.4
3.713
4.39
3.607
3.9367
2.4535
3.24386
2.873
2.421
2.93
2.7889
3.0991
4.065
4.065
3.618
3.566
3.074
3.012
2.965
4.425
4.3949
3.752
3.667
2.9039
3.418
3.601
3.337
2.13677
2.379
1.97556
-1.1046
-1.0741
-0.7866
-1.675
-1.659
-1.18118
-1.257
-1.5468
-1.32717
-1.71238
0
-0.31683
-3.6072
0
-3.39877
-3.136
-3.4474
-3.0951
-3.524
-6.2876
-3.56
-4.83
-4.06
-6.248
0
-3.01917
-1.301
-0.7185
-2.4617
-2.409
-2.65732
-2.2678
-2.2824
-2.454
-2.446
-2.5408
-2.5339
-2.53
-3.28
-5.5644
-2.9554
-2.949
-2.4647
-2.301
-2.008
-2.4146
-1.0769
-0.283
(Continued)
2-168
TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued )
Cmpd. no.
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
Name
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Formula
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CAS
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
Mol. wt.
153.8227
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
Ideal gas enthalpy of
formation, J/kmol × 1E-07
Ideal gas Gibbs energy of
formation, J/kmol × 1E-07
-9.581
-92.21
0
5.109
-11.23
-10.29
-8.57
-13.32
-14.477
-13.23
-12.857
-12.535
0.4
30.894
2.85
-12.33
-28.62
-22.61
-0.46
-7.703
3.23
5.33
-9.602
-33.17
-24.946
-59.43
-39.85
-12.47
-21.09
4.1
0
-4.08
-3.89
-5.354
-87.76
0
9.829
-6.045
-7.01
-6.209
-5.251
-6.136
-4.019
-3.543
-3.166
13.79
29.76
11.22
3.191
-10.95
-9.028
10.77
3.885
11.05
10.44
4.886
-6.349
3.318
-30.5
-10.02
12.27
6.165
25.16
0
-1.181
-1.054
-33.34
2.57
3.02
2.25
-12.941
-12.979
-9.552
-15.08
-16.28
-40.847
-7.142
-25.21
-8.356
-49.7
-44.77
-8.827
7.79
8.29
7.67
-7.259
-7.3945
-6.896
-6.52
-8.018
-22.574
7.308
-12.21
1.774
-43.9485
-39.19
Ideal gas entropy,
J/(kmol∙K) × 1E-05
Standard net enthalpy of
combustion, J/kmol × 1E-09
3.0991
2.62
2.23079
3.1403
2.758
2.956
2.341
3.155
3.0594
3.5604
3.5259
3.5075
3.86
2.4117
2.64396
2.97276
3.277
3.3426
3.10518
2.929
2.91267
2.37378
3.646
5.672
5.457
5.99
5.971
5.433
6.116
5.263
1.4486
3.276
3.297
2.92964
5.014
3.4353
3.4185
3.3674
3.0501
3.0828
2.7018
3.448
3.548
4.29
3.522
3.423
3.681
2.824
2.88194
-0.2653
0.5286
0
-2.976
-1.279
-0.38
-0.6705
-1.864
-1.863
-3.52783
-3.528
-3.52256
-4.951
-1.096
-2.5678
-3.656
-3.4639
-3.299
-3.532
-3.0709
-2.9393
-1.9593
-3.968
-5.958
-6.29422
-5.72
-6.116
-6.1809
-6.6161
-6.1037
-0.24625
-1.16
-1.1769
-4.94691
-2.825
-2.826
-2.802
-1.1104
-1.105
-0.51388
-1.72
-1.707
-2.4105
-2.8003
-2.5035
-2.9607
-0.773662
-0.823
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Difluoromethane
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
52.02339
101.19
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
-45.23
-14.38
-31.92
-31.14
-38.97
-38.42
14.57
-1.845
-17.68
-18.1
-17.2172
-17.9996
-2.42
-18.41
-19.17
-19.41
-60.5
-9.47
-3.724
-15.046
-62.742
-31.58
5.2
-11.6
-29.072
-45.646
-8.382
-23.495
-44.45
-4.715
2.992
-32.6
-53.78
-48.55
-17.15
-12.69
5.251
-1.73
-39.22
12.3428
-5.263
-38.83
-55.95
-33.37
-28.58
-28.61
-4.63
-46.36
-27.22
-59.15
0
-11.6566
-42.4747
6.42
-12.48
-12.37
-23.8
-20.11
18.49
6.839
-0.3125
3.52293
4.12124
3.44761
1.516
-11.28
-8.84
0.5717
-46.7749
-1.925
0.7302
-8.1441
-41.97
-18.16
17.5
11.96
4.981
11.57
-3.192
-16.785
-32.8
3.616
13.073
-19.05
-35.9
-31.22
3.955
4.48
6.844
10.3
-30.18
17.7987
-1.323
-30.31
-32.49
-9.042
-12.64
-13.3
-0.4814
-31.93
-11.52
-50.66
0
-6.9036
2.4658
4.12
3.989
4.27
3.726
4.038
2.833
2.7296
3.6592
3.65012
3.7451
3.70912
3.35291
2.667
3.26
4.1455
6.6
2.9953
2.8585
3.0627
4.245
3.0012
4.13
3.2
6.2415
9.3787
2.2912
2.8064
3.597
2.848
3.6063
4.55
4.23
4.417
3.826
3.783
2.192
3.21833
3.04891
2.5062
2.4299
3.282
5.097
5.076
3.8
4.069
2.961
4.025
3.881
4.07
2.02789
3.02629
-0.183031
-3.99
-3.70261
-4.095
-2.394
-2.996
-2.4189
-1.6146
-3.84761
-4.8639
-4.87084
-4.86436
-2.0441
-1.3284
-1.78871
-4.46075
-4.4662
-2.569
-1.7443
-1.6054
-4.41057
-2.1863
-5.8939
-4.0189
-7.51368
-12.3908
-1.42864
-1.235
-2.061
-1.5874
-4.3448
-4.41
-3.21203
-3.284
-4.87051
-4.2839
-1.323
-1.691
-1.0527
-1.481
-1.218
-1.50696
-4.448
-4.943
-3.103
-3.4863
-1.7366
-2.674
-3.12
-1.67471
-2.81451
2-169
(Continued)
2-170
TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued )
Cmpd. no.
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
Name
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Formula
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
CAS
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
Mol. wt.
Ideal gas enthalpy of
formation, J/kmol × 1E-07
Ideal gas Gibbs energy of
formation, J/kmol × 1E-07
Ideal gas entropy,
J/(kmol∙K) × 1E-05
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
-26.44
-23.43
-10.86
-19.22
-37.88
-3.48
0
-39.445
-26.48
-18.765
-53.62
-33.68
-35.3
-30.1
-30.0453
-6.289
-14.95
10.3
-37.417
-24.8
-16.694
-51.19
-31.62
-33.46
-27.9826
-27.76
-4.167
10.6
-12.92
12.37
10.5
9.5353
0
-3.629
-9.231
13.5143
-27.33
-2.063
-48.41
-8.38
-77.89
-36.8
-7.452
-20.094
-24
-41.19
18.49
-33.3
-2.297
-21.23
-21.03
-10.26
-14.71
-35.11
0.08225
0
9.083
-8.367
0.8165
-33.4
-12.55
-13.7
-12.25
-11.96
9.482
3.622
22.7
8.216
-9.92
-0.006634
-33.8
-13.39
-15.06
-13.0081
-12.6
8.7
19.9
2.759
21.85
19.9
15.917
0
-5.334
-9.53
12.4725
-27.54
-3.344
-36.21
3.192
-69.29
-28.8
-5.049
-16.232
-13.5
-32.42
19.384
-25.7
3.207
2.644
2.22734
2.19
2.4857
2.487
2.6714
1.26152
8.2023
4.5
4.2798
4.8
4.795
4.66
4.58
4.486
4.252
4.939
4.085
7.8102
4.22
3.8874
4.41
4.402
4.349
4.17856
4.092
3.863
3.76
4.546
3.694
3.72
2.3861
1.30571
1.98591
1.86786
2.01719
1.7367
2.056
3.412
3.124
4.003
3.5
1.8627
2.3988
3.2
3.198
2.4836
3.66
2.433
Standard net enthalpy of
combustion, J/kmol × 1E-09
-1.127
-0.5219
-0.5268
-0.5021
-0.2115
-1.9959
0
-10.5618
-4.136
-4.46473
-3.839
-4.285
-4.27
-4.098
-4.09952
-4.3499
-4.7865
-4.2717
-9.95145
-3.524
-3.8551
-3.23
-3.675
-3.67
-3.49
-3.492
-3.7397
-3.64
-4.1762
-3.661
-3.64
-0.5342
-0.24182
-0.06904
-0.0286
-0.62329
0.1524
-0.518
-2.0004
-2.1566
-0.7732
-1.93
-0.80262
-0.6382
-1.71
-1.461
-1.8487
-1.9303
-0.97508
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.0019096
-28.79
12.908
-15.37
-49.8
-30.3
-3.53
-4.18
26
-25.81
-10.2
13.8
-45.07
-21.5
-15.48
-33.2
-32.7
-35.26
-10.62
-0.38
0.74
-40.2
-21.64
-23.9
-5.96
-35.24
-26.6
-28.64
-6.24
-25.2
-26.26
-8.96
-2.29
-36
-57.95
-17.455
-27.8
-13.499
-31.24
-1.71
-42.75
-23.82
-8.23
-2.91
11.83
-28.3
-10.8
15.058
0
-10.21
0
-13.2089
-18.1
19.75
-1.405
-34.99
-14.54
6.668
6.045
30.25
-10.17
2.691
20.72
-30.53
-16.61
2.733
-12.9
-12.68
-15.24
3.63
10.38
11.38
-34.83
-11.71
-14.7
1.147
-29.5
-10.7
-13.51
0.0244
-12.18
-13.93
1.4509
-0.98
-25.4
-31.8
-0.5338
-9.321
-2.144
-17.76
5.808
-31.1
-11.1
1.793
1.853
21.73
-11.7
-4.73
22.408
0
-0.6125
0
-9.063
4.14
3.2151
3.4374
3.9
3.869
3.395
3.386
2.78
3.901
4.118
3.189
3.988
2.98277
3.433
3.75
3.853
3.853
3.399
3.264
3.305
3.287
3.0881
3.394
3.332
2.852
3.81
4.129
1.955
3.416
3.699
3.59
2.55
4.01
5.533
3.8089
4.32
2.955
3.263
2.9309
3.596
3.52
3.717
2.565
3.725
3.58
3.08
3.3315
1.46327
3.168
1.91609
2.60773
-3.772
-3.032
-3.23954
-2.622
-3.062
-3.1159
-3.1088
-2.93
-3.12818
-3.5723
-3.046
-2.686
-1.693
-4.25714
-4.058
-4.0574
-4.0318
-3.6741
-3.534
-3.5464
-1.357
-1.9314
-2.268
-2.354
-0.8924
-3.122
-3.4762
-1.06
-2.5311
-2.877
-2.957
-1.1517
-2.54
-5.056
-3.84915
-3.739
-2.64812
-2.4239
-2.5242
-2.078
-2.51739
-2.962
-1.999
-4.8214
-3.11
-1.77431
-4.9809
0
-1.25
2-171
(Continued)
2-172
TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued )
Cmpd. no.
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
Name
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Formula
CH3NO2
N2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
CAS
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
Mol. wt.
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
Ideal gas enthalpy of
formation, J/kmol × 1E-07
Ideal gas Gibbs energy of
formation, J/kmol × 1E-07
Ideal gas entropy,
J/(kmol∙K) × 1E-05
Standard net enthalpy of
combustion, J/kmol × 1E-09
-7.47
8.205
9.025
-43.579
-31.09
-22.874
-57.73
-37.79
-39.71
-10.35
-19.08
6.17
-41.512
-29.02
-20.875
-55.6
-35.73
-37.62
-32.16
-33.9
-8.194
-17.01
8.23
-71.95
0
14.2671
-35.311
-22.78
-14.676
-49.13
-29.57
-31.37
-25.92
-25.79
-2.162
-11.3
-10.84
14.44
12.89
20.12
-9.6399
-1.454
-37.14
19.05
-10.468
-25.46
-27.21
4.677
-18.49
-0.6934
10.416
8.657
10.74
-7.136
2.498
-31.7
-10.86
-12.61
11.23
5.28
24.34
9.91
-8
1.6
-32.5
-11.7
-13.43
-11.38
-12.81
10.57
4.457
23.5
-66.24
0
16.3164
7.426
-10.67
-0.8813
-34.7
-14.23
-15.88
-13.83
-13.44
7.837
1.814
1.94408
21.03
19.45
30.219
-3.2637
4.87212
-30.7001
20.08
-2.439
-15.99
-17.52
20.85
-12.37
2.751
2.1985
2.106
8.9866
5.266
5.064
5.59
5.579
5.523
5.041
5.724
4.8699
8.5945
4.896
4.6723
5.2
5.187
5.132
4.962
4.879
4.637
5.331
4.478
3.608
2.05147
2.38823
7.4181
3.777
3.4945
4.02
4.01
3.958
3.786
3.7
3.462
4.05
4.154
3.298
3.3084
3.945
3.1481
3.527
3.995
2.439
2.702
3.226
3.175
4.233
3.065
-0.6432
-0.0820482
-0.0902489
-11.7812
-5.35
-5.68455
-5.061
-5.506
-5.506
-5.5716
-6.006
-5.493
-11.1715
-4.74
-5.07415
-4.448
-4.895
-4.894
-4.6984
-4.711
-4.961
-5.3962
-4.88145
-0.1989
0
-0.142671
-9.34237
-2.91
-3.24494
-2.617
-3.064
-3.058
-2.87956
-2.8804
-3.13037
-3.564
-3.5641
-3.051
-3.0291
-6.8282
-2.921
-3.298
-3.1715
-1.8563
-2.04311
-1.844
-1.834
-5.232
-1.684
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.0791128
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
-45.35
5.155
-46.48
-7.05
0.79
2.023
-40.76
-7.59
-6.75
-42.15
-12.29
-161.494
14.74
-81.6
-29.684
-122.047
-39.572
-66.94
27.66
-33.244
-18.418
2.661
-3.376
-22.56
11.544
5.017
-14.2
-31.177
-9.58
-2.431
-0.95
-1.38
-22.401
-21.845
6.24
4.34
-27.043
-41.9
-31.49
30.46
2.845
-48.116
-24.1818
1.732
1.908
1.803
-35.82
9.688
-32.04
4.17
13.76
6.264
-29.36
-0.218
0.2583
-30.4
-6.92
-157.27
21.39
-70.11
-30.012
-111.653
-37.095
-55.01
42.3
6.599
-7.969
16.71
4.59
2.239
12.67
12.22
-8.097
5.771
11.41
9.899
12.61
11.71
1.394
1.828
26.79
28.44
4.116
-9.177
-22.79
30.6
4.195
-42.5514
-22.8572
11.876
12.2
12.14
2.949
2.877
4.023
3.242
4.0014
2.67
3.678
3.243
3.365
3.52
3.205
2.82651
3.451
4.398
2.481
2.91625
2.5651
4.48
5.263
7.0259
2.9729
3.6964
3.1
3.893
2.784
3.2099
3.371
6.6337
4.054
2.87
3.805
3.961
4.2296
4.2702
4.435
4.607
5.8493
6.363
3.28
2.794
2.7354
3.73966
1.88825
3.5854
3.5383
3.52165
-1.395
-1.80056
-2.672
-2.165
-4.95415
-1.9262
-2.041
-2.3398
-2.3458
-1.6476
-2.658
0.7055
-4.219
-1.3591
0.924
0.1422
-3.19
-9.053
-8.73282
-2.325
-5.3575
-2.76549
-5.0639
-2.4352
-3.734
-0.9685
-8.1229
-4.0405
-2.2449
-4.934
-4.9307
-5.06528
-5.06876
-2.6867
-3.2959
-6.9036
-6.726
-1.95
-2.362
-1.178
-1.544
-4.3318
-4.333
-4.333
The compounds are considered to be formed from the elements in their standard states at 298.15 K and 1 bar. These include C (graphite) and S (rhombic). Enthalpy of combustion is the net value for the compound in its standard state
at 298.15 K and 1 bar. Products of combustion are taken to be CO2 (gas), H2O (gas), F2(gas), Cl2 (gas), Br2 (gas), I2 (gas), SO2 (gas), N2 (gas), P4O10 (crystalline), SiO2 (crystobalite), and Al2O3 (crystal, alpha).
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation
of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
2-173
2-174
PHYSICAL AnD CHEMICAL DATA
TABLE 2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol), of Combustion Products
Temperature,
K
CO
CO2
H
OH
H2
N
NO
NO2
N2
N2O
O
O2
SO2
H2O
-2858
-1692
-1110
-529
0
-3414
-2079
-1383
-665
0
-2040
-1209
-793
-377
0
-2976
-1756
-1150
-546
0
-2774
-1656
-1091
-522
0
-2040
-1209
-793
-378
0
-2951
-1743
-1142
-543
0
-3495
-2104
-1392
-672
0
-2857
-1692
-1110
-528
0
-3553
-2164
-1438
-692
0
-2186
-1285
-840
-398
0
-2868
-1703
-1118
-533
0
-3736
-2258
-1496
-718
0
-3282
-1948
-1279
-609
0
300
320
340
360
380
54
638
1221
1805
2389
69
823
1594
2382
3184
38
454
870
1285
1701
55
654
1251
1847
2442
53
630
1209
1791
2373
38
454
870
1286
1701
55
652
1248
1845
2442
68
816
1571
2347
3130
54
636
1219
1802
2386
72
854
1654
2470
3302
41
478
913
1346
1777
54
643
1234
1828
2425
74
881
1702
2538
3387
62
735
1410
2088
2769
400
420
440
460
480
2975
3563
4153
4643
5335
4003
4835
5683
6544
7416
2117
2532
2948
3364
3779
3035
3627
4219
4810
5401
2959
3544
4131
4715
5298
2117
2533
2949
3364
3780
3040
3638
4240
4844
5450
3927
4735
5557
6392
7239
2971
3557
4143
4731
5320
4149
5010
5884
6771
7670
2207
2635
3063
3490
3918
3025
3629
4236
4847
5463
4250
5126
6015
6917
7831
3452
4139
4829
5523
6222
500
550
600
650
700
5931
7428
8942
10477
12023
8305
10572
12907
15303
17754
4196
5235
6274
7314
8353
5992
7385
8943
10423
11902
5882
6760
8811
10278
11749
4196
5235
6274
7314
8353
6059
7592
9144
10716
12307
8099
10340
12555
14882
17250
5911
7395
8894
10407
11937
8580
10897
13295
15744
18243
4343
5402
6462
7515
8570
6084
7653
9244
10859
12499
8758
11123
13544
16022
18548
6925
8699
10501
12321
14192
750
800
850
900
950
13592
15177
16781
18401
20031
20260
22806
25398
28030
30689
9392
10431
11471
12510
13550
13391
14880
16384
17888
19412
13223
14702
16186
17676
19175
9329
10431
11471
12510
13550
13919
15548
17195
18858
20537
19671
22136
24641
27179
29749
13481
15046
16624
18223
19834
20791
23383
26014
28681
31381
9620
10671
11718
12767
13812
14158
15835
17531
19241
20965
21117
23721
26369
29023
31714
16082
18002
19954
21938
23954
1000
1100
1200
1300
1400
21690
25035
28430
31868
35343
33397
38884
44473
50148
55896
14589
16667
18746
20824
22903
20935
24024
27160
30342
33569
20680
23719
26797
29918
33082
14589
16667
18746
20824
22903
22229
25653
29120
32626
36164
32344
37605
42946
48351
53808
21463
24760
28109
31503
34936
34110
39647
45274
50976
56740
14860
16950
19039
21126
23212
22703
26212
29761
33344
36957
34428
39914
45464
51069
56718
26000
30191
34506
38942
43493
1500
1600
1700
1800
1900
38850
42385
45945
49526
53126
61705
67569
73480
79431
85419
24982
27060
29139
31217
33296
36839
40151
43502
46889
50310
36290
39541
42835
46169
49541
24982
27060
29139
31218
33296
39729
43319
46929
50557
54201
59309
64846
70414
76007
81624
38405
41904
45429
48978
52548
62557
68420
74320
80254
86216
25296
27381
29464
31547
33630
40599
44266
47958
51673
55413
62404
68123
73870
79642
85436
48151
52908
57758
62693
67706
2000
2100
2200
2300
2400
56744
60376
64021
67683
71324
91439
97488
103562
109660
115779
35375
37453
39532
41610
43689
53762
57243
60752
64285
67841
52951
56397
59876
63387
66928
35375
37454
39534
41614
43695
57859
61530
65212
68904
72606
87259
92911
98577
104257
109947
56137
59742
63361
66995
70640
92203
98212
104240
110284
116344
35713
37796
39878
41962
44045
59175
62961
66769
70600
74453
91250
97081
102929
108792
114669
72790
77941
83153
88421
93741
2500
2600
2700
2800
2900
74985
78673
82369
86074
89786
121917
128073
134246
140433
146636
45768
47846
49925
52004
54082
71419
75017
78633
82267
85918
70498
74096
77720
81369
85043
45777
47860
49945
52033
54124
76316
80034
83759
87491
91229
115648
121357
127075
132799
138530
74296
77963
81639
85323
89015
122417
128501
134596
140701
146814
46130
48216
50303
52391
54481
78328
82224
86141
90079
94036
120559
126462
132376
138302
144238
99108
104520
109973
115464
120990
3000
3500
4000
4500
5000
93504
112185
130989
149895
168890
152852
184109
215622
247354
279283
56161
66554
75947
87340
97733
89584
108119
126939
145991
165246
88740
107555
126874
146660
166876
56218
66769
77532
88614
100111
94973
113768
132671
151662
170730
144267
173020
201859
230756
259692
92715
111306
130027
148850
167763
152935
183636
214453
245348
276299
56574
67079
77675
88386
99222
98013
118165
188705
159572
180749
150184
180057
210145
240427
270893
126549
154768
183552
212764
242313
200
240
260
280
298.15
Converted and usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.).
PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS
2-175
TABLE 2-97 Ideal Gas Entropies s°, kJ/(kmol· K), of Combustion Products
Temperature,
K
CO
CO2
H
OH
H2
N
NO
NO2
N2
N2O
O
O2
SO2
H2O
200
240
260
280
298.15
186.0
191.3
193.7
195.3
197.7
200.0
206.0
208.8
211.5
213.8
106.4
110.1
111.8
113.3
114.7
171.6
177.1
179.5
181.8
183.7
119.4
124.5
126.8
129.2
130.7
145.0
148.7
150.4
151.9
153.3
198.7
204.1
206.6
208.8
210.8
225.9
232.2
235.0
237.7
240.0
180.0
185.2
187.6
189.8
191.6
205.6
211.9
214.8
217.5
220.0
152.2
156.2
158.0
159.7
161.1
193.5
198.7
201.1
203.3
205.1
233.0
239.9
242.8
245.8
248.2
175.5
181.4
184.1
186.6
188.8
300
320
340
360
380
197.8
199.7
201.5
203.2
204.7
214.0
216.5
218.8
221.0
223.2
114.8
116.2
117.4
118.6
119.7
183.9
185.9
187.7
189.4
191.0
130.9
132.8
134.5
136.2
137.7
153.4
154.8
156.0
157.2
158.3
210.9
212.9
214.7
216.4
218.0
240.3
242.7
245.0
247.2
249.3
191.8
193.7
195.5
197.2
198.7
220.2
222.7
225.2
227.5
229.7
161.2
162.6
163.9
165.2
166.3
205.3
207.2
209.0
210.7
212.5
248.5
251.1
253.6
256.0
258.2
189.0
191.2
193.3
195.2
197.1
400
420
440
460
480
206.2
207.7
209.0
210.4
211.6
225.3
227.3
229.3
231.2
233.1
120.8
121.8
122.8
123.7
124.6
192.5
194.0
195.3
196.6
197.9
139.2
140.6
141.9
143.2
144.5
159.4
160.4
161.4
162.3
163.1
219.5
221.0
222.3
223.7
225.0
251.3
253.2
255.1
257.0
258.8
200.2
201.5
202.9
204.2
205.5
231.9
234.0
236.0
238.0
239.9
167.4
168.4
169.4
170.4
171.3
213.8
215.3
216.7
218.0
219.4
260.4
262.5
264.6
266.6
268.5
198.8
200.5
202.0
203.6
205.1
500
550
600
650
700
212.8
215.7
218.3
220.8
223.1
234.9
239.2
243.3
247.1
250.8
125.5
127.5
129.3
131.0
132.5
199.1
201.8
204.4
206.8
209.0
145.7
148.6
151.1
153.4
155.6
164.0
166.0
167.8
169.4
171.0
226.3
229.1
231.9
234.4
236.8
260.6
264.7
268.8
272.6
276.0
206.7
209.4
212.2
214.6
216.9
241.8
246.2
250.4
254.3
258.0
172.2
174.2
176.1
177.7
179.3
220.7
223.7
226.5
229.1
231.5
270.5
274.9
279.2
283.1
286.9
206.5
210.5
213.1
215.9
218.7
750
800
850
900
950
225.2
227.3
229.2
231.1
232.8
255.4
257.5
260.6
263.6
266.5
133.9
135.2
136.4
137.7
138.8
211.1
213.0
214.8
216.5
218.1
157.6
159.5
161.4
163.1
164.7
172.5
173.8
175.1
176.3
177.4
239.0
241.1
243.0
245.0
246.8
279.3
282.5
285.5
288.4
291.3
219.0
221.0
223.0
224.8
226.5
261.5
264.8
268.0
271.1
274.0
180.7
182.1
183.4
184.6
185.7
233.7
235.9
237.9
239.9
241.8
290.4
293.8
297.0
300.1
303.0
221.3
223.8
226.2
228.5
230.6
1000
1100
1200
1300
1400
234.5
237.7
240.7
243.4
246.0
269.3
274.5
279.4
283.9
288.2
139.9
141.9
143.7
145.3
146.9
219.7
222.7
225.4
228.0
230.3
166.2
169.1
171.8
174.3
176.6
178.5
180.4
182.2
183.9
185.4
248.4
251.8
254.8
257.6
260.2
293.9
298.9
303.6
307.9
311.9
228.2
231.3
234.2
236.9
239.5
276.8
282.1
287.0
291.5
295.8
186.8
188.8
190.6
192.3
193.8
243.6
246.9
250.0
252.9
255.6
305.8
311.0
315.8
320.3
324.5
232.7
236.7
240.5
244.0
247.4
1500
1600
1700
1800
1900
248.4
250.7
252.9
254.9
256.8
292.2
296.0
299.6
303.0
306.2
148.3
149.6
150.9
152.1
153.2
232.6
234.7
236.8
238.7
240.6
178.8
180.9
182.9
184.8
186.7
186.9
188.2
189.5
190.7
191.8
262.7
265.0
267.2
269.3
271.3
315.7
319.3
322.7
325.9
328.9
241.9
244.1
246.3
248.3
250.2
299.8
303.6
307.2
310.6
313.8
195.3
196.6
197.9
199.1
200.2
258.1
260.4
262.7
264.8
266.8
328.4
332.1
335.6
338.9
342.0
250.6
253.7
256.6
259.5
262.2
2000
2100
2200
2300
2400
258.7
260.5
262.2
263.8
265.4
309.3
312.2
315.1
317.8
320.4
154.3
155.3
156.3
157.2
158.1
242.3
244.0
245.7
247.2
248.7
188.4
190.1
191.7
193.3
194.8
192.9
193.9
194.8
195.8
196.7
273.1
274.9
276.6
278.3
279.8
331.8
334.5
337.2
339.7
342.1
252.1
253.8
255.5
257.1
258.7
316.9
319.8
322.6
325.3
327.9
201.3
202.3
203.2
204.2
205.0
268.7
270.6
272.4
274.1
275.7
345.0
347.9
350.6
353.2
355.7
264.8
267.3
269.7
272.0
274.3
2500
2600
2700
2800
2900
266.9
268.3
269.7
271.0
272.3
322.9
325.3
327.6
329.9
332.1
158.9
159.7
160.5
161.3
162.0
250.2
251.6
253.0
254.3
255.6
196.2
197.7
199.0
200.3
201.6
197.5
198.3
199.1
199.9
200.6
281.4
282.8
284.2
285.6
286.9
344.5
346.7
348.9
350.9
352.9
260.2
261.6
263.0
264.3
265.6
330.4
332.7
335.0
337.3
339.4
205.9
206.7
207.5
208.3
209.0
277.3
278.8
280.3
281.7
283.1
358.1
360.4
362.6
364.8
366.9
276.5
278.6
380.7
282.7
284.6
3000
3500
4000
4500
5000
273.6
279.4
284.4
288.8
292.8
334.2
343.8
352.2
359.7
366.4
162.7
165.9
168.7
171.1
173.3
256.8
262.5
267.6
272.1
276.1
202.9
208.7
213.8
218.5
222.8
201.3
204.6
207.4
210.1
212.5
288.2
294.0
299.0
303.5
307.5
354.9
363.8
371.5
378.3
384.4
266.9
272.6
277.6
282.1
286.0
341.5
350.9
359.2
366.5
373.0
209.7
212.9
215.8
218.3
220.6
284.4
290.7
296.2
301.1
305.5
368.9
378.1
386.1
393.3
399.7
286.5
295.2
302.9
309.8
316.0
Usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.). Equilibrium constants can be calculated by combining Δhf° values from
Table 2-95, hT - h298 from Table 2-96, and s° values from the above, using the formula ln kp = -ΔG/(RT), where ΔG = Δhf° + (hT - h298) - T s°.
2-176
PHYSICAL AnD CHEMICAL DATA
HEATS OF SOLUTIOn
TABLE 2-98 Heats of Solution of Inorganic Compounds in Water
Heat evolved, in kilocalories per gram formula weight, on solution in water at 18°C. Computed from data in Bichowsky and Rossini, Thermochemistry of Chemical
Substances, Reinhold, New York, 1936.
Substance
Dilution*
Formula
Heat,
kcal/mol
Aluminum bromide
chloride
aq
600
600
aq
aq
aq
aq
aq
aq
aq
aq
∞
aq
600
aq
∞
aq
∞
800
aq
aq
aq
aq
aq
AlBr3
AlCl3
AlCl3⋅6H2O
AlF3
AlF3⋅½H2O
AlF3⋅3½H2O
AlI3
Al2(SO4)3
Al2(SO4)3⋅6H2O
Al2(SO4)3⋅18H2O
NH4Br
NH4Cl
(NH4)2CrO4
(NH4)2Cr2O7
NH4I
NH4NO3
NH4BO3⋅H2O
(NH4)2SO4
NH4HSO4
(NH4)2SO3
(NH4)2SO3⋅H2O
SbF3
SbI3
H3AsO4
+85.3
+77.9
+13.2
+31
+19.0
-1.7
+89.0
+126
+56.2
+6.7
-4.45
-3.82
-5.82
-12.9
-3.56
-6.47
-9.0
-2.75
+0.56
-1.2
-4.13
-1.7
-0.8
-0.4
∞
∞
∞
∞
∞
∞
∞
∞
∞
aq
aq
aq
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
aq
aq
aq
aq
aq
aq
aq
aq
aq
Ba(BrO3)2⋅H2O
BaBr2
BaBr2⋅H2O
BaBr2⋅2H2O
Ba(ClO3)2
Ba(ClO3)2⋅H2O
BaCl2
BaCl2⋅H2O
BaCl2.2H2O
Ba(CN)2
Ba(CN)2⋅H2O
Ba(CN)2⋅2H2O
Ba(IO3)2
Ba(IO3)2⋅H2O
BaI2
BaI2⋅H2O
BaI2⋅2H2O
BaI2⋅2½H2O
BaI2⋅7H2O
Ba(NO3)2
Ba(ClO4)2
Ba(ClO4)2⋅3H2O
BaS
BeBr2
BeCl2
BeI2
BeSO4
BeSO4⋅H2O
BeSO4⋅2H2O
BeSO4⋅4H2O
BiI3
H3BO3
-15.9
+5.3
-0.8
-3.87
-6.7
-10.6
+2.4
-2.17
-4.5
+1.5
-2.4
-4.9
-9.1
-11.3
+10.5
+2.7
+0.14
-0.58
-6.61
-10.2
-2.8
-10.5
+7.2
+62.6
+51.1
+72.6
+18.1
+13.5
+7.9
+1.1
+3
-5.4
400
400
400
400
400
400
400
400
400
400
∞
∞
∞
∞
∞
∞
∞
∞
∞
CdBr2
CdBr2⋅4H2O
CdCl2
CdCl2⋅H2O
CdCl2⋅2½H2O
Cd(NO3)2⋅H2O
Cd(NO3)2⋅4H2O
CdSO4
CdSO4⋅H2O
CdSO4⋅2⅔H2O
Ca(C2H3O2)2
Ca(C2H3O2)2⋅H2O
CaBr2
CaBr2⋅6H2O
CaCl2
CaCl2⋅H2O
CaCl2⋅2H2O
CaCl2⋅4H2O
CaCl2⋅6H2O
+0.4
-7.3
+3.1
+0.6
-3.00
+4.17
-5.08
+10.69
+6.05
+2.51
+7.6
+6.5
+24.86
-0.9
+4.9
+12.3
+12.5
+2.4
-4.11
fluoride
iodide
sulfate
Ammonium bromide
chloride
chromate
dichromate
iodide
nitrate
perborate
sulfate
sulfate, acid
sulfite
Antimony fluoride
iodide
Arsenic acid
Barium bromate
bromide
chlorate
chloride
cyanide
iodate
iodide
nitrate
perchlorate
sulfide
Beryllium bromide
chloride
iodide
sulfate
Bismuth iodide
Boric acid
Cadmium bromide
chloride
nitrate
sulfate
Calcium acetate
bromide
chloride
Substance
Calcium—(Cont.)
formate
iodide
Dilution*
Formula
Heat,
kcal/mol
400
∞
∞
∞
∞
∞
∞
∞
aq
aq
∞
∞
∞
aq
+0.7
+28.0
+1.8
+4.1
+0.7
-3.2
-4.2
-7.99
-0.6
-1
+5.1
+3.6
-0.18
+18.6
+5.3
+2.0
+5.7
+18.4
-1.25
+18.5
+9.8
-2.9
+18.8
+15.0
-1.4
-3.6
+2.4
+0.5
+10.3
-2.6
-10.7
+15.9
+9.3
+3.65
-2.85
+11.6
Cuprous sulfate
aq
Ca(CHO2)2
CaI2
CaI2⋅8H2O
Ca(NO3)2
Ca(NO3)2⋅H2O
Ca(NO3)2⋅2H2O
Ca(NO3)2⋅3H2O
Ca(NO3)2⋅4H2O
Ca(H2PO4)2⋅H2O
CaHPO4⋅2H2O
CaSO4
CaSO4⋅½H2O
CaSO4⋅2H2O
CrCl2
CrCl2⋅3H2O
CrCl2⋅4H2O
CrI2
CoBr2
CoBr2⋅6H2O
CoCl2
CoCl2⋅2H2O
CoCl2⋅6H2O
CoI2
CoSO4
CoSO4⋅6H2O
CoSO4⋅7H2O
Cu(C2H3O2)2
Cu(CHO2)2
Cu(NO3)2
Cu(NO3)2⋅3H2O
Cu(NO3)2⋅6H2O
CuSO4
CuSO4⋅H2O
CuSO4⋅3H2O
CuSO4⋅5H2O
Cu2SO4
Ferric chloride
1000
1000
1000
800
aq
400
400
400
aq
400
400
400
400
FeCl3
FeCl3⋅2½H2O
FeCl3⋅6H2O
Fe(NO3)3⋅9H2O
FeBr2
FeCl2
FeCl2⋅2H2O
FeCl2⋅4H2O
FeI2
FeSO4
FeSO4⋅H2O
FeSO4⋅4H2O
FeSO4⋅7H2O
+31.7
+21.0
+5.6
-9.1
+18.0
+17.9
+8.7
+2.7
+23.3
+14.7
+7.35
+1.4
-4.4
400
400
aq
aq
aq
400
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
Pb(C2H3O2)2
Pb(C2H3O2)2⋅3H2O
PbBr2
PbCl2
Pb(CHO2)2
Pb(NO3)2
LiBr
LiBr⋅H2O
LiBr⋅2H2O
LiBr⋅3H2O
LiCl
LiCl⋅H2O
LiCl⋅2H2O
LiCl⋅3H2O
LiF
LiOH
LiOH⋅⅛H2O
LiOH⋅H2O
LiI
LiI⋅½H2O
LiI⋅H2O
LiI⋅2H2O
LiI⋅3H2O
LiNO3
LiNO3⋅3H2O
+1.4
-5.9
-10.1
-3.4
-6.9
-7.61
+11.54
+5.30
+2.05
-1.59
+8.66
+4.45
+1.07
-1.98
-0.74
+4.74
+4.39
+9.6
+14.92
+10.08
+6.93
+3.43
-0.17
+0.466
-7.87
nitrate
phosphate, monodibasic
sulfate
Chromous chloride
iodide
Cobaltous bromide
chloride
iodide
sulfate
Cupric acetate
formate
nitrate
sulfate
nitrate
Ferrous bromide
chloride
iodide
sulfate
Lead acetate
bromide
chloride
formate
nitrate
Lithium bromide
chloride
fluoride
hydroxide
iodide
nitrate
aq
aq
aq
400
400
400
aq
400
400
400
aq
aq
200
200
200
800
*The numbers represent moles of water used to dissolve 1 g formula weight of substance; ∞ means “infinite dilution”; and aq means “aqueous solution of unspecified
dilution.”
HEATS OF SOLUTIOn
2-177
TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued )
Dilution*
Substance
Lithium—(Cont.)
sulfate
Magnesium bromide
chloride
iodide
nitrate
phosphate
sulfate
sulfide
Manganic nitrate
sulfate
Manganous acetate
bromide
chloride
formate
iodide
sulfate
Mercuric acetate
bromide
chloride
nitrate
Mercurous nitrate
Nickel bromide
Nickel chloride
iodide
nitrate
sulfate
Phosphoric acid, orthopyroPotassium acetate
aluminum sulfate
Formula
Heat,
kcal/mol
+6.71
+3.77
∞
∞
Li2SO4
Li2SO4⋅H2O
∞
∞
∞
∞
∞
∞
∞
∞
∞
aq
∞
∞
∞
∞
∞
∞
aq
400
400
400
aq
aq
aq
aq
aq
aq
400
400
400
aq
aq
aq
aq
aq
aq
aq
400
400
400
aq
aq
aq
aq
aq
MgBr2
MgBr2⋅H2O
MgBr2⋅6H2O
MgCl2
MgCl2⋅2H2O
MgCl2⋅4H2O
MgCl2⋅6H2O
MgI2
Mg(NO3)2⋅6H2O
Mg3(PO4)2
MgSO4
MgSO4⋅H2O
MgSO4⋅2H2O
MgSO4⋅4H2O
MgSO4⋅6H2O
MgSO4⋅7H2O
MgS
Mn(NO3)2
Mn(NO3)2⋅3H2O
Mn(NO3)2⋅6H2O
Mn2(SO4)3
Mn(C2H3O2)2
Mn(C2H3O2)2⋅4H2O
MnBr2
MnBr2⋅H2O
MnBr2⋅4H2O
MnCl2
MnCl2⋅2H2O
MnCl2⋅4H2O
Mn(CHO2)2
Mn(CHO2)2⋅2H2O
MnI2
MnI2⋅H2O
MnI2⋅2H2O
MnI2⋅4H2O
MnI2⋅6H2O
MnSO4
MnSO4⋅H2O
MnSO4⋅7H2O
Hg(C2H3O2)2
HgBr2
HgCl2
Hg(NO3)2⋅½H2O
Hg2(NO3)2⋅2H2O
+43.7
+35.9
+19.8
+36.3
+20.8
+10.5
+3.4
+50.2
-3.7
+10.2
+21.1
+14.0
+11.7
+4.9
+0.55
-3.18
+25.8
+12.9
-3.9
-6.2
+22
+12.2
+1.6
+15
+14.4
+16.1
+16.0
+8.2
+1.5
+4.3
-2.9
+26.2
+24.1
+22.7
+19.9
+21.2
+13.8
+11.9
-1.7
-4.0
-2.4
-3.3
-0.7
-11.5
aq
aq
800
800
800
800
aq
200
200
200
200
400
400
aq
aq
∞
600
600
NiBr2
NiBr2⋅3H2O
NiCl2
NiCl2⋅2H2O
NiCl2⋅4H2O
NiCl2⋅6H2O
NiI2
Ni(NO3)2
Ni(NO3)2⋅6H2O
NiSO4
NiSO4⋅7H2O
H3PO4
H3PO4⋅½H2O
H4P2O7
H4P2O7⋅1½H2O
KC2H3O2
KAl(SO4)2
KAl(SO4)2⋅3H2O
KAl(SO4)2⋅12H2O
KHCO3
KBrO3
KBr
K2CO3
K2CO3⋅½H2O
K2CO3⋅1½H2O
KClO3
KCl
K2CrO4
KCr(SO4)2
KCr(SO4)2⋅H2O
KCr(SO4)2⋅2H2O
KCr(SO4)2⋅6H2O
KCr(SO4)2⋅12H2O
+19.0
+0.2
+19.23
+10.4
+4.2
-1.15
+19.4
+11.8
-7.5
+15.1
-4.2
+2.79
-0.1
+25.9
+4.65
+3.55
+48.5
+26.6
-10.1
-5.1
-10.13
-5.13
+6.58
+4.25
-0.43
-10.31
-4.404
-4.9
+55
+42
+33
+7
-9.5
bicarbonate
bromate
bromide
carbonate
2000
∞
∞
∞
chlorate
chloride
chromate
chrome sulfate
∞
∞
2185
600
Substance
Potassium—(Cont.)
cyanide
dichromate
fluoride
hydrosulfide
hydroxide
iodate
iodide
nitrate
oxalate
perchlorate
permanganate
phosphate, dihydrogen
pyrosulfite
sulfate
sulfate, acid
sulfide
sulfite
thiocyanate
thionate, dithiosulfate
Silver acetate
nitrate
Sodium acetate
arsenate
bicarbonate
borate, tetrabromide
carbonate
chlorate
chloride
chromate
cyanide
fluoride
hydrosulfide
Sodium hydroxide
iodide
metaphosphate
nitrate
nitrite
perchlorate
phosphate di
triphosphate di
diphosphite, monodipyrophosphate
di-
Dilution*
Formula
Heat,
kcal/mol
∞
400
aq
aq
aq
∞
800
∞
aq
aq
∞
aq
∞
KCN
K2Cr2O7
KF
KF⋅2H2O
KF⋅4H2O
KHS
KHS⋅¼H2O
KOH
KOH⋅¾H2O
KOH⋅H2O
KOH⋅7H2O
KIO3
KI
KNO3
K2C2O4
K2C2O4⋅H2O
KClO4
KMnO4
KH2PO4
K2S2O5
K2S2O5⋅½H2O
K2SO4
KHSO4
K2S
K2SO3
K2SO3⋅H2O
KCNS
K2S2O6
K2S2O3
-3.0
-17.8
+3.96
-1.85
-6.05
+0.86
+1.21
+12.91
+4.27
+3.48
+0.86
-6.93
-5.23
-8.633
-4.6
-7.5
-12.94
-10.4
+4.7
-11.0
-10.22
-6.32
-3.10
-11.0
+1.8
+1.37
-6.08
-13.0
-4.5
aq
200
∞
∞
500
500
1800
900
900
∞
∞
∞
∞
∞
∞
∞
∞
800
800
800
200
200
200
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
600
∞
aq
∞
1600
1600
1600
1600
1600
1600
600
600
800
800
1600
1600
1200
1200
AgC2H3O2
AgNO3
NaC2H3O2
NaC2H3O2⋅3H2O
Na3AsO4
Na3AsO4⋅12H2O
NaHCO3
Na2B4O7
Na2B4O7⋅10H2O
NaBr
NaBr⋅2H2O
Na2CO3
Na2CO3⋅H2O
Na2CO3⋅7H2O
Na2CO3⋅10H2O
NaClO3
NaCl
Na2CrO4
Na2CrO4⋅4H2O
Na2CrO4⋅10H2O
NaCN
NaCN⋅½H2O
NaCN⋅2H2O
NaF
NaHS
NaHS⋅2H2O
NaOH
NaOH⋅½H2O
NaOH⋅⅔H2O
NaOH⋅¾H2O
NaOH⋅H2O
NaI
NaI⋅2H2O
NaPO3
NaNO3
NaNO2
NaClO4
Na2HPO4
Na3PO4
Na3PO4⋅12H2O
Na2HPO4⋅2H2O
Na2HPO4⋅7H2O
Na2HPO4⋅12H2O
NaH2PO3
NaH2PO3⋅2½H2O
Na2HPO3
Na2HPO3⋅5H2O
Na4P2O7
Na4P2O7⋅10H2O
Na2H2P2O7
Na2H2P2O7⋅6H2O
-5.4
-4.4
+4.085
-4.665
+15.6
-12.61
-4.1
+10.0
-16.8
-0.58
-4.57
+5.57
+2.19
-10.81
-16.22
-5.37
-1.164
+2.50
-7.52
-16.0
-0.37
-0.92
-4.41
-0.27
+4.62
-1.49
+10.18
+8.17
+7.08
+6.48
+5.17
+1.57
-3.89
+3.97
-5.05
-3.6
-4.15
+5.21
+13
-15.3
-0.82
-12.04
-23.18
+0.90
-5.29
+9.30
-4.54
+11.9
-11.7
-2.2
-14.0
200
1600
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
400
(Continued)
2-178
PHYSICAL AnD CHEMICAL DATA
TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued )
Substance
Sodium—(Cont.)
sulfate
sulfate, acid
sulfide
sulfite
thiocyanate
thionate, diSodium thiosulfate
Stannic bromide
Stannous bromide
iodide
Strontium acetate
bromide
Dilution*
Formula
Heat,
kcal/mol
∞
∞
800
800
∞
∞
∞
∞
∞
∞
∞
aq
aq
aq
aq
aq
aq
aq
∞
∞
∞
∞
∞
∞
∞
Na2SO4
Na2SO4⋅10H2O
NaHSO4
NaHSO4⋅H2O
Na2S
Na2S⋅4½H2O
Na2S⋅5H2O
Na2S⋅9H2O
Na2SO3
Na2SO3⋅7H2O
NaCNS
Na2S2O6
Na2S2O6⋅2H2O
Na2S2O3
Na2S2O3⋅5H2O
SnBr4
SnBr2
SnI2
Sr(C2H3O2)2
Sr(C2H3O2)2⋅½H2O
SrBr2
SrBr2⋅H2O
SrBr2⋅2H2O
SrBr2⋅4H2O
SrBr2⋅6H2O
+0.28
-18.74
+1.74
+0.15
+15.2
+0.09
-6.54
-16.65
+2.8
-11.1
-1.83
-5.80
-11.86
+2.0
-11.30
+15.5
-1.6
-5.8
+6.2
+5.9
+16.4
+9.25
+6.5
+0.4
-6.1
Substance
Dilution*
Strontium—(Cont.)
chloride
iodide
nitrate
sulfate
Sulfuric acid, pyroZinc acetate
bromide
chloride
iodide
nitrate
sulfate
Formula
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
∞
SrCl2
SrCl2⋅H2O
SrCl2⋅2H2O
SrCl2⋅6H2O
SrI2
SrI2⋅H2O
SrI2⋅2H2O
SrI2⋅6H2O
Sr(NO3)2
Sr(NO3)2⋅4H2O
SrSO4
H2S2O7
+11.54
+6.4
+2.95
-7.1
+20.7
+12.65
+10.4
-4.5
-4.8
-12.4
+0.5
-18.08
400
400
400
400
400
aq
400
400
400
400
400
400
Zn(C2H3O2)2
Zn(C2H3O2)2⋅H2O
Zn(C2H3O2)2⋅2H2O
ZnBr2
ZnCl2
ZnI2
Zn(NO3)2⋅3H2O
Zn(NO3)2⋅6H2O
ZnSO4
ZnSO4⋅H2O
ZnSO4⋅6H2O
ZnSO4⋅7H2O
+9.8
+7.0
+3.9
+15.0
+15.72
+11.6
-5
-6.0
+18.5
+10.0
-0.8
-4.3
note: To convert kilocalories per mole to British thermal units per pound-mole, multiply by 1.799 × 10-3.
TABLE 2-99 Heats of Solution of Organic Compounds in Water (at Infinite Dilution
and Approximately Room Temperature)
Recalculated and rearranged from International Critical Tables, vol. 5, pp. 148–150. cal/mol = Btu/(lb⋅mol) × 1.799.
Solute
Acetic acid (solid), C2H4O2
Acetylacetone, C5H8O2
Acetylurea, C3H6N2O2
Aconitic acid, C6H6O6
Ammonium benzoate, C7H9NO2
picrate
succinate (n-)
Aniline, hydrochloride, C6H8ClN
Barium picrate
Benzoic acid, C7H6O2
Camphoric acid, C10H16O4
Citric acid, C6H8O7
Dextrin, C12H20O10
Fumaric acid, C4H4O4
Hexamethylenetetramine, C6H12N4
Hydroxybenzamide (m-), C7H7NO2
(m-), (HCl)
(o-), C7H7NO2
(p-)
Hydroxybenzoic acid (o-), C7H6O3
(p-), C7H6O3
Hydroxybenzyl alcohol (o-), C7H8O2
Inulin, C36H62O31
Isosuccinic acid, C4H6O4
Itaconic acid, C5H6O4
Lactose, C12H22O11⋅H2O
Lead picrate
(2H2O)
Magnesium picrate
(8H2O)
Maleic acid, C4H4O4
Malic acid, C4H6O5
Malonic acid, C3H4O4
Mandelic acid, C8H2O3
Mannitol, C6H14O6
Menthol, C10H20O
Nicotine dihydrochloride, C10H16Cl2N2
Nitrobenzoic acid (m-), C7H5NO4
(o-), C7H5NO4
(p-), C7H5NO4
Nitrophenol (m-), C6H5NO3
(o-), C6H5NO3
(p-), C6H5NO3
Heat of solution,
cal/mol
solute*
-2,251
-641
-6,812
-4,206
-2,700
-8,700
-3,489
-2,732
-4,708
-6,501
-502
-5,401
268
-5,903
4,780
-4,161
-7,003
-4,340
-5,392
-6,350
-5,781
-3,203
-96
-3,420
-5,922
-3,705
-7,098
-13,193
14,699
-15,894
-4,441
-3,150
-4,493
-3,090
-5,260
0
6,561
-5,593
-5,306
-8,891
-5,210
-6,310
-4,493
Solute
Oxalic acid, C2H2O4
(2H2O)
Phenol (solid), C6H6O
Phthalic acid, C8H6O4
Picric acid, C6H3N3O7
Piperic acid, C12H10O4
Piperonylic acid, C8H6O4
Potassium benzoate
citrate
tartrate (n-) (0.5 H2O)
Pyrogallol, C6H6O3
Pyrotartaric acid
Quinone
Raffinose, C18H32O16 (5H2O)
Resorcinol, C6H6O2
Silver malonate (n-)
Sodium citrate (tri-)
picrate
potassium tartrate
(4H2O)
succinate (n-)
(6H2O)
tartrate (n-)
(2H2O)
Strontium picrate
(6H2O)
Succinic acid, C4H6O4
Succinimide, C4H5NO2
Sucrose, C12H22O11
Tartaric acid (d-)
Thiourea, CH4N2S
Urea, CH4N2O
acetate
formate
nitrate
oxalate
Vanillic acid
Vanillin
Zinc picrate
(8H2O)
Heat,
kcal/mol
Heat of solution,
cal/mol
solute*
-2,290
-8,485
-2,605
-4,871
-7,098
-10,492
-9,106
-1,506
2,820
-5,562
-3,705
-5,019
-3,991
-9,703
-3,960
-9,799
5,270
-6,441
-1,817
-12,342
2,390
-10,994
-1,121
-5,882
7,887
-14,412
-6,405
-4,302
-1,319
-3,451
-5,330
-3,609
-8,795
-7,194
-10,803
-17,806
-5,160
-5,210
-11,496
-15,894
*+ denotes heat evolved, and - denotes heat absorbed. The data in the International Critical Tables were calculated by E. Anderson.
THERMAL EXPAnSIOn AnD COMPRESSIBILITY
2-179
THERMAL EXPAnSIOn AnD COMPRESSIBILITY
Unit Conversion For this subsection, the following unit conversion is
applicable: °F = 9⁄5°C + 32.
Additional References Some of the tables given under this subject
are reprinted by permission from the Smithsonian Tables. For other data on
thermal expansion, see International Critical Tables. The tabular index is in
volume 3, and the data are in volume 2.
Thermal Expansion of Gases No tables of coefficients of thermal
expansion of gases are given in this edition. The coefficient at constant pressure, 1/u (∂u/∂T)p, for an ideal gas is merely the reciprocal of the absolute
temperature. For a real gas or liquid, both it and the coefficient at constant
volume 1/p (∂p/∂T)v should be calculated either from the equation of state
or from tabulated PVT data.
For expansion of liquids and solids, see the following tables.
TABLE 2-100 Linear Expansion of the Solid Elements*
C is the true expansion coefficient at the given temperature; M is the mean coefficient between given temperatures; where one temperature is given, the true coefficient at that temperature is indicated; α and β are coefficients in formula lt = l0(1 + αt + βt2); l0 is length at 0°C (unless otherwise indicated, when, if x is the reference
temperature, lt = lx[1 + α(t - tx) + β(t - tx)2]; lt is length at t °C).
Element
Temp., °C
C × 104
Aluminum
Aluminum
Antimony
Arsenic
Bismuth
Cadmium
Cadmium
Carbon, diamond
graphite
Chromium
Cobalt
Copper
Copper
Gold
Gold
Indium
Iodine
Iridium
Iridium
Iron, soft
cast
wrought
steel
Lead (99.9)
20
300
20
20
20
0
0
50
50
0.224
0.284
0.136∙
0.05
0.014∙
0.54∙
0.20⊥
0.012
0.06
20
20
200
20
0.123
0.162
0.170
0.140
40
0.417
20
0.065
40
20
20
20
0.1210
0.118
0.119
0.114
100
280
20
0.291
0.343
0.254
20
0.233
Molybdenum
20
0.053
Nickel
20
0.126
Osmium
Palladium
40
20
0.066
0.1173
Platinum
20
20
0.0887
0.0893
40
40
0
40
20
20
0.0850
0.0963
0.439
0.0763
0.1846
0.195
Magnesium
Manganese
†
Potassium
Rhodium
Ruthenium
Selenium
Silicon
Silver
Sodium
Steel, 36.4Ni
Tantalum†
20
0.065
Tellurium
Thallium
Tin
20
40
20
20
27
20‡
20‡
20
0.016∙
0.302
0.214
0.305∙
0.0444
0.643∙
0.125⊥
0.358
†
Tungsten
Zinc
Temp. range, °C
M × 104
100
500
20
0.235
0.311
0.080⊥
20
-180, -140
-180, -140
0.103⊥
0.59∙
0.117⊥
20,
100
0.068
17,
-191,
100
300
100
17
0.166
0.175
0.143
0.132
-190,
17
0.837
α × 104
β × 106
0,
500
0.22
0.009
20,
20,
100
100
0.526∙
0.214⊥
20,
6,
0,
500
121
625
0.086
0.121
0.161
0.0064
0.0040
0,
520
0.142
0.0022
0.0636
0.0679
0.0032
0.0011
Temp. range, °C
0,
80
1070, 1720
0,
20,
20,
100
0.11
100
200
0.291
0.300
-100, + 20
20, 100
0, 100
-190,
0
0, 100
25, 100
25, 500
0, 100
0.240
0.260
0.228
0.159
0.052
0.049
0.055
0.130
0,
6,
50
21
0.83
0.0876
0, 100
-3, +18
0, 100
0.660
0.0249
0.197
-190, -17
20, 260
20, 340
-78,
0
0, 100
20
0.622
0.031
0.055
0.059
0.0655
0.272⊥
20
100
-100
100
100
0.154⊥
0.045
0.656∙
0.639∙
0.141⊥
0,
-140,
+20,
+20,
0,
0,
0,
100,
750
750
750
240
0.1158
0.1170
0.1118
0.269
0.0053
0.0053
0.0053
0.011
+ 20,
500
0.2480
0.0096
20, 300
-142,
19
19, +305
0.216
0.0515
0.0501
0.0121
0.0057
0.0014
-190, + 20
+ 20, +300
500, 1000
0.1308
0.1236
0.1346
0.0166
0.0066
0.0033
-190,
0,
-190,
0,
0,
+100
1000
-100
+ 80
1000
0.1152
0.1167
0.0875
0.0890
0.0887
0.00517
0.0022
0.00314
0.00121
0.00132
-75, -112
0.0746
-75,
0,
20,
0,
260,
340,
20,
-67
875
500
50
500
500
400
0.0182
0.1827
0.1939
0.72
0.144
0.136
0.0646
0.0009
8,
95
0.2033
0.0263
-105, +502
+ 0, 400
0.0428
0.354
0.00058
0.010
0.00479
0.00295
*Smithsonian Tables. For more complete tabulations see Table 142, Smithsonian Physical Tables, 9th ed., 1954; Handbook of Chemistry and Physics, 40th ed.,
pp. 2239–2245. Chemical Rubber Publishing Co.; Goldsmith, and Waterman, WADC-TR-58-476, 1959; Johnson (ed.), WADD-TR-60-56, 1960, etc.
†
Molybdenum, 300 to 2500°C; lt = l300[1 + 5.00 × 10-6(t - 300) + 10.5 × 10-10(t - 300)2]
Tantalum, 300 to 2800°C; lt = l300[1 + 6.60 × 10-6(t - 300) + 5.2 × 10-10(t - 300)2]
Tungsten, 300 to 2700°C; lt = l300[1 + 4.44 × 10-6(t - 300) + 4.5 × 10-10(t - 300)2]
Beryllium, 20 to 100°C; 12.3 × 10-6 per °C.
Columbium, 0 to 100°C; 7.2 × 10-6 per °C.
Tantalum, 20 to 100°C; 6.6 × 10-6 per °C.
‡
These values for zinc were taken from Grüneisen and Goens, Z. Physik., 29:141 (1924).
2-180
PHYSICAL AnD CHEMICAL DATA
TABLE 2-101
Linear Expansion of Miscellaneous Substances*
The coefficient of cubical expansion may be taken as three times the linear coefficient. In the following table, t is the temperature or range of temperature, and C, the
coefficient of expansion.
t, °C
Substance
Amber
Bakelite, bleached
Brass:
Cast
Wire
Wire
71.5 Cu + 27.7 Zn +
0.3 Sn + 0.5 Pb
71 Cu + 29 Zn
Bronze:
3 Cu + 1 Sn
3 Cu + 1 Sn
3 Cu + 1 Sn
86.3 Cu + 9.7 Sn + 4 Zn
97.6 Cu + hard
2.2 Sn + soft
0.2 P
Caoutchouc
Caoutchouc
Celluloid
Constantan
Duralumin, 94Al
{
0–30
0–09
20–60
C × 104
0.50
0.61
0.22
0–100
0–100
0–100
0.1875
0.1930
0.1783–0.193
40
0–100
0.1859
0.1906
16.6–100
16.6–350
16.6–957
40
0–80
0–80
0.1844
0.2116
0.1737
0.1782
0.1713
0.1708
16.7–25.3
20–70
4–29
20–100
20–300
25.3–35.4
0–100
0–100
0–100
0–100
0.657–0.686
0.770
1.00
0.1523
0.23
0.25
0.842
0.1950
0.1836
0.1523
0.1552
Substance
Jena thermometer 59III
Jena thermometer 59III
Gutta percha
Ice
Iceland spar:
Parallel to axis
Perpendicular to axis
Lead tin (solder) 2 Pb
+ 1 Sn
Limestone
Magnalium
Manganin
Marble
Monel metal
Paraffin
Paraffin
Paraffin
Platinum-iridium, 10 Pt
+ 1 Ir
Platinum-silver, 1 Pt +
2 Ag
Porcelain
Porcelain Bayeux
Quartz:
Parallel to axis
Parallel to axis
Perpend. to axis
Quartz glass
Quartz glass
Quartz glass
Rock salt
Rubber, hard
Rubber, hard
Speculum metal
Steel, 0.14 C, 34.5 Ni
t, °C
0–100
−191–+16
20
−20–−1
C × 104
Substance
0.058
0.424
1.983
0.51
Topas:
Parallel to lesser horizontal axis
Parallel to greater horizontal axis
Parallel to vertical axis
Tourmaline:
Parallel to longitudinal
axis
Parallel to horizontal
axis
Type metal
Vulcanite
Wedgwood ware
Wood:
Parallel to fiber:
Ash
Beech
Chestnut
Elm
Mahogany
Maple
Oak
Pine
Walnut
Across the fiber:
Beech
Chestnut
Elm
Mahogany
Maple
Oak
Pine
Walnut
Wax white
Wax white
Wax white
Wax white
0–80
0–80
0.2631
0.0544
0–100
25–100
12–39
15–100
25–100
25–600
0–16
16–38
38–49
0.2508
0.09
0.238
0.181
0.117
0.14
0.16
1.0662
1.3030
4.7707
40
0.0884
0–100
20–790
1000–1400
0.1523
0.0413
0.0553
t, °C
C × 104
0−100
0.0832
0−100
0−100
0.0836
0.0472
0−100
0.0937
0−100
16.6−254
0−18
0−100
0.0773
0.1952
0.6360
0.0890
0−100
2.34
2.34
2.34
2.34
2.34
2.34
2.34
2.34
0.0951
0.0257
0.0649
0.0565
0.0361
0.0638
0.0492
0.0541
0.0658
Ebonite
Fluorspar, CaF2
0–80
0.0797
German silver
−190 to + 16
0.0521
2.34
0.614
Gold-platinum, 2 Au + 1 Pt
0–80
0.1337
2.34
0.325
Gold-copper, 2 Au + 1 Cu
–190 to + 16
−0.0026
2.34
0.443
Glass:
16 to 500
0.0057
2.34
0.404
Tube
0–100
0.0833
16 to 1000
0.0058
2.34
0.484
Tube
0–100
0.0828
40
0.4040
2.34
0.544
Plate
0–100
0.0891
0
0.691
2.34
0.341
Crown (mean)
0–100
0.0897
–160
0.300
2.34
0.484
Crown (mean)
50–60
0.0954
0–100
0.1933
10−26
2.300
Flint
50–60
0.0788
25–100
0.037
26−31
3.120
III
Jena ther- 16
0–100
0.081
25–600
0.136
31−43
4.860
mometer normal
43−57
15.227
*Smithsonian Tables. For a more complete tabulation see Tables 143, 144. Smithsonian Physical Tables. 9th ed., 1954, also reprinted in American Institute of Physics
Handbook, McGraw-Hill, New York, 1957; Handbook of Chemistry and Physics, 40th ed., pp. 2239–2245, Chemical Rubber Publishing Co. For data on many solids prior to
1926, see Gruneisen, Handbuch der Physik, vol. 10, pp. 1–52, 1926, translation available as N.A.S.A. RE 2-18-59W, 1959. For eight plastic solids below 300 K, see Scott,
Cryogenic Engineering, p. 331, Van Nostrand, Princeton, NJ, 1959. For 11 other materials to 300 K, see Scott, loc. cit., p. 333. For quartz and silica, see Cook, Brit. J. Appl.
Phys., 7, 285 (1956).
}
THERMAL EXPAnSIOn AnD COMPRESSIBILITY
TABLE 2-102
Volume Expansion of Liquids*
TABLE 2-103
If V0 is the volume at 0°, then at t° the expansion formula is Vt = V0(1 + αt + βt2 + γ t3).
The table gives values of α, β, and γ, and of C, the true coefficient of volume expansion
at 20° for some liquids and solutions. The temperature range of the observation is ∆t.
Values for the coefficient of volume expansion of liquids can be derived from the tables
of specific volumes of the saturated liquid given as a function of temperature later in
this section. C = (dV/dt)/V0
Liquid
Range
α × 103
β × 106
γ × 108
C × 103
at 20°
Acetic acid
16−107
1.0630
0.12636
1.0876 1.071
Acetone
0−54
1.3240
3.8090
−0.87983 1.487
Alcohol:
Amyl
−15–80
0.9001
0.6573
1.18458 0.902
Ethyl, 30% by volume
18−39
0.2928 10.790
−11.87
Ethyl, 50% by volume
0−39
0.7450
1.85
0.730
Ethyl, 99.3% by volume
27−46
1.012
2.20
1.12
Ethyl, 500 atm pressure
0−40
0.866
Ethyl, 3000 atm pressure
0−40
0.524
Methyl
0−61
1.1342
1.3635
0.8741 1.199
Benzene
11−81
1.17626 1.27776
0.80648 1.237
Bromine
0−59
1.06218 1.87714 −0.30854 1.132
Calcium chloride:
5.8% solution
18−25
0.07878 4.2742
0.250
40.9% solution
17−24
0.42383 0.8571
0.458
Carbon disulfide
−34–60
1.13980 1.37065
1.91225 1.218
500 atm pressure
0−50
0.940
3000 atm pressure
0−50
0.581
Carbon tetrachloride
0−76
1.18384 0.89881
1.35135 1.236
Chloroform
0−63
1.10715 4.66473 −1.74328 1.273
Ether
−15–38
1.51324 2.35918
4.00512 1.656
Glycerin
0.4853
0.4895
0.505
Hydrochloric acid,
33.2% solution
0−33
0.4460
0.215
0.455
Mercury
0−100
0.18182 0.0078
0.18186
Olive oil
0.6821
1.1405
−0.539
0.721
Pentane
0−33
1.4646
3.09319
1.6084 1.608
Potassium chloride,
24.3% solution
16−25
0.2695
2.080
0.353
Phenol
36−157
0.8340
0.10732
0.4446 1.090
Petroleum, 0.8467 density
24−120
0.8994
1.396
0.955
Sodium chloride, 20.6%
solution
0−29
0.3640
1.237
0.414
Sodium sulfate, 24%
solution
11−40
0.3599
1.258
0.410
Sulfuric acid:
10.9% solution
0−30
0.2835
2.580
0.387
100.0%
0−30
0.5758 −0.432
0.558
Turpentine
−9−106
0.9003
1.9595
−0.44998 0.973
Water
0−33
−0.06427 8.5053
−6.7900 0.207
*Smithsonian Tables, Table 269. For a detailed discussion of mercury data, see Cook,
Brit. J. Appl. Phys., 7, 285 (1956). For data on nitrogen and argon, see Johnson (ed.),
WADD-TR-60-56, 1960.
Bromoform1 7.7 − 50°C.
Vt = 0.34204[1 + 0.00090411(t − 7.7) + 0.0000006766(t − 7.7)2]
0.34204 is the specific volume of bromoform at 7.7°C.
Glycerin2 −62 to 0°C.
Vt = V0(1 + 4.83 × 10−4t − 0.49 × 10−6t2)
0 − 80°C.
Vt = V0(1 + 4.83 × 10−4t + 0.49 × 10−6t2)
3
Mercury 0 − 300°C.
Vt − V0[1 + 10−8(18,153.8t + 0.7548t2 + 0.001533t2 + 0.00000536t4)]
1
Sherman and Sherman, J. Am. Chem. Soc., 50, 1119 (1928). (An obvious error in their
equation has been corrected.)
2
Samsoen, Ann. phys., (10) 9, 91 (1928).
3
Harlow, Phil. Mag., (7) 7, 674 (1929).
2-181
Volume Expansion of Solids*
If v2 and v1 are the volumes at t2 and t1, respectively, then v2 = v1(1 + C∆t), C being the
coefficient of cubical expansion and ∆t the temperature interval. Where only a single
temperature is stated, C represents the true coefficient of volume expansion at that
temperature.
Substance
t or ∆t
C × 104
Antimony
Beryl
Bismuth
Copper†
Diamond
Emerald
Galena
Glass, common tube
hard
Jena, borosilicate 59 III
pure silica
Gold
Ice
Iron
Lead†
Paraffin
Platinum
Porcelain, Berlin
chloride
nitrate
sulfate
Quartz
Rock salt
Rubber
Silver
Sodium
Stearic acid
Sulfur, native
Tin
Zinc†
0−100
0−100
0−100
0−100
40
40
0−100
0−100
0−100
20−100
0−80
0−100
−20 to −1
0−100
0−100
20
0−100
20
0−100
0−100
20
0−100
50−60
20
0−100
20
33.8−45.4
13.2−50.3
0−100
0−100
0.3167
0.0105
0.3948
0.4998
0.0354
0.0168
0.558
0.276
0.214
0.156
0.0129
0.4411
1.1250
0.3550
0.8399
5.88
0.265
0.0814
1.094
1.967
1.0754
0.3840
1.2120
4.87
0.5831
2.13
8.1
2.23
0.6889
0.8928
*Smithsonian Tables, Table 268.
†
See additional data below.
Aluminum1
100 − 530°C.
V = V0(1 + 2.16 × 10−5t + 0.95 × 10−8t2)
1
Cadmium
130 − 270°C.
V = V0(1 + 8.04 × 10−5t + 5.9 × 10−8t2)
1
Copper
110 − 300°C.
V = V0(1 + 1.62 × 10−5t + 0.20 × 10−8t2)
Colophony2
0 − 34°C.
V = V0(1 + 2.21 × 10−4t + 0.31 × 10−6t2)
34 − 150°C.
V = V34[1 + 7.40 × 10−4(t − 34) + 5.91 × 10−6(t − 34)2]
1
Lead
100 − 280°C.
V = V0(1 + 1.60 × 10−5t + 3.2 × 10−8t2)
2
Shellac
0 − 46°C.
V = V0(1 + 2.73 × 10−4t + 0.39 × 10−6t2)
46 − 100°C.
V = V46[1 + 13.10 × 10−4(t − 46) + 0.62 × 10−6(t − 46)2]
Silica (vitreous)3
0 − 300°C.
Vt = V0[1 + 10−8(93.6t + 0.7776t2 − 0.003315t2 + 0.000005244t4)
Sugar (cane, amorphous)2 0 − 67°C.
Vt = V0(1 + 2.34 × 10−4t + 0.14 × 10−6t2)
67 − 160°C.
Vt = V67[1 + 5.02 × 10−4(t − 67) + 0.43 × 10−6(t − 67)2]
Zinc1
120 − 360°C.
Vt = V0(1 + 8.50 × 10−5t + 3.9 × 10−8t2)
1
2
3
Uffelmann, Phil. Mag., (7) 10, 633 (1930).
Samsoen, Ann. phys., (10) 9, 83 (1928).
Harlow, Phil. Mag., (7) 7, 674 (1929).
2-182
PHYSICAL AnD CHEMICAL DATA
GAS EXPAnSIOn: JOULE-THOMSOn EFFECT
Introduction The Joule-Thomson coefficient, (∂T/∂P)H , is the change
in gas temperature with pressure during an adiabatic expansion (a throttling
process, at constant enthalpy H). The temperature at which the Joule-Thomson
coefficient changes sign is called the Joule-Thomson inversion temperature.
Joule-Thomson coefficients for substances listed in Table 2-104 are given
in tables in the Thermodynamic Properties section.
Unit Conversions To convert the Joule-Thomson coefficient µ, in
degrees Celsius per atmosphere to degrees Fahrenheit per atmosphere,
multiply by 1.8. Temperature conversion: °F = 9⁄5°C + 32; °R = 9⁄5 K.
To convert bars to pounds-force per square inch, multiply by 14.504; to
convert bars to kilopascals, multiply by 100.
TABLE 2-104 Additional References Available for the Joule-Thomson Coefficient
Temp. range, °C
Pressure range, atm
Gas
0–10
10–50
50–200
12, 15, 19
35
15, 19, 35
Ammonia
Argon
Benzene
Butane
Carbon dioxide
12, 15, 16
19, 35
28
39
31
26
7, 8, 28
37
17
Air
Carbon monoxide
Deuterium
Dowtherm A
Ethane
Ethylene
Helium
Hydrogen
46
45
1, 38
24, 30
39
31
26
7, 8, 37
17
22, 24, 25
1∗
46
45
>200
<0
0–300
19, 35
12, 15, 16
19, 35
28
39
31
26
7, 8, 9, 10
37
17
39
31
39
7, 8, 37
7, 8, 37
1,∗ 22, 24
25
17
1,∗ 22, 24,
25
1, 38
22, 24, 25
30
6
38
24, 30
6
Methane
Mixtures
Natural gas
Nitrogen
13, 28, 40
13, 40
33
13, 40
Nitrous oxide
Pentane
Propane
Steam
26, 34, 44
41
28, 29, 42
34
43
29, 42, 47
42, 47
1, 38
22, 24, 25
30
33
13
34
33
13, 40
46
45
9, 10
38
24
6
9, 11
33
9, 10, 13
28, 40
9, 10
26, 34, 44
43
28, 29, 42
45
>300
Other references
3, 4, 18
2, 3
31
46
48
13
19
29, 42, 47
29, 47
∗See also 14 (generalized chart); 18 (review, to 1919); 20–22; 23 (review, to 1948); 27 (review, to 1905); 32, 36, 41, 50.
References: 1. Baehr. Z. Elektrochem., 60, 515 (1956). 2. Beattie, J. Math. Phys., 9, 11 (1930). 3. Beattie, Phys. Rev., 35, 643 (1930). 4. Bradley and Hale, Phys. Rev., 29, 258
(1909). 5. Brown and Dean, Bur. Stand. J. Res., 60, 161 (1958). 6. Budenholzer, Sage, et al., Ind. Eng. Chem., 29, 658 (1937). 7. Burnett, Phys. Rev., 22, 590 (1923). 8. Burnett,
Univ. Wisconsin Bull. 9(6), 1926. 9. Charnley, Ph.D. thesis. University of Manchester, 1952. 10. Charnley, Isles, et al., Proc. R. Soc. (London), A217, 133 (1953). 11. Charnley,
Rowlinson, et al., Proc. R. Soc. (London), A230, 354 (1955). 12. Dalton, Commun. Phys. Lab. Univ. Leiden, no. 109c, 1909. 13. Deming and Deming, Phys. Rev., 48, 448 (1935).
14. Edmister, Pet. Refiner, 28, 128 (1949). 15. Eucken, Clusius, et al., Z. Tech. Phys., 13, 267 (1932). 16. Eumorfopoulos and Rai, Phil. Mag., 7, 961 (1926). 17. Huang, Lin,
et al., Z. Phys., 100, 594 (1936). 18. Hoxton, Phys. Rev., 13, 438 (1919). 19. Ishkin and Kaganev, J. Tech. Phys. U.S.S.R., 26, 2323 (1956). 20. Isles, Ph.D. thesis, Leeds University.
21. Jenkin and Pye, Phil. Trans. R. Soc. (London), A213, 67 (1914); A215, 353 (1915). 22. Johnston, J. Am. Chem. Soc., 68, 2362 (1946). 23. Johnston, Trans. Am. Soc. Mech.
Eng., 70, 651 (1948). 24. Johnston, Bezman, et al., J. Am. Chem. Soc., 68, 2367 (1946). 25. Johnston, Swanson, et al., J. Am. Chem. Soc., 68, 2373 (1946). 26. Kennedy, Sage,
et al., Ind. Eng. Chem., 28, 718 (1936). 27. Kester, Phys. Rev., 21, 260 (1905). 28. Keyes and Collins, Proc. Nat. Acad. Sci., 18, 328 (1932). 29. Kleinschmidt, Mech. Eng., 45, 165
(1923); 48, 155 (1926). 30. Koeppe, Kältetechnik, 8, 275 (1956). 31. Lindsay and Brown, Ind. Eng. Chem., 27, 817 (1935). 32. Noell, dissertation, Munich, 1914, Forschungsdienst, 184, p. 1, 1916. 33. Palienko, Tr. Inst. Ispol’ z. Gaza, Akad. Nauk Ukr. SSR, no. 4, p. 87, 1956. 34. Pattee and Brown, Ind. Eng. Chem., 26, 511, (1934). 35. Roebuck, Proc.
Am. Acad. Arts Sci., 60, 537 (1925); 64, 287 (1930). 36. Roebuck, see 49 below, 37. Roebuck and Murrell, Phys. Rev., 55, 240 (1939). 38. Roebuck and Osterberg, Phys. Rev.,
37, 110 (1931); 43, 60 (1933). 39. Roebuck and Osterberg, Phys. Rev., 46, 785 (1934). 40. Roebuck and Osterberg, Phys. Rev., 48, 450 (1935). 41. Roebuck, Murrell, et al.,
J. Am. Chem. Soc., 64, 400 (1942). 42. Sage, unpublished data, California Institute of Technology, 1959. 43. Sage and Lacy, Ind. Eng. Chem., 27, 1484 (1934). 44. Sage,
Kennedy, et al., Ind. Eng. Chem., 28, 601 (1936). 45. Sage, Webster, et al., Ind. Eng. Chem., 29, 658 (1937). 46. Ullock, Gaffert, et al., Trans. Am. Inst. Chem. Eng., 32, 73
(1936). 47. Yang, Ind. Eng. Chem., 45, 786 (1953). 48. Zelmanov, J. Phys. U.S.S.R., 3, 43 (1940). 49. Roebuck, recalculated data. 50. Michels et al., van der Waals laboratory
publications. Gunn, Cheuh, and Prausnitz, Cryogenics, 6, 324 (1966), review equations relating the inversion temperatures and pressures. The ability of various equations of state to relate these was also discussed by Miller, Ind. Eng. Chem. Fundam., 9, 585 (1970); and Juris and Wenzel, Am. Inst. Chem. Eng. J., 18, 684 (1972). Perhaps
the most detailed review is that of Hendricks, Peller, and Baron. NASA Tech. Note D 6807, 1972.
CRITICAL COnSTAnTS
TABLE 2-105 Approximate Inversion-Curve Locus
in Reduced Coordinates (Tr = T/Tc ; Pr = P/Pc)*
Pr
0
0.5
1
1.5
2
2.5
3
4
TrL
TrU
0.782
4.984
0.800
4.916
0.818
4.847
0.838
4.777
0.859
4.706
0.880
4.633
0.903
4.550
0.953
4.401
Pr
5
6
7
8
9
10
11
11.79
TrL
1.01
1.08
1.16
1.25
1.35
1.50
1.73
2.24
TrU
4.23
4.06
3.88
3.68
3.45
3.18
2.86
2.24
∗Calculated from the best three-constant equation recommended by Miller, Ind.
Eng. Chem. Fundam., 9, 585 (1970). TrL refers to the lower curve, and TrU, to the upper
curve.
Additional References For other inorganic substances see Mathews,
Chem. Rev., 72 (1972):71–100. For other organics see Kudchaker, Alani, and
Zwolinski, Chem. Rev., 68 (1968): 659–735.
TABLE 2-106
Cmpd. no.
2-183
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
Critical Constants and Acentric Factors of Inorganic and Organic Compounds
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CF4
Cl2
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
7782-50-5
Mol. wt.
TC, K
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
153.8227
88.0043
70.906
466
761
591.95
606
508.2
545.5
308.3
506
615
540
132.45
405.65
645.6
150.86
824
562.05
689
751
702.3
830
720.15
662
718
773
584.15
670.15
503.8
464
452
425
425.12
680
676
563.1
535.9
419.5
435.5
428.6
575.4
660.5
570.1
554
440
537.2
615.7
585.4
304.21
552
132.92
556.35
227.51
417.15
PC, MPa
5.57
6.6
5.786
4
4.701
4.85
6.138
5
5.66
4.66
3.774
11.28
4.25
4.898
5.05
4.895
4.74
4.47
4.215
3.352
4.374
3.11
4.06
3.38
10.3
4.5191
5.565
6.929
4.36
4.32
3.796
5.21
4.02
4.414
4.1885
4.02
4.21
4.1
3.09
2.89
3.97
4.06
4.6
4.41
4.06
3.88
7.383
7.9
3.499
4.56
3.745
7.71
VC, m3/kmol
0.154
0.215
0.177
0.304
0.209
0.193
0.112
0.197
0.208
0.216
0.09147
0.07247
0.337
0.07459
0.346
0.256
0.315
0.344
0.3132
0.5677
0.382
0.442
0.367
0.497
0.135
0.324
0.204
0.152
0.22
0.221
0.255
0.303
0.305
0.273
0.27
0.241
0.234
0.238
0.389
0.497
0.307
0.307
0.208
0.258
0.293
0.291
0.094
0.16
0.0944
0.276
0.143
0.124
ZC
0.221
0.224
0.208
0.241
0.233
0.206
0.268
0.234
0.23
0.224
0.313
0.242
0.267
0.291
0.255
0.268
0.261
0.246
0.226
0.276
0.279
0.25
0.25
0.261
0.286
0.263
0.271
0.273
0.255
0.27
0.274
0.279
0.218
0.258
0.254
0.278
0.272
0.274
0.251
0.262
0.257
0.271
0.262
0.255
0.232
0.232
0.274
0.275
0.299
0.272
0.283
0.276
Acentric factor
0.262493
0.421044
0.466521
0.455328
0.306527
0.341926
0.191185
0.319832
0.538324
0.310664
0
0.252608
0.350169
0
0.5585
0.2103
0.262789
0.602794
0.343214
0.501941
0.363116
0.433236
0.312604
0.402873
0.128997
0.250575
0.205275
0.153426
0.165877
0.195032
0.200164
0.630463
0.704256
0.58828
0.580832
0.184495
0.201877
0.217592
0.439393
0.394149
0.271361
0.25059
0.246976
0.282553
0.675003
0.3601
0.223621
0.110697
0.0481621
0.192552
0.178981
0.0688183
(Continued)
2-184
TABLE 2-106
Cmpd. no.
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued )
Name
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Di–isopropyl amine
Di–isopropyl ether
Di–isopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Formula
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
CAS
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
Mol. wt.
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
90.121
104.14758
54.09044
TC, K
PC, MPa
VC, m3/kmol
632.35
460.35
536.4
416.25
503.15
489
705.85
697.55
704.65
631
400.15
459.93
553.8
650.1
653
560.4
511.7
507
398
664
674
617.7
722.1
688
616.6
696
619.85
38.35
628
650.15
611
584.1
683.95
705
684.75
523
561.6
510
560
572
736.6
496.6
466.7
557.15
386.44
445
351.255
523.1
500.05
576
507.8
543
473.2
4.5191
5.27
5.472
6.68
4.425
4.54
4.56
5.01
5.15
3.209
5.924
4.98
4.08
4.26
4
4.35
4.51
4.8
5.54
3.97
2.6
2.11
2.28
2.308
2.223
2.13
2.37
1.6617
6.03
5.4769
7.17
2.46
4.07
4.07
4.07
5.07
5.37
6.08
4.24
4.24
4.27
3.71
3.64
3.96
4.5198
4.34
5.784
3.2
2.88
3.02
3.773
3.446
4.87
0.308
0.192
0.239
0.141
0.243
0.247
0.312
0.282
0.277
0.434
0.151
0.21
0.308
0.322
0.311
0.291
0.26
0.245
0.162
0.355
0.575
0.617
0.639
0.645
0.584
0.624
0.552
0.060263
0.276
0.2616
0.223
0.487
0.351
0.351
0.351
0.24
0.22
0.185
0.291
0.291
0.349
0.301
0.28
0.318
0.179
0.195
0.123
0.418
0.386
0.416
0.297
0.35
0.221
ZC
0.265
0.264
0.293
0.272
0.257
0.276
0.242
0.244
0.244
0.265
0.269
0.273
0.273
0.254
0.229
0.272
0.276
0.279
0.271
0.255
0.267
0.254
0.243
0.26
0.253
0.23
0.254
0.314
0.319
0.265
0.315
0.247
0.251
0.244
0.251
0.28
0.253
0.265
0.265
0.259
0.243
0.27
0.263
0.272
0.252
0.229
0.244
0.308
0.267
0.262
0.265
0.267
0.274
Acentric factor
0.249857
0.188591
0.221902
0.151
0.215047
0.198553
0.448034
0.43385
0.50721
0.327406
0.275605
0.18474
0.208054
0.369047
0.299006
0.212302
0.194874
0.19611
0.127829
0.264134
0.520066
0.492328
0.813724
0.606986
0.480456
0.587421
0.51783
−0.14486
0.125025
0.206724
0.20945
0.447646
0.27898
0.219189
0.284638
0.233943
0.286595
0.198622
0.252928
0.256391
0.952882
0.303856
0.281065
0.29002
0.275052
0.222428
0.277138
0.388315
0.338683
0.404427
0.32768
0.352222
0.238542
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
2-185
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
240.46774
114.18546
100.20194
437.2
500
591.15
606.15
596.15
615
400.1
649.6
537.3
766
402
503.04
729
777.4
587
766.8
550
658
768
305.32
514
523.3
456.15
617.15
698
655
571
609.15
569.5
282.34
593
720
537
469.15
508.4
674.6
583
489
567
499.15
546
500.23
559.95
144.12
560.09
375.31
317.42
420
771
588
490.15
5.2
736
620
540.2
5.34
3.15
2.93843
2.93843
2.93843
5.36
5.37
4.42
2.91
2.78
3.56
5.53
5.65
2.76
5.2081
3.08
3.14
1.82
1.16
4.872
6.137
3.88
5.62
3.609
3.18
3.41
2.95
3.04
3.4
5.041
6.29
8.2
6.85
7.19
4.74
2.778
2.46
3.41
3.32
5.49
3.362
3.37007
3.33
5.1724
4.55051
5.028
5.87511
6.59
7.8
5.81
5.5
0.2275
1.34
3.16
2.74
0.18
0.361
0.45
0.46
0.46
0.252
0.17
0.26199
0.393
0.53
0.258
0.201
0.227
0.529
0.238
0.503
0.402
0.755
1.34
0.1455
0.168
0.286
0.207
0.374
0.489
0.389
0.403
0.43
0.375
0.131
0.264
0.191
0.173
0.140296
0.229
0.528
0.487
0.329
0.369
0.207
0.345
0.339
0.403
0.066547
0.269
0.159
0.113
0.0851
0.163
0.125
0.218
0.0573
1.11
0.434
0.428
0.264
0.274
0.269
0.268
0.273
0.264
0.2744
0.214
0.256
0.231
0.275
0.266
0.212
0.226
0.254
0.243
0.276
0.251
0.243
0.279
0.241
0.255
0.307
0.263
0.268
0.244
0.25
0.258
0.269
0.281
0.337
0.262
0.265
0.25876
0.257
0.262
0.247
0.276
0.26
0.274
0.256
0.275
0.288
0.287
0.263
0.256
0.252
0.161
0.198
0.149
0.294
0.302
0.244
0.266
0.261
0.299885
0.249251
0.232569
0.232443
0.237864
0.205916
0.200221
0.31771
0.296407
0.656848
0.129957
0.194256
0.280551
0.580691
0.279262
0.43889
0.449684
0.576385
0.906878
0.099493
0.643558
0.366409
0.284788
0.30347
0.477055
0.632579
0.401075
0.245525
0.270095
0.0862484
0.472367
0.506776
0.200735
0.197447
0.284736
0.801289
0.494378
0.305629
0.389061
0.187751
0.394373
0.347328
0.269778
0.0530336
0.247183
0.217903
0.194721
0.167887
0.412381
0.312521
0.201538
−0.390032
0.769688
0.405751
0.349469
(Continued)
2-186
TABLE 2-106
Cmpd. no.
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued )
Name
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
Formula
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
CAS
Mol. wt.
TC, K
PC, MPa
VC, m3/kmol
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
677.3
632.3
608.3
606.6
611.4
537.4
645
547
723
594
507.6
660.2
611.3
585.3
587.61
582.82
504
544
623
516.2
549
653.15
33.19
363.15
324.65
456.65
461.15
373.53
605
471.85
834
662
190.564
512.5
718
506.55
402.4
536
430.05
693
490
460.4
643
577.2
465
470
492
512.74
593
463.2
554.5
442
572.1
3.043
3.085
3
2.92
2.94
2.92
2.77
3.21
1.4
3.46
3.025
3.308
3.446
3.311
3.287
3.32
3.21
3.53
3.08
3.62
3.53
14.7
1.313
8.552
8.31
5.39
6.48
8.96291
3.7
4.54
6.1
4.79
4.599
8.084
4.98
4.75
5.63
4.25
7.46
3.59
3.83
3.38
3.89
3.93
3.447
3.42
4.38
3.371
3.47
4.2
3.473
4.17
3.48
0.466
0.444
0.447
0.433
0.434
0.402
0.465
0.387
1.04
0.378
0.371
0.408
0.382
0.385
0.378
0.378
0.348
0.331
0.412
0.322
0.331
0.158
0.064147
0.1
0.081
0.139
0.069
0.0985
0.292
0.221
0.279
0.28
0.0986
0.117
0.267
0.228
0.164
0.27
0.154
0.436
0.291
0.306
0.347
0.329
0.292
0.292
0.248
0.329
0.36
0.275
0.34
0.246
0.369
ZC
0.252
0.261
0.265
0.251
0.251
0.263
0.24
0.273
0.243
0.266
0.266
0.246
0.259
0.262
0.254
0.259
0.267
0.258
0.245
0.272
0.256
0.428
0.305
0.283
0.249
0.197
0.117
0.284
0.215
0.256
0.245
0.244
0.286
0.222
0.223
0.257
0.276
0.258
0.321
0.272
0.274
0.27
0.252
0.269
0.26
0.256
0.266
0.26
0.253
0.3
0.256
0.279
0.27
Acentric factor
0.759934
0.562105
0.567733
0.407565
0.418982
0.343194
0.422568
0.377799
0.717404
0.361818
0.301261
0.733019
0.558598
0.553
0.384626
0.380086
0.285121
0.218301
0.368101
0.332699
0.221387
0.314282
−0.215993
0.073409
0.131544
0.409913
0.382283
0.0941677
0.61405
0.275913
0.738273
0.331817
0.0115478
0.565831
0.435111
0.331255
0.211537
0.342296
0.281417
0.420541
0.187439
0.227875
0.589443
0.59002
0.234056
0.28703
0.137046
0.313008
0.3229
0.308085
0.377519
0.225204
0.236055
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-187
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F 3N
CH3NO2
N 2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
686
614
617
532.7
542
526
483
437.8
535.5
533
487.2
497
574.6
488
464.48
553.4
553.1
469.95
566
694
497.7
546.49
407.8
506.2
417.9
530.6
476.25
565
352.5
654
497.1
437
748.4
44.4
593
126.2
234
588.15
309.57
180.15
758
658.5
594.6
710.7
670.9
649.5
593.1
681
598.05
747
638.9
568.7
694.26
652.3
629.8
4
3.79
3.79
3.79
4.13
4.13
3.95
4.4
4.15
4.26
6
3.41
3.27
5.48
3.762
3.8
4.021
7.23
3.68
2.54
3.04
3.042
3.64
3.972
4
4.004
3.801
3.97
4.7
3.36
3.286
4.67
4.05
2.653
5.16
3.4
4.4607
6.31
7.245
6.48
1.21
2.68
2.29
2.514
2.527
2.5408
2.428
2.31
2.61
1.27
2.96
2.49
2.779
2.783
2.749
0.374
0.374
0.374
0.319
0.303
0.303
0.289
0.221
0.267
0.254
0.172
0.329
0.369
0.202
0.276
0.31
0.328
0.145
0.323
0.572
0.368
0.38
0.259
0.275
0.239
0.282
0.276
0.307
0.205
0.399
0.329
0.21
0.407
0.0417
0.236
0.08921
0.11875
0.173
0.0974
0.058
1.26
0.543
0.551
0.584
0.576
0.577
0.524
0.571
0.497
1.19
0.488
0.486
0.523
0.509
0.512
0.262
0.278
0.276
0.273
0.278
0.286
0.284
0.267
0.249
0.244
0.255
0.272
0.253
0.273
0.269
0.256
0.28718
0.268
0.253
0.252
0.27
0.254
0.278
0.26
0.275
0.256
0.265
0.259
0.329
0.247
0.262
0.27
0.265
0.3
0.247
0.289
0.272
0.223
0.274
0.251
0.242
0.266
0.255
0.248
0.261
0.271
0.258
0.233
0.261
0.243
0.272
0.256
0.252
0.261
0.269
0.221299
0.68049
0.67904
0.228759
0.23179
0.229606
0.275755
0.231374
0.323369
0.209108
0.255551
0.307786
0.355671
0.300694
0.26555
0.320845
0.24611
0.158174
0.280233
0.791271
0.279149
0.344201
0.183521
0.615203
0.19484
0.346586
0.276999
0.273669
0.131449
0.32297
0.246542
0.241564
0.302034
−0.0395988
0.380324
0.0377215
0.119984
0.348026
0.140894
0.582944
0.852231
0.473309
0.44346
0.778706
0.584074
0.6092
0.436736
0.52604
0.470974
0.811359
0.441993
0.399552
0.773427
0.569694
0.58814
(Continued)
2-188
TABLE 2-106
Cmpd. no.
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued )
Name
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
Formula
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
CAS
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
Mol. wt.
TC, K
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
632.7
627.7
566.9
667.3
574
828
154.58
261
708
566.1
469.7
639.16
588.1
561
561.08
560.95
464.8
584.3
598
481.2
519
869
694.25
653
791
394
369.83
536.8
508.3
636
503.6
600.81
561.3
549.73
496.95
638.35
364.85
538
517
536.6
PC, MPa
2.64
2.704
2.663
2.52
2.88
8.2
5.043
5.57
1.48
3.845
3.37
3.63
3.897
3.7
3.694
3.74
3.56
3.536
3.47
4.17
4.03
2.9
6.13
4.06
4.72
5.25
4.248
5.169
4.765
3.12
5.038
4.668
4.26
3.36
4.74
3.2
4.6
4.02
4.75
4.63
VC, m3/kmol
0.497
0.496953
0.464
0.518
0.442
0.227
0.0734
0.089
0.969
0.313
0.313
0.35
0.326
0.326
0.301
0.336
0.2934
0.385
0.359
0.277
0.276
0.554
0.229
0.37
0.421
0.165
0.2
0.219
0.222
0.437
0.204
0.235
0.242
0.345
0.26
0.44
0.185
0.285
0.254
0.254
ZC
0.249
0.257
0.262
0.235
0.267
0.27
0.288
0.228
0.244
0.256
0.27
0.239
0.258
0.259
0.238
0.269
0.27
0.28
0.251
0.289
0.258
0.222
0.243
0.277
0.302
0.264
0.276
0.254
0.25
0.258
0.246
0.22
0.221
0.254
0.298
0.265
0.281
0.256
0.281
0.264
Acentric factor
0.454874
0.440561
0.392149
0.449744
0.42329
0.286278
0.0221798
0.211896
0.68632
0.313152
0.251506
0.706632
0.57483
0.554979
0.343288
0.344846
0.237218
0.26853
0.320705
0.289925
0.175199
0.470716
0.44346
0.412323
0.702495
0.104121
0.152291
0.6209
0.663
0.341975
0.281254
0.579579
0.350057
0.388902
0.279839
0.344391
0.137588
0.308779
0.21381
0.231789
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O 2S
F 6S
O 3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
626
683
259
636
838
430.75
318.69
490.85
883.6
857
693
540.15
720
631.95
568
579.35
591.75
602
675
535.15
433.25
664.5
649.1
543.8
573.5
846
828
639
703.9
519.13
454
432
543.15
647.096
617
630.3
616.2
6.1
5.96
3.72
3.84
5
7.8841
3.76
8.21
3.486
2.99
1.57
5.19
3.65
5.16
2.87
5.69
4.108
4.48
1.68
3.04
4.07
3.454
3.232
2.57
2.82
3.39
3.04
1.95
2.119
3.958
4.86
5.67
3.06
22.064
3.541
3.732
3.511
0.239
0.291
0.202
0.352
0.33
0.122
0.19852
0.127
0.424
0.731
0.897
0.224
0.408
0.249
0.461
0.219
0.316
0.281
0.826
0.39
0.254
0.414
0.43
0.468
0.455
0.479
0.572
0.685
0.715
0.27
0.205
0.179
0.408
0.0559472
0.375
0.37
0.378
0.28
0.305
0.349
0.256
0.237
0.269
0.282
0.255
0.201
0.307
0.244
0.259
0.249
0.245
0.28
0.259
0.264
0.252
0.247
0.266
0.287
0.259
0.258
0.266
0.269
0.231
0.253
0.252
0.259
0.248
0.264
0.283
0.276
0.229
0.259
0.264
0.259
1.10651
0.494515
0.38584
0.297097
0.743044
0.245381
0.215146
0.42396
0.94695
0.551265
0.643017
0.225354
0.335255
0.199551
0.244953
0.196972
0.264012
0.259135
0.617397
0.316193
0.206243
0.366553
0.37871
0.303455
0.2903
0.862257
0.897249
0.530316
0.623622
0.351307
0.106852
0.100107
0.281543
0.344861
0.326485
0.31013
0.321839
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation
of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
2-189
2-190
PHYSICAL AnD CHEMICAL DATA
COMPRESSIBILITIES
Introduction The compressibility factor Z can be calculated by using
the defining equation Z = PV/(RT), where P is pressure, V is molar volume, R
is the gas constant, and T is absolute temperature. Values of P, V, and T for
substances listed in Table 2-109 are given in tables in the Thermodynamic
Properties section. For the units used in these tables, R is 0.008314472
MPadm3/(mol ⋅ K). Values at temperatures and pressures other than those
in the tables can be generated for many of the substances in Table 2-109 by
TABLE 2-107
going to http://webbook.nist.gov and selecting NIST Chemistry WebBook,
then Thermophysical Properties of Fluid Systems High Accuracy Data.
Results can be pasted into a spreadsheet to facilitate calculation of the compressibility factor.
Unit Conversions For this subsection, the following unit conversion is
applicable: °R = 9⁄5 K. To convert bars to pounds-force per cubic inch, multiply by 14.504. To convert bars to kilopascals, multiply by 100.
Compressibilities of Liquids*
At the constant temperature T, the compressibility β = (1/ V0 )(dV/dP). In general as P increases, β decreases rapidly at first and then slowly; the change of β with T is large
at low pressures but very small at pressures above 1000 to 2000 megabars. 1 megabar = 0.987 atm = 106 dynes/cm2 based upon the older usage, 1 bar = 1 dyne/cm2.
Substance
Temp.,
°C
Pressure,
megabars
Compressibility per
megabar
β × 106
Substance
Temp.,
°C
Pressure,
megabars
Compressibility per
megabar
β × 106
Substance
Temp.,
°C
Pressure,
megabars
Compressibility per
megabar
β × 106
Acetone
14
23
111
Ethyl acetate
20
400
75
Methyl alcohol
15
23
103
Acetone
20
500
61
alcohol
14
23
100
alcohol
20
200
95
Acetone
20
1,000
52
alcohol
20
500
63
alcohol
20
400
80
Acetone
40
12,000
9
alcohol
20
1,000
54
alcohol
20
500
65
Amyl alcohol
14
23
88
alcohol
20
12,000
8
alcohol
20
1,000
54
alcohol, iso.
20
200
84
bromide
20
200
100
alcohol
20
12,000
8
alcohol, iso.
20
400
70
bromide
20
400
82
Nitric acid
0
17
32
alcohol, n
20
500
61
bromide
20
500
70
Oils:
alcohol, n
20
1,000
46
bromide
20
1,000
54
Almond
15
5
53
alcohol, n
20
12,000
8
bromide
20
12,000
8
Castor
15
5
46
alcohol, n
40
12,000
8
chloride
15
23
151
Linseed
15
5
51
Benzene
17
5
89
chloride
20
500
102
Olive
15
5
55
Benzene
20
200
77
chloride
20
1,000
66
Rapeseed
20
59
Benzene
20
400
67
chloride
20
12,000
8
Phosphorus trichloride
10
250
71
Bromine
20
200
56
ether
25
23
188
trichloride
20
500
63
Bromine
20
400
51
ether
20
500
84
trichloride
20
1,000
47
Butyl alcohol, iso
18
8
97
ether
20
1,000
61
trichloride
20
12,000
8
alcohol, iso
20
200
81
ether
20
12,000
10
Propyl alcohol (n)
20
200
77
alcohol, iso
20
400
64
iodide
20
200
81
alcohol (n)
20
400
67
alcohol, iso
20
500
56
iodide
20
400
69
alcohol (n?)
20
500
65
alcohol, iso
20
1,000
46
iodide
20
500
64
alcohol (n?)
20
1,000
47
alcohol, iso
20
12,000
8
iodide
20
1,000
50
alcohol (n?)
20
12,000
7
Carbon bisulfide
16
21
86
iodide
20
12,000
8
Toluene
20
200
74
bisulfide
20
500
57
Gallium
30
300
3.97
Toluene
20
400
64
bisulfide
20
1,000
48
Glycerol
15
5
22
Turpentine
20
74
bisulfide
20
12,000
6
Hexane
20
200
117
Water
20
13
49
tetrachloride
20
200
86
Hexane
20
400
91
Water
20
200
43
tetrachloride
20
400
73
Kerosene
20
500
55
Water
20
400
41
Chloroform
20
200
83
Kerosene
20
1,000
45
Water
20
500
39
Chloroform
20
400
70
Kerosene
20
12,000
8
Water
40
500
38
Dichloroethylsulfide
32
1,000
34
Mercury
20
300
3.95
Water
40
1,000
33
Dichloroethylsulfide
32
2,000
24
Mercury
22
500
3.97
Water
40
12,000
9
Ethyl acetate
13
23
103
Mercury
22
1,000
3.91
Xylene, meta
20
200
69
acetate
20
200
90
Mercury
22
12,000
2.37
meta
20
400
60
* Smithsonian Tables, Table 106.
Scott (Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959) gives data for liquid nitrogen (p. 283), oxygen (p. 276), and hydrogen (p. 303). For a convenient index
to the high-pressure work of Bridgman, see American Institute of Physics Handbook, p. 2-163, McGraw-Hill, New York, 1957.
TABLE 2-108
Compressibilities of Solids
Many data on the compressibility of solids obtained prior to 1926 are contained in Gruneisen, Handbuch der Physik, vol. 10, Springer,
Berlin, 1926, pp. 1–52; also available as translation, NASA RE 2-18-59W, 1959. See also Tables 271, 273, 276, 278, and other material in
Smithsonian Physical Tables, 9th ed., 1954. For a review of high-pressure work to 1946, see Bridgman, Rev. Mod. Phys., 18, 1 (1946).
THERMODYnAMIC PROPERTIES
2-191
THERMODYnAMIC PROPERTIES
Explanation of Tables The following subsection presents thermodynamic properties of a number of fluids. In some cases, transport properties
are also included.
Property tables generated from the NIST database (Lemmon, E. W., M. O.
McLinden, and M. L. Huber, NIST Standard Reference Database 23) are listed in
Table 2-109. The number of digits provided in these tables was chosen for uniformity of appearance and formatting and does not represent the uncertainties
of the physical quantities: They are the result of calculations from the standard
thermophysical property formulations within a fixed format. They were generated using REFPROP software (Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology,
Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1).
Megan Friend helped produce these tables initially for Perry’s 8th edition.
Because properties for many compounds also can be generated by the user
at the NIST website, only more commonly used compounds’ properties are
given here. For other compounds, go to http://webbook.nist.gov and select
NIST Chemistry WebBook > Thermophysical Properties of Fluid Systems
High Accuracy Data. After selecting the desired unit system and temperature
and/or pressure increments for which properties are to be generated, the
resulting table can be copied into a spreadsheet.
Notation
cp = isobaric specific heat
cv = isochoric specific heat
e = specific internal energy
h = enthalpy
k = thermal conductivity
p = pressure
s = specific entropy
t = temperature
T = absolute temperature
u = specific internal energy
µ = viscosity
v = specific volume
f = subscript denoting saturated liquid
g = subscript denoting saturated vapor
Unit Conversions For this subsection, the following unit conversions
are applicable:
cp, specific heat: To convert kilojoules per kilogram-kelvin to British thermal units (Btu) per pound–degree Fahrenheit, multiply by 0.23885.
e, internal energy: To convert kilojoules per kilogram to Btu per pound,
multiply by 0.42992.
g, gravity acceleration: To convert meters per second squared to feet per
second squared, multiply by 3.2808.
h, enthalpy: To convert kilojoules per kilogram to Btu per pound, multiply
by 0.42992.
k, thermal conductivity: To convert watts per meter-kelvin to Btu–feet per
hour–square foot–degree Fahrenheit, multiply by 0.57779.
p, pressure: To convert bars to kilopascals, multiply by 100; to convert bars
to pounds-force per square inch, multiply by 14.504; and to convert millimeters of mercury to pounds-force per square inch, multiply by 0.01934.
s, entropy: To convert kilojoules per kilogram-kelvin to Btu per pound–
degree Rankine, multiply by 0.23885.
t, temperature: °F = 9⁄ 5°C + 32.
T, absolute temperature: °R = 9⁄ 5 K.
u, internal energy: To convert kilojoules per kilogram to Btu per pound,
multiply by 0.42992.
µ, viscosity: To convert pascal-seconds to pound-force–seconds per square
foot, multiply by 0.020885; to convert pascal-seconds to cp, multiply by 1000.
v, specific volume: To convert cubic meters per kilogram to cubic feet per
pound, multiply by 16.018.
r, density: To convert kilograms per cubic meter to pounds per cubic foot,
multiply by 0.062428.
Additional References Bretsznajder, Prediction of Transport and
Other Physical Properties of Fluids, Pergamon, New York, 1971. D’Ans and
Lax, Handbook for Chemists and Physicists (in German), 3 vols., SpringerVerlag, Berlin. Engineering Data Book, 12th ed., 2004, Natural Gas Processors Suppliers Association, Tulsa, Okla. Ganic, Hartnett, and Rohsenow,
Handbook of Heat Transfer, 2nd ed., McGraw-Hill, New York, 1984. Gray,
American Institute of Physics Handbook, 3d ed., McGraw-Hill, New York,
1972. Kay and Laby, Tables of Physical and Chemical Constants, Longman,
London, various editions and dates. Landolt-Börnstein Tables, many volumes and dates, Springer-Verlag, Berlin. Partington, Advanced Treatise
on Physical Chemistry, Longman, London, 1950. Raznjevic, Handbook of
Thermodynamic Tables and Charts, McGraw-Hill, New York, 1976 and
other editions. Reynolds, Thermodynamic Properties in SI, Department of
Mechanical Engineering, Stanford University, 1979. Stephan and Lucas,
Viscosity of Dense Fluids, Plenum, New York and London, 1979. Vargaftik,
Tables of the Thermophysical Properties of Gases and Liquids, Wiley, New
York, 1975. Vargaftik, Filippov, Tarzimanov, and Totskiy, Thermal Conductivity of Liquids and Gases (in Russian), Standartov, Moscow, 1978. Weast,
Handbook of Chemistry and Physics, Chemical Rubber Co., Boca Raton, FL,
97th print edition (2016) and online.
2-192
PHYSICAL AnD CHEMICAL DATA
TABLE 2-109
Thermodynamic Properties of Acetone
Temperature
K
Pressure
MPa
178.50
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
375.00
390.00
405.00
420.00
435.00
450.00
465.00
480.00
495.00
508.10
2.3265E-06
2.8743E-06
1.9454E-05
9.6588E-05
0.00037556
0.0012008
0.0032765
0.0078514
0.016899
0.033259
0.060720
0.10404
0.16891
0.26188
0.39033
0.56235
0.78681
1.0733
1.4324
1.8759
2.4172
3.0725
3.8632
4.6924
178.50
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
375.00
390.00
405.00
420.00
435.00
450.00
465.00
480.00
495.00
508.10
2.3265E-06
2.8743E-06
1.9454E-05
9.6588E-05
0.00037556
0.0012008
0.0032765
0.0078514
0.016899
0.033259
0.060720
0.10404
0.16891
0.26188
0.39033
0.56235
0.78681
1.0733
1.4324
1.8759
2.4172
3.0725
3.8632
4.6924
200.00
250.00
300.00
328.84
0.10000
0.10000
0.10000
0.10000
328.84
350.00
400.00
450.00
500.00
550.00
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
200.00
250.00
300.00
350.00
400.00
416.48
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
416.48
450.00
500.00
550.00
1.0000
1.0000
1.0000
1.0000
Density
mol/dm3
Volume
dm3/mol
Int.
energy
kJ/mol
0.063601
0.063715
0.064868
0.066048
0.067264
0.068525
0.069840
0.071218
0.072673
0.074217
0.075867
0.077643
0.079569
0.081677
0.084008
0.086616
0.089578
0.093001
0.097051
0.10200
0.10832
0.11706
0.13145
0.21277
0.47366
0.64687
2.3835
4.1282
5.8823
7.6487
9.4311
11.234
13.060
14.915
16.802
18.725
20.687
22.693
24.746
26.852
29.015
31.243
33.546
35.938
38.445
41.117
44.096
49.249
0.47366
0.64687
2.3835
4.1282
5.8823
7.6488
9.4314
11.234
13.062
14.918
16.807
18.733
20.701
22.714
24.779
26.900
29.085
31.343
33.685
36.130
38.707
41.476
44.604
50.247
0.0080825
0.0090488
0.018316
0.026935
0.035003
0.042602
0.049806
0.056674
0.063259
0.069601
0.075739
0.081702
0.087517
0.093209
0.098798
0.10431
0.10975
0.11516
0.12056
0.12599
0.13150
0.13720
0.14341
0.15437
0.082500
0.082598
0.083407
0.084076
0.084758
0.085541
0.086468
0.087553
0.088794
0.090180
0.091697
0.093329
0.095063
0.096886
0.098794
0.10078
0.10286
0.10504
0.10736
0.10986
0.11265
0.11600
0.12077
0.11544
0.11550
0.11604
0.11660
0.11731
0.11825
0.11946
0.12094
0.12270
0.12474
0.12704
0.12962
0.13249
0.13568
0.13924
0.14328
0.14794
0.15350
0.16042
0.16967
0.18350
0.20893
0.28551
1765.7
1757.0
1672.3
1591.8
1514.4
1439.4
1366.3
1294.8
1224.5
1155.2
1086.7
1018.8
951.24
883.84
816.36
748.57
680.21
610.99
540.51
468.19
392.99
312.66
221.66
0
637,900.
520,660.
83,324.
18,065.
4,973.1
1,656.0
642.89
282.74
137.74
72.996
41.482
24.979
15.782
10.377
7.0503
4.9192
3.5050
2.5368
1.8547
1.3611
0.99393
0.71168
0.48154
0.21277
36.689
36.764
37.528
38.314
39.121
39.947
40.790
41.649
42.522
43.406
44.302
45.207
46.119
47.033
47.946
48.849
49.733
50.582
51.376
52.083
52.648
52.968
52.771
49.249
38.173
38.260
39.149
40.059
40.989
41.936
42.897
43.869
44.849
45.834
46.821
47.806
48.784
49.751
50.698
51.615
52.490
53.305
54.033
54.636
55.050
55.154
54.631
50.247
0.21928
0.21801
0.20686
0.19803
0.19103
0.18546
0.18104
0.17754
0.17479
0.17266
0.17102
0.16980
0.16892
0.16831
0.16791
0.16768
0.16754
0.16745
0.16734
0.16711
0.16664
0.16569
0.16367
0.15437
0.050120
0.050280
0.051928
0.053740
0.055800
0.058169
0.060883
0.063945
0.067329
0.070988
0.074863
0.078895
0.083030
0.087227
0.091459
0.095718
0.10001
0.10438
0.10887
0.11357
0.11865
0.12436
0.13126
0.058440
0.058600
0.060265
0.062119
0.064267
0.066795
0.069763
0.073198
0.077094
0.081429
0.086172
0.091302
0.096822
0.10277
0.10927
0.11649
0.12481
0.13483
0.14772
0.16583
0.19480
0.25197
0.42947
172.60
173.29
179.95
186.29
192.29
197.94
203.19
207.99
212.26
215.93
218.90
221.08
222.35
222.60
221.70
219.53
215.94
210.76
203.80
194.82
183.50
169.39
151.36
0
0.065254
0.069389
0.074210
0.077500
2.9626
8.8328
14.913
18.575
2.9691
8.8397
14.921
18.583
0.021248
0.047436
0.069594
0.081247
0.083638
0.086143
0.090180
0.093199
0.11621
0.11902
0.12473
0.12941
45.137
46.843
50.998
55.474
60.316
65.522
47.730
49.643
54.255
59.166
64.436
70.066
0.16988
0.17552
0.18783
0.19939
0.21049
0.22122
0.078579
0.079533
0.085418
0.092823
0.10033
0.10753
0.090892
0.090386
0.094849
0.10175
0.10903
0.11612
220.94
229.44
246.85
262.23
276.40
289.72
2.9486
8.8130
14.885
21.312
28.263
30.714
3.0138
8.8824
14.959
21.392
28.351
30.806
0.021178
0.047357
0.069499
0.089316
0.10788
0.11389
0.083649
0.086152
0.090182
0.095644
0.10213
0.10452
0.11619
0.11896
0.12460
0.13326
0.14605
0.15210
1649.7
1396.0
1162.0
936.35
707.25
627.32
50.387
54.081
59.388
64.832
53.120
57.281
63.156
69.107
0.16747
0.17709
0.18947
0.20081
0.10335
0.10087
0.10402
0.10950
0.13228
0.11921
0.11743
0.12100
212.13
233.76
256.99
275.55
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
JouleThomson
K/MPa
Saturated Properties
15.723
15.695
15.416
15.141
14.867
14.593
14.319
14.041
13.760
13.474
13.181
12.880
12.568
12.243
11.904
11.545
11.163
10.753
10.304
9.8043
9.2319
8.5423
7.6072
4.7000
1.5677E-06
1.9207E-06
1.2001E-05
5.5355E-05
0.00020108
0.00060385
0.0015555
0.0035368
0.0072603
0.013699
0.024107
0.040034
0.063362
0.096367
0.14184
0.20329
0.28530
0.39420
0.53918
0.73472
1.0061
1.4051
2.0767
4.7000
−0.43351
−0.43308
−0.42849
−0.42274
−0.41520
−0.40545
−0.39322
−0.37827
−0.36033
−0.33907
−0.31399
−0.28437
−0.24915
−0.20678
−0.15495
−0.090162
−0.0069455
0.10371
0.25760
0.48516
0.85357
1.5474
3.3240
14.310
3845.4
3637.4
2139.7
1312.0
834.10
547.82
370.79
258.27
184.97
136.14
102.93
79.878
63.590
51.884
43.343
37.032
32.325
28.797
26.154
24.184
22.717
21.551
20.240
14.310
Single-Phase Properties
15.325
14.411
13.475
12.903
0.038565
0.035712
0.030709
0.027083
0.024272
0.022008
15.333
14.423
13.491
12.483
11.308
10.852
0.36582
0.31254
0.26538
0.23391
25.930
28.002
32.563
36.923
41.200
45.437
0.065220
0.069336
0.074123
0.080107
0.088431
0.092149
2.7336
3.1996
3.7681
4.2751
1645.6
1391.1
1155.7
1024.0
−0.42678
−0.39768
−0.33922
−0.28685
81.384
58.339
30.192
18.173
12.201
8.8355
−0.42708
−0.39848
−0.34115
−0.24033
−0.042437
0.074613
29.536
20.211
12.984
9.1542
THERMODYnAMIC PROPERTIES
2-193
TABLE 2-109 Thermodynamic Properties of Acetone (Continued )
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int.
energy
kJ/mol
15.367
14.471
13.560
12.588
11.490
10.123
7.8139
1.7344
0.065073
0.069106
0.073747
0.079439
0.087035
0.098782
0.12798
0.57657
2.8871
8.7271
14.762
21.128
27.958
35.450
44.435
60.563
3.2125
9.0726
15.130
21.525
28.393
35.944
45.075
63.446
15.410
14.528
13.641
12.709
11.683
10.491
8.9733
6.6600
0.064894
0.068831
0.073307
0.078687
0.085592
0.095320
0.11144
0.15015
2.8125
8.6237
14.616
20.916
27.629
34.864
42.815
52.079
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
JouleThomson
K/MPa
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
0.020868
0.047011
0.069085
0.088784
0.10711
0.12488
0.14406
0.17943
0.083704
0.086197
0.090197
0.095584
0.10186
0.10898
0.11961
0.12191
0.11609
0.11871
0.12408
0.13214
0.14320
0.16059
0.23343
0.17820
1667.9
1417.7
1189.0
972.15
759.27
538.79
262.33
205.69
−0.42837
−0.40187
−0.34909
−0.25988
−0.10136
0.26123
2.3418
10.650
3.4614
9.3120
15.349
21.703
28.485
35.818
43.930
53.581
0.020488
0.046589
0.068589
0.088163
0.10626
0.12352
0.14060
0.15896
0.083781
0.086264
0.090234
0.095554
0.10166
0.10827
0.11552
0.12442
0.11598
0.11843
0.12351
0.13100
0.14066
0.15332
0.17314
0.22174
1689.9
1443.6
1220.9
1013.1
815.03
622.74
433.48
255.34
−0.42983
−0.40569
−0.35775
−0.27983
−0.15336
0.080235
0.63674
2.7218
Single-Phase Properties (Cont.)
200.00
250.00
300.00
350.00
400.00
450.00
500.00
550.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
550.00
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
250.00
300.00
350.00
400.00
450.00
500.00
550.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
15.320
14.657
14.023
13.409
12.813
12.234
11.674
0.065276
0.068228
0.071312
0.074574
0.078044
0.081739
0.085664
7.2620
12.852
18.631
24.654
30.941
37.489
44.286
13.790
19.675
25.763
32.112
38.745
45.663
52.852
0.040421
0.061873
0.080632
0.097579
0.11320
0.12777
0.14147
0.088285
0.092127
0.097243
0.10299
0.10892
0.11478
0.12045
0.11631
0.11946
0.12424
0.12980
0.13553
0.14112
0.14639
1791.8
1616.6
1466.4
1337.4
1226.9
1133.0
1053.8
−0.43634
−0.42000
−0.39555
−0.36734
−0.33807
−0.30922
−0.28171
450.00
500.00
550.00
500.00
500.00
500.00
15.616
15.306
15.012
0.064037
0.065335
0.066615
27.237
33.413
39.856
59.256
66.081
73.163
0.097266
0.11164
0.12514
0.11562
0.12123
0.12669
0.13393
0.13909
0.14416
2201.1
2129.8
2067.5
−0.39010
−0.37710
−0.36510
The values in this table were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23:
Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg,
Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial
Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the
single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of
the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties in the equation of state are 0.1% in the saturated liquid density between 280 and 310 K, 0.5% in density in the liquid phase below 380 K, and 1% in
density elsewhere, including all states at pressures above 100 MPa. The uncertainties in vapor pressure are 0.5% above 270 K (0.25% between 290 and 390 K), and the
uncertainties in heat capacities and speeds of sound are 1%. These uncertainties (in caloric properties and sound speeds) may be higher at pressures above the saturation pressure and at temperatures above 320 K in the liquid phase and at supercritical conditions.
2-194
TABLE 2-110
Thermodynamic Properties of Air
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
59.75
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
0.005265
0.005546
0.006797
0.008270
0.009994
0.012000
0.014320
0.016988
0.020042
0.023520
0.027461
0.031908
0.036905
0.042498
0.048733
0.055659
0.063326
0.071786
0.081091
0.091294
0.10245
0.11462
0.12785
0.14221
0.15775
0.17453
0.19262
0.21207
0.23295
0.25531
0.27922
0.30475
0.33196
0.36091
0.39166
0.42429
0.45886
0.49543
0.53408
0.57486
0.61786
0.66313
0.71074
0.76077
0.81329
0.86836
0.92606
0.98645
1.0496
1.1156
1.1845
1.2564
1.3314
1.4095
1.4908
1.5753
33.067
33.031
32.888
32.745
32.601
32.457
32.312
32.166
32.020
31.873
31.725
31.576
31.427
31.277
31.126
30.974
30.821
30.668
30.513
30.357
30.200
30.042
29.883
29.722
29.560
29.397
29.232
29.066
28.898
28.729
28.558
28.385
28.210
28.033
27.854
27.673
27.489
27.304
27.115
26.924
26.730
26.533
26.333
26.130
25.923
25.713
25.499
25.281
25.058
24.831
24.598
24.361
24.118
23.868
23.613
23.350
0.030242
0.030275
0.030406
0.030539
0.030674
0.030810
0.030949
0.031089
0.031231
0.031375
0.031521
0.031669
0.031820
0.031972
0.032127
0.032285
0.032445
0.032608
0.032773
0.032941
0.033112
0.033287
0.033464
0.033645
0.033829
0.034017
0.034209
0.034404
0.034604
0.034808
0.035017
0.035230
0.035449
0.035672
0.035901
0.036137
0.036378
0.036625
0.036880
0.037142
0.037411
0.037688
0.037975
0.038270
0.038575
0.038891
0.039217
0.039556
0.039908
0.040273
0.040653
0.041050
0.041464
0.041896
0.042350
0.042826
−1.0619
−1.0481
−0.99308
−0.93803
−0.88298
−0.82792
−0.77286
−0.71777
−0.66267
−0.60755
−0.55239
−0.49720
−0.44196
−0.38669
−0.33135
−0.27597
−0.22051
−0.16499
−0.10939
−0.05371
0.002063
0.057934
0.11391
0.17000
0.22621
0.28255
0.33903
0.39566
0.45245
0.50940
0.56653
0.62386
0.68138
0.73912
0.79709
0.85529
0.91375
0.97248
1.0315
1.0908
1.1505
1.2104
1.2708
1.3315
1.3926
1.4542
1.5162
1.5787
1.6417
1.7053
1.7695
1.8343
1.8997
1.9659
2.0329
2.1007
−1.0617
−1.0480
−0.99287
−0.93778
−0.88267
−0.82755
−0.77241
−0.71725
−0.66205
−0.60681
−0.55152
−0.49619
−0.44079
−0.38533
−0.32979
−0.27417
−0.21846
−0.16265
−0.10673
−0.05070
0.005456
0.061749
0.11819
0.17478
0.23155
0.28849
0.34562
0.40296
0.46051
0.51829
0.57631
0.63459
0.69315
0.75199
0.81115
0.87062
0.93044
0.99063
1.0512
1.1122
1.1736
1.2354
1.2978
1.3606
1.4240
1.4880
1.5525
1.6177
1.6836
1.7502
1.8176
1.8858
1.9549
2.0250
2.0960
2.1682
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound
speed
m/s
JouleThomson
K/MPa
Therm.
cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.034011
0.033955
0.033731
0.033512
0.033298
0.033089
0.032884
0.032683
0.032486
0.032294
0.032105
0.031920
0.031739
0.031562
0.031388
0.031217
0.031050
0.030886
0.030725
0.030568
0.030413
0.030262
0.030113
0.029968
0.029826
0.029686
0.029550
0.029417
0.029286
0.029158
0.029033
0.028911
0.028792
0.028676
0.028563
0.028453
0.028346
0.028241
0.028140
0.028042
0.027948
0.027856
0.027768
0.027684
0.027603
0.027525
0.027452
0.027383
0.027317
0.027256
0.027200
0.027149
0.027103
0.027062
0.027028
0.027000
0.055064
0.055062
0.055060
0.055062
0.055069
0.055081
0.055098
0.055120
0.055148
0.055181
0.055220
0.055266
0.055317
0.055376
0.055441
0.055514
0.055594
0.055682
0.055779
0.055884
0.055998
0.056122
0.056256
0.056400
0.056556
0.056723
0.056902
0.057094
0.057300
0.057521
0.057757
0.058009
0.058278
0.058566
0.058874
0.059202
0.059553
0.059928
0.060329
0.060757
0.061216
0.061707
0.062232
0.062796
0.063401
0.064052
0.064753
0.065508
0.066323
0.067206
0.068163
0.069205
0.070341
0.071585
0.072951
0.074459
1030.3
1028.3
1020.3
1012.2
1004.0
995.77
987.48
979.13
970.72
962.24
953.70
945.10
936.43
927.70
918.90
910.04
901.11
892.11
883.05
873.91
864.71
855.44
846.09
836.67
827.18
817.61
807.96
798.24
788.44
778.56
768.59
758.55
748.42
738.20
727.90
717.51
707.03
696.46
685.80
675.05
664.20
653.26
642.22
631.08
619.84
608.50
597.06
585.51
573.85
562.09
550.21
538.21
526.10
513.86
501.48
488.97
−0.40785
−0.40743
−0.40565
−0.40375
−0.40173
−0.39958
−0.39729
−0.39485
−0.39227
−0.38952
−0.38660
−0.38352
−0.38024
−0.37677
−0.37310
−0.36922
−0.36511
−0.36076
−0.35616
−0.35130
−0.34616
−0.34074
−0.33500
−0.32894
−0.32254
−0.31577
−0.30862
−0.30107
−0.29308
−0.28464
−0.27572
−0.26628
−0.25629
−0.24573
−0.23455
−0.22270
−0.21016
−0.19686
−0.18275
−0.16779
−0.15189
−0.13501
−0.11705
−0.09794
−0.07758
−0.05588
−0.03271
−0.00795
0.018543
0.046927
0.077386
0.11012
0.14538
0.18342
0.22456
0.26917
171.43
171.02
169.40
167.78
166.16
164.53
162.91
161.28
159.65
158.01
156.37
154.73
153.09
151.44
149.79
148.14
146.49
144.83
143.16
141.50
139.83
138.15
136.48
134.80
133.11
131.42
129.78
128.11
126.44
124.76
123.07
121.38
119.69
118.00
116.30
114.61
112.91
111.21
109.51
107.81
106.11
104.41
102.71
101.01
99.316
97.623
95.933
94.247
92.565
90.888
89.216
87.551
85.893
84.242
82.599
80.965
376.64
371.92
353.83
336.91
321.09
306.27
292.39
279.38
267.17
255.71
244.94
234.81
225.28
216.31
207.85
199.88
192.35
185.23
178.51
172.14
166.11
160.39
154.96
149.80
144.90
140.23
135.78
131.54
127.50
123.63
119.93
116.38
112.98
109.72
106.59
103.58
100.68
97.879
95.179
92.571
90.048
87.605
85.236
82.937
80.703
78.529
76.412
74.347
72.331
70.361
68.432
66.542
64.688
62.867
61.075
59.311
Saturated Properties
−0.01536
−0.01513
−0.01422
−0.01333
−0.01245
−0.01158
−0.01073
−0.00989
−0.00906
−0.00824
−0.00744
−0.00664
−0.00586
−0.00508
−0.00432
−0.00357
−0.00282
−0.00209
−0.00136
−0.00064
6.86E-05
0.000772
0.001467
0.002156
0.002838
0.003513
0.004181
0.004844
0.005501
0.006153
0.006799
0.007440
0.008077
0.008708
0.009336
0.009960
0.010579
0.011195
0.011808
0.012418
0.013025
0.013630
0.014232
0.014833
0.015431
0.016029
0.016625
0.017221
0.017816
0.018411
0.019006
0.019602
0.020200
0.020799
0.021400
0.022004
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
132.63
1.6633
1.7546
1.8495
1.9479
2.0499
2.1557
2.2653
2.3787
2.4960
2.6173
2.7427
2.8721
3.0055
3.1431
3.2845
3.4295
3.5770
3.7228
3.7858
59.75
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
0.002432
0.002584
0.003274
0.004111
0.005120
0.006325
0.007756
0.009442
0.011416
0.013713
0.016372
0.019431
0.022933
0.026921
0.031443
0.036547
0.042282
0.048702
0.055859
0.063810
0.072611
0.082321
0.093001
0.10471
0.11751
0.13147
0.14665
0.16312
0.18094
0.20018
0.22091
0.24320
0.26712
0.29273
0.32011
0.34934
0.38047
0.41359
0.44878
0.48609
0.52562
0.56742
0.61159
23.080
22.801
22.514
22.217
21.908
21.588
21.253
20.903
20.534
20.144
19.727
19.278
18.788
18.242
17.616
16.863
15.869
14.198
10.448
0.004907
0.005192
0.006475
0.008005
0.009817
0.011948
0.014438
0.017326
0.020659
0.024481
0.028841
0.033789
0.039379
0.045664
0.052702
0.060550
0.069268
0.078918
0.089564
0.10127
0.11410
0.12813
0.14343
0.16006
0.17811
0.19765
0.21875
0.24150
0.26598
0.29228
0.32048
0.35068
0.38298
0.41747
0.45426
0.49345
0.53517
0.57953
0.62667
0.67671
0.72980
0.78609
0.84575
0.043328
0.043857
0.044417
0.045011
0.045645
0.046323
0.047052
0.047841
0.048700
0.049643
0.050691
0.051871
0.053225
0.054818
0.056765
0.059300
0.063015
0.070432
0.095715
203.80
192.59
154.45
124.93
101.86
83.693
69.263
57.715
48.406
40.849
34.673
29.595
25.394
21.899
18.975
16.515
14.437
12.671
11.165
9.8746
8.7639
7.8043
6.9721
6.2475
5.6145
5.0595
4.5715
4.1408
3.7597
3.4214
3.1203
2.8516
2.6111
2.3954
2.2014
2.0265
1.8686
1.7255
1.5957
1.4777
1.3702
1.2721
1.1824
2.1695
2.2392
2.3100
2.3821
2.4554
2.5303
2.6069
2.6854
2.7662
2.8496
2.9363
3.0269
3.1227
3.2253
3.3379
3.4661
3.6243
3.8680
4.4004
2.2415
2.3161
2.3922
2.4697
2.5490
2.6302
2.7135
2.7992
2.8878
2.9796
3.0753
3.1759
3.2827
3.3976
3.5243
3.6695
3.8497
4.1302
4.7627
0.022611
0.023223
0.023840
0.024462
0.025092
0.025731
0.026380
0.027041
0.027717
0.028412
0.029131
0.029880
0.030668
0.031512
0.032436
0.033492
0.034804
0.036863
0.041603
0.026979
0.026965
0.026961
0.026966
0.026982
0.027010
0.027053
0.027113
0.027194
0.027300
0.027438
0.027618
0.027855
0.028171
0.028607
0.029242
0.030266
0.032343
0.076131
0.077996
0.080090
0.082459
0.085163
0.088280
0.091919
0.096227
0.10142
0.10781
0.11589
0.12645
0.14089
0.16186
0.19519
0.25624
0.40151
1.0148
476.31
463.48
450.49
437.29
423.88
410.23
396.30
382.04
367.40
352.31
336.67
320.36
303.21
285.00
265.37
243.75
219.07
189.12
0
4.8774
4.8825
4.9025
4.9225
4.9424
4.9621
4.9817
5.0012
5.0205
5.0397
5.0587
5.0774
5.0960
5.1144
5.1326
5.1505
5.1682
5.1856
5.2028
5.2196
5.2362
5.2525
5.2684
5.2841
5.2994
5.3143
5.3289
5.3431
5.3569
5.3703
5.3832
5.3958
5.4079
5.4195
5.4307
5.4413
5.4514
5.4610
5.4701
5.4785
5.4864
5.4936
5.5002
5.3730
5.3800
5.4081
5.4361
5.4639
5.4915
5.5189
5.5461
5.5731
5.5998
5.6263
5.6525
5.6784
5.7040
5.7292
5.7541
5.7786
5.8027
5.8264
5.8497
5.8726
5.8949
5.9169
5.9383
5.9591
5.9795
5.9993
6.0185
6.0372
6.0552
6.0726
6.0893
6.1054
6.1207
6.1354
6.1492
6.1624
6.1747
6.1862
6.1968
6.2066
6.2154
6.2233
0.096708
0.096323
0.094825
0.093392
0.092020
0.090705
0.089445
0.088235
0.087074
0.085959
0.084887
0.083855
0.082862
0.081906
0.080983
0.080094
0.079235
0.078406
0.077604
0.076828
0.076076
0.075348
0.074643
0.073957
0.073292
0.072645
0.072016
0.071403
0.070806
0.070224
0.069655
0.069099
0.068556
0.068024
0.067503
0.066991
0.066489
0.065995
0.065510
0.065031
0.064560
0.064094
0.063633
0.020805
0.020809
0.020825
0.020843
0.020864
0.020886
0.020911
0.020938
0.020968
0.021000
0.021035
0.021072
0.021113
0.021156
0.021201
0.021250
0.021302
0.021356
0.021414
0.021474
0.021538
0.021605
0.021674
0.021747
0.021822
0.021901
0.021983
0.022068
0.022155
0.022246
0.022340
0.022436
0.022536
0.022638
0.022744
0.022852
0.022964
0.023078
0.023196
0.023317
0.023441
0.023568
0.023698
0.029217
0.029225
0.029261
0.029302
0.029348
0.029399
0.029455
0.029518
0.029587
0.029663
0.029746
0.029836
0.029934
0.030040
0.030155
0.030278
0.030410
0.030552
0.030703
0.030865
0.031037
0.031220
0.031415
0.031621
0.031840
0.032072
0.032317
0.032577
0.032851
0.033141
0.033447
0.033770
0.034111
0.034472
0.034853
0.035256
0.035681
0.036132
0.036610
0.037116
0.037654
0.038225
0.038834
154.83
155.14
156.38
157.60
158.81
159.99
161.16
162.30
163.42
164.53
165.60
166.66
167.69
168.70
169.69
170.65
171.58
172.49
173.37
174.23
175.05
175.85
176.62
177.36
178.07
178.75
179.40
180.02
180.61
181.17
181.69
182.19
182.65
183.08
183.47
183.84
184.17
184.46
184.72
184.95
185.14
185.30
185.42
0.31767
0.37057
0.42848
0.49214
0.56243
0.64047
0.72765
0.82574
0.93703
1.0646
1.2125
1.3865
1.5951
1.8510
2.1752
2.6058
3.2246
4.2808
6.3978
58.283
57.634
55.151
52.832
50.666
48.640
46.742
44.963
43.293
41.724
40.248
38.858
37.548
36.313
35.146
34.043
32.999
32.010
31.072
30.183
29.337
28.534
27.769
27.041
26.346
25.684
25.051
24.447
23.869
23.316
22.786
22.278
21.791
21.324
20.876
20.445
20.031
19.632
19.249
18.879
18.523
18.180
17.848
79.340
77.724
76.119
74.523
72.938
71.363
69.798
68.243
66.700
65.170
63.658
62.176
60.751
59.445
58.409
58.054
59.591
67.802
57.571
55.852
54.152
52.467
50.794
49.130
47.469
45.809
44.141
42.460
40.755
39.013
37.215
35.332
33.316
31.072
28.384
24.467
5.2938
5.3199
5.4244
5.5291
5.6340
5.7391
5.8444
5.9500
6.0559
6.1621
6.2688
6.3759
6.4835
6.5917
6.7005
6.8099
6.9202
7.0312
7.1431
7.2560
7.3700
7.4851
7.6014
7.7192
7.8384
7.9591
8.0817
8.2060
8.3324
8.4610
8.5919
8.7254
8.8616
9.0008
9.1433
9.2893
9.4390
9.5929
9.7513
9.9145
10.083
10.257
10.438
4.2197
4.2382
4.3119
4.3855
4.4590
4.5324
4.6057
4.6788
4.7519
4.8248
4.8976
4.9703
5.0429
5.1154
5.1878
5.2602
5.3325
5.4048
5.4771
5.5494
5.6217
5.6940
5.7664
5.8389
5.9116
5.9844
6.0574
6.1307
6.2043
6.2781
6.3524
6.4272
6.5024
6.5782
6.6547
6.7318
6.8098
6.8887
6.9686
7.0495
7.1317
7.2153
7.3003
2-195
(Continued)
2-196
TABLE 2-110 Thermodynamic Properties of Air (Continued )
Temperature
K
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
132.63
Pressure
MPa
Density
mol/dm3
0.65820
0.70732
0.75903
0.81341
0.87055
0.93052
0.9934
1.0593
1.1282
1.2004
1.2757
1.3545
1.4366
1.5223
1.6115
1.7045
1.8013
1.9020
2.0067
2.1156
2.2287
2.3462
2.4682
2.5949
2.7266
2.8633
3.0055
3.1536
3.3084
3.4712
3.6462
3.7858
0.90895
0.97587
1.0467
1.1217
1.2011
1.2852
1.3742
1.4684
1.5682
1.6740
1.7862
1.9053
2.0318
2.1664
2.3097
2.4625
2.6259
2.8009
2.9889
3.1913
3.4103
3.6481
3.9078
4.1934
4.5101
4.8653
5.2697
5.7405
6.3074
7.0343
8.1273
10.448
Volume
dm3/mol
1.1002
1.0247
0.95535
0.89147
0.83254
0.77810
0.72772
0.68102
0.63767
0.59737
0.55985
0.52486
0.49217
0.46160
0.43296
0.40608
0.38082
0.35702
0.33457
0.31335
0.29323
0.27412
0.25590
0.23847
0.22173
0.20554
0.18976
0.17420
0.15854
0.14216
0.12304
0.095715
Sound
speed
m/s
JouleThomson
K/MPa
Therm.
cond.
mW/(m⋅K)
Viscosity
mPa⋅s
0.039483
0.040176
0.040918
0.041714
0.042570
0.043492
0.044490
0.045573
0.046751
0.048038
0.049450
0.051005
0.052727
0.054644
0.056790
0.059209
0.061956
0.065102
0.068738
0.072988
0.078015
0.084052
0.091426
0.10063
0.11241
0.12801
0.14959
0.18134
0.23261
0.32992
0.59804
185.51
185.55
185.57
185.54
185.48
185.38
185.24
185.07
184.85
184.60
184.30
183.97
183.59
183.17
182.71
182.21
181.66
181.08
180.45
179.78
179.06
178.31
177.51
176.68
175.81
174.91
173.96
172.98
171.93
170.79
169.40
0
17.528
17.218
16.918
16.628
16.346
16.072
15.805
15.546
15.292
15.044
14.800
14.561
14.324
14.090
13.856
13.623
13.388
13.151
12.909
12.661
12.405
12.137
11.854
11.553
11.229
10.874
10.480
10.033
9.5119
8.8740
7.9854
6.3978
10.626
10.821
11.024
11.237
11.459
11.693
11.939
12.198
12.473
12.764
13.074
13.406
13.762
14.145
14.559
15.008
15.499
16.039
16.635
17.298
18.042
18.884
19.849
20.968
22.288
23.877
25.841
28.367
31.807
37.001
46.996
7.3870
7.4755
7.5659
7.6586
7.7537
7.8514
7.9521
8.0560
8.1634
8.2749
8.3907
8.5114
8.6375
8.7696
8.9086
9.0552
9.2104
9.3755
9.5518
9.7412
9.9456
10.168
10.411
10.681
10.982
11.324
11.720
12.191
12.775
13.553
14.798
0.021087
0.020796
0.021504
0.022817
0.024150
0.025246
0.026091
0.026734
0.027229
0.027619
0.030116
0.029149
0.029830
0.031137
0.032467
0.033562
0.034406
0.035049
0.035544
0.035934
198.24
347.36
446.40
523.89
589.60
648.15
701.76
751.59
798.38
842.62
17.423
2.2510
0.50305
−0.12430
−0.41124
−0.56194
−0.64963
−0.70457
−0.74078
−0.76547
9.4692
26.384
39.944
51.755
62.543
72.680
82.381
91.781
100.97
110.01
7.1068
18.537
27.090
34.176
40.394
46.051
51.325
56.325
61.127
65.783
0.013532
0.017351
0.027868
0.027368
0.061355
0.065680
658.25
582.97
−0.14308
−0.00232
104.97
93.879
88.326
73.903
6.2479
12.289
18.218
24.326
30.698
37.311
44.114
51.065
58.128
65.278
0.060461
0.093372
0.10851
0.11877
0.12677
0.13340
0.13908
0.14405
0.14847
0.15245
0.024739
0.020859
0.021526
0.022830
0.024159
0.025253
0.026096
0.026738
0.027233
0.027622
0.044597
0.029563
0.029954
0.031194
0.032498
0.033582
0.034419
0.035057
0.035550
0.035939
185.23
348.45
448.46
525.96
591.54
649.96
703.44
753.17
799.86
844.02
15.779
2.1789
0.47425
−0.13809
−0.41899
−0.56686
−0.65304
−0.70711
−0.74278
−0.76711
11.965
26.684
40.110
51.868
62.628
72.748
82.438
91.830
101.01
110.05
7.9625
18.672
27.179
34.242
40.446
46.094
51.361
56.357
61.155
65.808
1.2820
12.042
0.012483
0.079244
0.028034
0.021131
0.058181
0.031423
710.56
355.63
−0.21837
1.8817
111.13
28.389
96.436
19.420
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
5.5060
5.5112
5.5156
5.5193
5.5221
5.5240
5.5250
5.5251
5.5241
5.5221
5.5188
5.5143
5.5085
5.5012
5.4924
5.4819
5.4695
5.4550
5.4383
5.4190
5.3969
5.3715
5.3424
5.3089
5.2701
5.2248
5.1713
5.1069
5.0268
4.9209
4.7566
4.4004
6.2302
6.2360
6.2408
6.2444
6.2469
6.2481
6.2480
6.2465
6.2436
6.2391
6.2330
6.2252
6.2156
6.2039
6.1901
6.1740
6.1554
6.1341
6.1097
6.0819
6.0504
6.0147
5.9740
5.9277
5.8746
5.8133
5.7417
5.6563
5.5513
5.4143
5.2053
4.7627
0.063177
0.062726
0.062277
0.061832
0.061389
0.060947
0.060506
0.060065
0.059623
0.059180
0.058735
0.058286
0.057833
0.057375
0.056910
0.056437
0.055955
0.055461
0.054954
0.054432
0.053890
0.053326
0.052735
0.052112
0.051448
0.050732
0.049950
0.049076
0.048067
0.046830
0.045064
0.041603
0.023833
0.023970
0.024112
0.024258
0.024408
0.024563
0.024722
0.024887
0.025058
0.025234
0.025418
0.025608
0.025807
0.026015
0.026232
0.026461
0.026701
0.026956
0.027226
0.027514
0.027823
0.028155
0.028516
0.028910
0.029344
0.029827
0.030371
0.030994
0.031726
0.032619
0.033814
5.6800
9.8544
14.072
18.500
23.201
28.145
33.282
38.568
43.966
49.453
6.4941
12.348
18.231
24.323
30.686
37.293
44.094
51.042
58.104
65.253
0.080463
0.11269
0.12770
0.13794
0.14593
0.15255
0.15823
0.16320
0.16762
0.17160
1.2007
1.5924
1.2383
1.6321
5.5251
9.8022
14.046
18.485
23.190
28.138
33.278
38.565
43.964
49.451
1.0983
9.5710
Single-Phase Properties
100
300
500
700
900
1100
1300
1500
1700
1900
100
106.22
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
1
1
108.1
300
500
700
900
1100
1300
1500
1700
1900
1
1
1
1
1
1
1
1
1
1
100
300
5
5
0.12283
0.040103
0.024046
0.017175
0.013359
0.010931
0.009249
0.008016
0.007073
0.006329
26.593
25.232
1.3836
0.40205
0.23974
0.17119
0.13319
0.10902
0.092279
0.079999
0.070604
0.063185
27.222
2.0232
8.1414
24.936
41.586
58.223
74.855
91.486
108.12
124.75
141.38
158.00
0.037604
0.039632
0.72278
2.4873
4.1711
5.8415
7.5079
9.1727
10.837
12.500
14.163
15.827
0.036735
0.49426
500
700
900
1100
1300
1500
1700
1900
5
5
5
5
5
5
5
5
1.1814
0.84321
0.65711
0.53874
0.45667
0.39636
0.35015
0.31361
0.84642
1.1859
1.5218
1.8562
2.1898
2.5229
2.8559
3.1887
13.935
18.417
23.146
28.107
33.256
38.550
43.954
49.445
18.167
24.347
30.755
37.388
44.205
51.165
58.234
65.389
0.094907
0.10529
0.11334
0.11999
0.12568
0.13066
0.13509
0.13907
0.021621
0.022885
0.024197
0.025282
0.026119
0.026757
0.027249
0.027636
0.030478
0.031434
0.032632
0.033664
0.034473
0.035095
0.035577
0.035958
458.30
535.45
600.34
658.10
711.01
760.23
806.49
850.28
0.36370
−0.19118
−0.44905
−0.58606
−0.66646
−0.71716
−0.75073
−0.77366
40.969
52.433
63.045
73.076
82.707
92.057
101.21
110.22
27.606
34.545
40.682
46.287
51.523
56.497
61.278
65.917
100
300
500
700
900
1100
1300
1500
1700
1900
10
10
10
10
10
10
10
10
10
10
27.863
4.0370
2.3157
1.6542
1.2922
1.0618
0.90165
0.78374
0.69321
0.62149
0.035889
0.24771
0.43183
0.60452
0.77388
0.94184
1.1091
1.2759
1.4426
1.6090
0.99444
9.2885
13.802
18.336
23.092
28.070
33.231
38.532
43.943
49.438
1.3533
11.766
18.120
24.382
30.831
37.489
44.321
51.292
58.368
65.528
0.011382
0.072612
0.088894
0.099422
0.10752
0.11420
0.11990
0.12489
0.12932
0.13330
0.028284
0.021441
0.021733
0.022952
0.024243
0.025317
0.026146
0.026780
0.027268
0.027653
0.055716
0.033664
0.031078
0.031710
0.032786
0.033760
0.034537
0.035139
0.035608
0.035981
763.47
369.50
471.81
547.83
611.64
668.47
720.60
769.17
814.87
858.18
−0.27969
1.5212
0.25100
−0.24405
−0.47890
−0.60517
−0.67990
−0.72730
−0.75881
−0.78039
117.77
31.116
42.260
53.257
63.641
73.538
83.082
92.372
101.48
110.45
105.78
20.637
28.194
34.944
40.985
46.531
51.728
56.673
61.432
66.054
100
300
500
700
900
1100
1300
1500
1700
1900
100
100
100
100
100
100
100
100
100
100
33.161
21.138
15.089
11.803
9.7481
8.3307
7.2877
6.4847
5.8456
5.3239
0.030156
0.047309
0.066273
0.084722
0.10258
0.12004
0.13722
0.15421
0.17107
0.18783
0.24746
7.0356
12.371
17.367
22.408
27.580
32.880
38.287
43.779
49.340
3.2631
11.767
18.999
25.840
32.667
39.584
46.602
53.708
60.886
68.123
0.001378
0.049067
0.067619
0.079134
0.087711
0.09465
0.10051
0.10559
0.11009
0.11411
0.031980
0.023981
0.023117
0.023855
0.024903
0.025831
0.026565
0.027131
0.027569
0.027915
0.048218
0.038366
0.034686
0.034011
0.034331
0.034845
0.035323
0.035723
0.036049
0.036317
1192.4
818.47
772.41
790.14
821.78
857.40
894.00
930.40
966.13
1001.0
−0.47290
−0.49747
−0.55640
−0.62591
−0.67702
−0.71435
−0.74281
−0.76506
−0.78264
−0.79653
179.20
86.312
71.549
73.572
79.057
85.797
93.151
100.84
108.75
116.78
252.46
53.642
42.159
43.339
46.948
51.158
55.511
59.875
64.208
68.504
300
500
700
900
1100
1300
1500
1700
1900
500
500
500
500
500
500
500
500
500
34.106
29.826
26.714
24.283
22.305
20.651
19.243
18.027
16.963
0.029320
0.033528
0.037433
0.041180
0.044833
0.048423
0.051966
0.055473
0.058952
6.2145
11.583
16.768
22.008
27.358
32.814
38.354
43.961
49.623
20.875
28.348
35.484
42.598
49.775
57.025
64.337
71.698
79.098
0.033155
0.052311
0.064323
0.073261
0.080460
0.086515
0.091746
0.096353
0.10047
0.028875
0.026614
0.026496
0.026991
0.027539
0.028000
0.02836
0.02864
0.02886
0.039265
0.036111
0.035494
0.035702
0.036073
0.036415
0.036693
0.036911
0.037085
1678.8
1573.6
1514.8
1482.8
1468.3
1465.1
1469.3
1478.5
1491.1
−0.57656
−0.65015
−0.67879
−0.68796
−0.69130
−0.69354
−0.69594
−0.69875
−0.70188
208.23
178.50
161.67
151.95
146.88
144.95
145.84
148.48
152.39
181.12
120.62
97.470
86.531
81.387
79.411
79.312
80.393
82.251
300
500
700
900
1100
1300
1500
1700
1900
1000
1000
1000
1000
1000
1000
1000
1000
1000
40.130
36.567
33.895
31.736
29.916
28.338
26.946
25.701
24.577
0.024919
0.027347
0.029503
0.031510
0.033427
0.035288
0.037111
0.038909
0.040688
6.8286
12.271
17.554
22.890
28.327
33.857
39.461
45.123
50.830
31.747
39.618
47.057
54.399
61.754
69.145
76.573
84.032
91.519
0.024761
0.044944
0.057468
0.066695
0.074073
0.080246
0.085561
0.090229
0.094392
0.032271
0.029334
0.028754
0.028917
0.029215
0.029476
0.029675
0.029821
0.029928
0.041510
0.037843
0.036801
0.036702
0.036858
0.037051
0.037224
0.037369
0.037491
2208.5
2104.7
2033.9
1984.7
1951.3
1929.3
1915.7
1908.3
1905.8
−0.50493
−0.57316
−0.60504
−0.61882
−0.62560
−0.62968
−0.63251
−0.63465
−0.63632
274.96
247.30
230.60
219.72
212.46
207.70
204.81
203.41
203.25
337.76
219.41
174.51
149.43
133.76
123.58
116.94
112.74
110.27
This table was generated for a standard three-component dry air containing mole fractions 0.7812 nitrogen, 0.2096 oxygen, and 0.0092 argon. The values in this table were generated from the NIST REFPROP software
(Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology,
Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., Jacobsen, R. T, Penoncello, S. G., and Friend, D. G., “Thermodynamic
Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa,” J. Phys. Chem. Ref. Data 29(3):331–385, 2000. The source for viscosity and thermal conductivity is Lemmon,
E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004.
Properties at the freezing point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a
given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper
line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated speed of
sound values is 0.2% and that for calculated heat capacities is 1%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is 0.5%, increasing to 1.0% at 2000 K and 2000 MPa.
For viscosity, the uncertainty is 1% in the dilute gas. The uncertainty is around 2% between 270 and 300 K and increases to 5% outside of this region. There are very few measurements between 130 and 270 K for air to
validate this claim, and the uncertainties may be even higher in this supercritical region. For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple points. The
uncertainties range from 3% between 140 and 300 K to 5% at the triple point and at high temperatures. The uncertainties above 100 MPa are not known due to a lack of experimental data.
2-197
2-198
FIG. 2-3
Pressure-enthalpy diagram for dry air. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23,
NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of E. W.
Lemmon, R. T. Jacobsen,, S. G. Penoncello, and D. G. Friend.
THERMODYnAMIC PROPERTIES
TABLE 2-111
Air
Other tables include Stewart, R. B., S. G. Penoncello, et al., University of Idaho CATS report, 85-5, 1985 (0.1-700 bar, 85-750 K),
and Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., and Friend, D. G., Thermodynamic Properties of Air and Mixtures of
Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa, J. Phys. Chem. Ref. Data, 29(3): 331-385, 2000. Tables
including reactions with hydrocarbons include Gordon, S., NASA Techn. Paper 1907, 4 vols., 1982. See also Gupta, R. N., K-P.
Lee, et al., NASA RP 1232, 1990 (89 pp.) and RP 1260, 1991 (75 pp.). Analytic expressions for high temperatures were given by
Matsuzaki, R., Jap. J. Appl. Phys., 21, 7 (1982): 1009-1013 and Japanese National Aerospace Laboratory report NAL TR 671, 1981
(45 pp.). Functions from 1500 to 15,000 K were tabulated by Hilsenrath, J. and M. Klein, AEDC-TR-65-58 = AD 612 301, 1965
(333 pp.). Tables from 10000 to 10,000,000 K were authored by Gilmore, F. R., Lockheed rept. 3-27-67-1, vol 1., 1967 (340 pp.),
also published as Radiative Properties of Air, IFI/Plenum, New York, 1969 (648 pp.). Saturation and superheat tables and a
chart to 7000 psia, 660°R appear in Stewart, R. B., R. T. Jacobsen, et al., Thermodynamic Properties of Refrigerants, ASHRAE,
Atlanta, Ga, 1986 (521 pp.). For specific heat, thermal conductivity, and viscosity see Thermophysical Properties of Refrigerants,
ASHRAE, 1993.
Air, Moist
For other data in this handbook, please see Figure 2-2 and the psychrometric tables, figures and descriptions in Section 12.
An ASHRAE publication, Thermodynamic Properties of Dry Air and Water and S. I. Psychrometric Charts, 1983 (360 pp.),
extensively reviews moist air properties. Gandiduson, P., Chem. Eng., Oct. 29, 1984 gives on page 118 a nomograph from 50 to
120°F, while equations in SI units were given by Nelson, B., Chem. Eng. Progr. 76, 5 (May 1980): 83–85. Liley, P. E., 2000 Solved
Problems in M.E. Thermodynamics, McGraw-Hill, New York, 1989, gives four simple equations with which most calculations
can be made. Devres, Y.O., Appl. Energy 48 (1994): 1–18 gives equations with which three known properties can be used to
determine four others. Klappert, M. T. and G. F. Schilling, Rand RM-4244-PR = AD 604 856, 1984 (40 pp.) gives tables from 100
to 270 K, while programs from −60 to 2°F are given by Sando, F. A., ASHRAE Trans., 96, 2 (1990): 299–308.
Viscosity references include Kestin, J. and J. H. Whitelaw, Int. J. Ht. Mass Transf. 7, 11 (1964): 1245–1255; Studnokov, E. L.,
Inz.-Fiz. Zhur. 19, 2 (1970): 338–340; Hochramer, D. and F. Munczak, Setzb. Ost. Acad. Wiss II 175, 10 (1966): 540–550. For thermal conductivity see, for instance, Mason, E. A. and L. Monchick, Humidity and Moisture Control in Science and Industry,
Reinhold, New York, 1965 (257–272).
2-199
2-200
TABLE 2-112 Thermodynamic Properties of Ammonia
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int.
energy
kJ/mol
Enthalpy
kJ/mol
0.00000
0.32333
1.0480
1.7825
2.5265
3.2793
4.0403
4.8093
5.5862
6.3712
7.1651
7.9691
8.7850
9.6153
10.463
11.333
12.232
13.169
14.158
15.224
16.424
17.969
20.640
0.00014154
0.32353
1.0484
1.7833
2.5279
3.2818
4.0445
4.8160
5.5963
6.3861
7.1866
7.9993
8.8265
9.6714
10.538
11.432
12.361
13.335
14.373
15.503
16.790
18.478
21.499
23.661
23.770
24.006
24.233
24.450
24.655
24.846
25.021
25.179
25.317
25.435
25.528
25.595
25.632
25.634
25.595
25.505
25.350
25.107
24.734
24.144
23.047
20.640
25.279
25.424
25.737
26.038
26.325
26.596
26.847
27.077
27.281
27.459
27.606
27.720
27.796
27.830
27.816
27.746
27.606
27.381
27.042
26.539
25.768
24.386
21.499
Entropy
kJ/(mol⋅K)
Sound
speed
m/s
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
0.00000
0.0016351
0.0051707
0.0085874
0.011894
0.015098
0.018205
0.021222
0.024154
0.027010
0.029797
0.032525
0.035203
0.037843
0.040458
0.043065
0.045682
0.048339
0.051075
0.053961
0.057149
0.061223
0.068559
0.049972
0.049837
0.049521
0.049207
0.048906
0.048613
0.048327
0.048047
0.047774
0.047511
0.047266
0.047044
0.046856
0.046715
0.046636
0.046642
0.046767
0.047064
0.047619
0.048589
0.050319
0.054109
0.071565
0.071988
0.072971
0.073950
0.074883
0.075764
0.076608
0.077448
0.078328
0.079296
0.080412
0.081747
0.083390
0.085465
0.088145
0.091701
0.096576
0.10357
0.11435
0.13314
0.17550
0.38707
2124.2
2080.2
1992.7
1913.7
1839.2
1766.9
1695.6
1624.5
1553.1
1481.0
1407.8
1333.2
1256.7
1177.9
1096.5
1011.8
923.38
830.62
732.78
628.75
515.88
384.58
0
0.12931
0.12714
0.12273
0.11884
0.11536
0.11224
0.10942
0.10684
0.10447
0.10227
0.10021
0.098259
0.096395
0.094589
0.092817
0.091046
0.089242
0.087355
0.085316
0.083003
0.080169
0.075992
0.068559
0.026510
0.026650
0.027053
0.027583
0.028245
0.029043
0.029978
0.031050
0.032253
0.033581
0.035028
0.036584
0.038244
0.040004
0.041868
0.043844
0.045954
0.048233
0.050744
0.053589
0.056957
0.061281
0.035130
0.035345
0.035961
0.036783
0.037836
0.039142
0.040728
0.042623
0.044859
0.047476
0.050530
0.054099
0.058302
0.063320
0.069443
0.077150
0.087280
0.10141
0.12286
0.16000
0.24170
0.59477
354.12
357.91
365.94
373.38
380.19
386.30
391.66
396.20
399.86
402.59
404.30
404.95
404.45
402.70
399.61
395.05
388.86
380.83
370.69
357.96
341.67
318.22
0
Therm.
Joule-Thomson
cond.
K/MPa
mW/(m⋅K)
Viscosity
µPa⋅s
Saturated Properties
195.50
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
380.00
390.00
400.00
405.40
0.0060912
0.0086509
0.017739
0.033790
0.060407
0.10223
0.16494
0.25531
0.38107
0.55092
0.77436
1.0617
1.4240
1.8728
2.4205
3.0802
3.8660
4.7929
5.8778
7.1402
8.6045
10.305
11.339
43.035
42.754
42.111
41.442
40.748
40.032
39.293
38.533
37.748
36.939
36.101
35.230
34.320
33.363
32.350
31.264
30.087
28.788
27.321
25.606
23.465
20.232
13.212
195.50
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
380.00
390.00
400.00
405.40
0.0060912
0.0086509
0.017739
0.033790
0.060407
0.10223
0.16494
0.25531
0.38107
0.55092
0.77436
1.0617
1.4240
1.8728
2.4205
3.0802
3.8660
4.7929
5.8778
7.1402
8.6045
10.305
11.339
0.0037635
0.0052305
0.010249
0.018721
0.032214
0.052667
0.082417
0.12421
0.18126
0.25729
0.35664
0.48448
0.64702
0.85202
1.1094
1.4325
1.8399
2.3598
3.0375
3.9558
5.2979
7.6973
13.212
0.023237
0.023389
0.023747
0.024130
0.024541
0.024980
0.025450
0.025952
0.026491
0.027072
0.027700
0.028385
0.029138
0.029973
0.030912
0.031986
0.033237
0.034737
0.036602
0.039054
0.042616
0.049426
0.075690
265.71
191.19
97.573
53.415
31.043
18.987
12.133
8.0506
5.5168
3.8867
2.8040
2.0641
1.5455
1.1737
0.90139
0.69810
0.54350
0.42377
0.32922
0.25279
0.18875
0.12992
0.075690
−0.23362
−0.22917
−0.21883
−0.20813
−0.19712
−0.18561
−0.17327
−0.15963
−0.14414
−0.12612
−0.10470
−0.078790
−0.046923
−0.0070718
0.043673
0.10967
0.19774
0.31928
0.49497
0.76738
1.2455
2.3557
5.0513
171.13
152.55
120.01
96.215
78.430
64.852
54.280
45.905
39.175
33.701
29.207
25.489
22.391
19.794
17.599
15.728
14.112
12.690
11.400
10.172
8.9038
7.3513
5.0513
818.99
803.14
768.02
733.17
698.80
665.09
632.16
600.07
568.85
538.50
508.99
480.25
452.23
424.83
397.96
371.51
345.32
319.25
293.07
266.57
239.65
216.00
19.636
19.684
19.860
20.132
20.503
20.978
21.560
22.258
23.079
24.034
25.138
26.408
27.872
29.568
31.559
33.945
36.900
40.752
46.149
54.556
70.114
113.54
559.57
507.28
414.98
346.68
294.94
254.85
223.08
197.34
176.06
158.12
142.74
129.33
117.49
106.91
97.325
88.555
80.430
72.796
65.493
58.315
50.877
41.802
6.8396
6.9515
7.2115
7.4846
7.7679
8.0587
8.3552
8.6558
8.9595
9.2664
9.5771
9.8938
10.220
10.561
10.927
11.330
11.792
12.346
13.053
14.025
15.527
18.529
Single-Phase Properties
200.00
239.56
239.56
300.00
400.00
500.00
600.00
700.00
200.00
298.05
298.05
300.00
400.00
500.00
600.00
700.00
200.00
300.00
362.03
362.03
400.00
500.00
600.00
700.00
200.00
300.00
398.32
398.32
400.00
500.00
600.00
700.00
300.00
400.00
500.00
600.00
700.00
300.00
400.00
500.00
600.00
700.00
300.00
400.00
500.00
600.00
700.00
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
100.00
100.00
100.00
100.00
100.00
500.00
500.00
500.00
500.00
500.00
1000.0
1000.0
1000.0
1000.0
1000.0
42.756
40.064
0.051595
0.040502
0.030171
0.024091
0.020060
0.017188
42.774
35.403
0.45697
0.45215
0.31157
0.24426
0.20197
0.17248
42.852
35.450
28.505
2.4828
1.8706
1.3046
1.0412
0.87563
42.947
35.714
20.945
7.1390
6.5455
2.8656
2.1650
1.7835
38.995
33.105
27.067
21.518
17.303
45.670
42.416
39.515
36.909
34.550
49.944
47.551
45.362
43.378
41.556
0.023388
0.024960
19.382
24.690
33.144
41.509
49.849
58.179
0.023379
0.028246
2.1883
2.2117
3.2095
4.0940
4.9513
5.7977
0.023336
0.028209
0.035081
0.40277
0.53459
0.76650
0.96040
1.1420
0.023284
0.028000
0.047744
0.14008
0.15278
0.34897
0.46190
0.56069
0.025644
0.030207
0.036945
0.046473
0.057794
0.021896
0.023576
0.025307
0.027094
0.028943
0.020022
0.021030
0.022045
0.023053
0.024064
0.32270
3.2461
24.646
26.378
29.297
32.514
36.096
40.068
0.31651
7.8111
25.512
25.592
29.019
32.359
35.994
39.994
0.28942
7.8852
13.365
25.309
27.540
31.630
35.527
39.662
0.25644
7.7848
17.655
23.303
23.801
30.616
34.920
39.241
6.5830
13.432
20.212
26.825
33.074
4.7114
10.633
16.367
22.007
27.680
4.1818
9.8612
15.432
20.911
26.418
0.32504
3.2486
26.584
28.847
32.612
36.665
41.081
45.885
0.33989
7.8393
27.700
27.804
32.229
36.453
40.945
45.792
0.40611
8.0263
13.540
27.323
30.213
35.462
40.329
45.373
0.48928
8.0648
18.132
24.704
25.329
34.106
39.539
44.848
9.1474
16.453
23.907
31.472
38.854
15.660
22.421
29.021
35.554
42.152
24.204
30.891
37.477
43.964
50.481
0.0016320
0.014960
0.11237
0.12080
0.13162
0.14065
0.14869
0.15609
0.0016010
0.031996
0.098633
0.098979
0.11177
0.12119
0.12937
0.13684
0.0014649
0.032243
0.048887
0.086956
0.094581
0.10634
0.11521
0.12298
0.0012980
0.031903
0.060394
0.076892
0.078458
0.098525
0.10844
0.11663
0.027511
0.048523
0.065147
0.078942
0.090326
0.018023
0.037482
0.052215
0.064127
0.074295
0.011750
0.030984
0.045686
0.057514
0.067559
0.049842
0.048626
0.029005
0.028021
0.030417
0.033897
0.037731
0.041678
0.049890
0.047085
0.036271
0.035866
0.031641
0.034312
0.037928
0.041791
0.050097
0.047090
0.047152
0.048722
0.038466
0.036193
0.038798
0.042289
0.050342
0.047164
0.053149
0.060447
0.057611
0.038603
0.039862
0.042896
0.048894
0.046636
0.045999
0.046723
0.048331
0.052877
0.051527
0.050431
0.050614
0.051816
0.055176
0.054864
0.053323
0.052940
0.053649
0.071983
0.075726
0.039079
0.036849
0.038883
0.042280
0.046083
0.050015
0.071938
0.081465
0.053356
0.052493
0.041627
0.043338
0.046628
0.050341
0.071739
0.080899
0.10538
0.10501
0.061581
0.048779
0.049210
0.051836
0.071495
0.079960
0.30653
0.46915
0.30552
0.057806
0.052806
0.053796
0.072740
0.073557
0.075495
0.075193
0.072317
0.067831
0.066802
0.065418
0.065476
0.066615
0.065784
0.066677
0.065150
0.064819
0.065697
2080.3
1770.0
386.05
434.39
497.93
550.96
597.69
640.16
2081.5
1347.9
404.91
407.16
488.94
546.79
595.60
639.15
2086.8
1361.2
811.17
378.95
441.81
528.14
586.79
635.17
2093.5
1394.2
409.04
323.12
336.28
505.64
577.38
631.50
1774.7
1378.2
1081.8
918.11
861.52
2597.1
2353.2
2176.9
2044.6
1943.8
3230.2
2997.6
2842.8
2728.6
2639.0
−0.22921
−0.18613
65.377
27.493
10.681
5.5276
3.2702
2.0841
−0.22959
−0.084271
26.163
25.620
10.494
5.4884
3.2544
2.0746
−0.23126
−0.089577
0.34968
12.419
9.6373
5.2830
3.1693
2.0254
−0.23328
−0.10159
2.0704
7.6606
7.7633
4.9335
3.0278
1.9491
−0.19551
−0.11309
0.049919
0.23722
0.32753
−0.25055
−0.25064
−0.25260
−0.24722
−0.23682
−0.25989
−0.25431
−0.26084
−0.26235
−0.25820
803.24
666.56
20.955
25.100
37.215
53.119
68.607
78.312
804.23
485.81
26.145
26.308
38.087
53.750
69.123
78.751
808.60
487.57
313.94
41.693
45.730
57.294
71.791
80.941
814.02
496.50
218.73
101.04
95.455
63.922
76.053
84.235
622.86
431.98
305.65
234.79
196.04
989.00
804.05
674.00
582.63
511.57
1324.0
1138.9
996.49
887.73
797.25
507.47
256.42
8.0459
10.161
13.971
17.863
21.682
25.391
509.28
131.82
9.8313
9.9115
13.927
17.877
21.717
25.434
517.30
132.49
71.291
12.475
14.036
18.073
21.941
25.662
527.29
136.36
43.632
17.793
17.230
18.722
22.393
26.035
193.71
96.237
60.386
46.188
41.237
376.31
188.46
120.77
91.251
77.538
554.62
274.91
174.11
129.02
107.14
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport
Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth,
R., Harms-Watzenberg, F., and Baehr, H. D., “Eine neue Fundamentalgleichung fuer Ammoniak,” DKV-Tagungsbericht, 20:167–181, 1993. The source for viscosity is Fenghour, A., Wakeham, W. A., Vesovic, V., Watson, J. T.
R., Millat, J., and Vogel, E., “The Viscosity of Ammonia,” J. Phys. Chem. Ref. Data 24:1649–1667, 1995. The source for thermal conductivity is Tufeu, R., Ivanov, D. Y., Garrabos, Y., and Le Neindre, B., “Thermal Conductivity
of Ammonia in a Large Temperature and Pressure Range Including the Critical Region,” Ber. Bunsenges. Phys. Chem. 88:422–427, 1984.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given
isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line).
Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5%
for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%.
2-201
2-202
TABLE 2-113
Temperature
K
Thermodynamic Properties of Carbon Dioxide
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
180.63
176.15
169.67
163.28
156.98
150.75
144.58
138.47
132.40
126.35
120.31
114.25
108.17
102.03
95.810
89.546
83.558
80.593
256.70
242.01
222.19
204.23
187.88
172.96
159.30
146.74
135.14
124.40
114.40
105.02
96.174
87.731
79.548
71.409
62.936
53.107
11.014
11.301
11.745
12.221
12.736
13.297
13.917
14.610
15.396
16.306
17.381
18.687
20.325
22.468
25.424
29.821
37.215
53.689
10.951
11.135
11.409
11.689
11.976
12.272
12.579
12.902
13.245
13.614
14.017
14.469
14.987
15.601
16.361
17.357
18.792
21.306
Saturated Properties
216.59
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
304.13
0.51796
0.59913
0.73509
0.89291
1.0747
1.2825
1.5185
1.7850
2.0843
2.4188
2.7909
3.2033
3.6589
4.1607
4.7123
5.3177
5.9822
6.7131
7.3773
26.777
26.497
26.078
25.646
25.201
24.742
24.264
23.767
23.246
22.697
22.114
21.491
20.817
20.077
19.247
18.284
17.100
15.434
10.625
0.037345
0.037740
0.038347
0.038992
0.039680
0.040418
0.041213
0.042075
0.043018
0.044059
0.045219
0.046531
0.048037
0.049808
0.051957
0.054693
0.058480
0.064793
0.094118
3.5030
3.7943
4.2235
4.6554
5.0908
5.5303
5.9749
6.4256
6.8836
7.3505
7.8282
8.3190
8.8266
9.3560
9.9154
10.519
11.197
12.036
13.928
3.5223
3.8169
4.2517
4.6902
5.1334
5.5821
6.0375
6.5007
6.9733
7.4571
7.9544
8.4681
9.0024
9.5633
10.160
10.810
11.547
12.471
14.622
0.022943
0.024279
0.026209
0.028110
0.029986
0.031840
0.033678
0.035505
0.037326
0.039148
0.040979
0.042829
0.044711
0.046643
0.048657
0.050805
0.053196
0.056151
0.063094
0.042895
0.042682
0.042383
0.042103
0.041843
0.041605
0.041393
0.041212
0.041079
0.041029
0.041109
0.041351
0.041750
0.042270
0.042900
0.043734
0.045175
0.049288
0.085960
0.086338
0.087024
0.087886
0.088954
0.090263
0.091866
0.093831
0.096251
0.099258
0.10306
0.10798
0.11457
0.12385
0.13790
0.16176
0.21098
0.38279
975.85
951.21
915.16
879.09
842.88
806.38
769.44
731.78
693.01
652.58
610.07
565.46
519.14
471.54
422.75
371.95
315.91
245.67
0
−0.14430
−0.13180
−0.11104
−0.086994
−0.059053
−0.026454
0.011808
0.057087
0.11121
0.17663
0.25672
0.35639
0.48324
0.64959
0.87650
1.2037
1.7218
2.7258
5.8665
216.59
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
304.13
0.51796
0.59913
0.73509
0.89291
1.0747
1.2825
1.5185
1.7850
2.0843
2.4188
2.7909
3.2033
3.6589
4.1607
4.7123
5.3177
5.9822
6.7131
7.3773
0.31268
0.35941
0.43766
0.52878
0.63442
0.75654
0.89743
1.0599
1.2472
1.4637
1.7149
2.0080
2.3535
2.7663
3.2702
3.9074
4.7654
6.1028
10.625
3.1982
2.7824
2.2849
1.8912
1.5762
1.3218
1.1143
0.94353
0.80180
0.68320
0.58314
0.49800
0.42490
0.36150
0.30579
0.25593
0.20985
0.16386
0.094118
17.286
17.329
17.387
17.438
17.481
17.515
17.538
17.550
17.549
17.532
17.498
17.441
17.359
17.241
17.078
16.848
16.509
15.935
13.928
18.943
18.996
19.067
19.127
19.175
19.210
19.230
19.234
19.220
19.185
19.125
19.037
18.913
18.746
18.519
18.209
17.764
17.035
14.622
0.094138
0.093276
0.092055
0.090878
0.089736
0.088622
0.087526
0.086439
0.085352
0.084254
0.083133
0.081972
0.080750
0.079437
0.077987
0.076319
0.074270
0.071364
0.063094
0.027691
0.028120
0.028782
0.029488
0.030241
0.031042
0.031899
0.032827
0.033844
0.034955
0.036164
0.037482
0.038949
0.040628
0.042629
0.045155
0.048677
0.054908
0.039992
0.040943
0.042489
0.044244
0.046248
0.048555
0.051242
0.054421
0.058244
0.062912
0.068721
0.076168
0.086123
0.10020
0.12177
0.15906
0.23904
0.52463
222.78
223.15
223.49
223.57
223.40
222.96
222.24
221.22
219.87
218.19
216.15
213.75
210.96
207.72
203.94
199.45
193.84
185.33
0
26.174
25.084
23.617
22.288
21.077
19.969
18.950
18.005
17.117
16.277
15.476
14.704
13.947
13.185
12.387
11.509
10.459
9.0093
5.8665
Single-Phase Properties
250.00
450.00
650.00
850.00
1050.0
0.10000
0.10000
0.10000
0.10000
0.10000
0.048542
0.026758
0.018506
0.014148
0.011452
250.00
450.00
650.00
850.00
1050.0
1.0000
1.0000
1.0000
1.0000
1.0000
0.53250
0.27038
0.18527
0.14131
0.11430
250.00
287.43
5.0000
5.0000
287.43
450.00
650.00
850.00
1050.0
5.0000
5.0000
5.0000
5.0000
5.0000
250.00
450.00
650.00
850.00
1050.0
10.000
10.000
10.000
10.000
10.000
18.448
24.664
32.199
40.636
49.704
20.509
28.401
37.602
47.705
58.436
0.11415
0.13712
0.15397
0.16750
0.17883
0.026766
0.034775
0.040192
0.043944
0.046573
0.035428
0.043148
0.048529
0.052271
0.054895
247.79
324.41
385.01
437.11
483.65
17.399
4.0212
1.6551
0.78058
0.34646
12.950
29.346
45.466
60.295
73.843
12.565
21.901
29.873
36.707
42.692
1.8779
3.6985
5.3976
7.0767
8.7487
18.023
24.546
32.133
40.591
49.671
19.901
28.244
37.530
47.668
58.419
0.093263
0.11771
0.13473
0.14830
0.15965
0.029361
0.034954
0.040239
0.043965
0.046585
0.042504
0.043866
0.048779
0.052397
0.054970
235.08
322.89
385.36
438.06
484.84
17.606
3.9880
1.6311
0.76632
0.33777
13.584
29.620
45.651
60.435
73.956
12.691
21.954
29.907
36.732
42.712
0.041563
0.053196
6.2824
10.202
6.4902
10.468
0.034925
0.049681
0.041321
0.043268
0.090937
0.14775
762.21
398.39
142.22
92.760
153.15
75.598
0.28090
0.70647
1.0755
1.4237
1.7650
16.977
24.000
31.842
40.395
49.524
18.381
27.533
37.219
47.513
58.349
0.077209
0.10313
0.12091
0.13469
0.14613
0.043774
0.035769
0.040445
0.044055
0.046637
0.13705
0.047478
0.049898
0.052945
0.055297
201.86
317.50
387.59
442.64
490.31
11.974
3.8034
1.5263
0.70611
0.30129
27.323
31.164
46.589
61.117
74.494
16.808
22.429
30.157
36.899
42.836
24.459
2.9910
1.8632
1.3930
1.1205
0.040885
0.33433
0.53671
0.71790
0.89248
6.0862
23.276
31.482
40.155
49.347
6.4950
26.619
36.849
47.334
58.271
0.034120
0.095787
0.11461
0.12866
0.14021
0.041488
0.036785
0.040693
0.044164
0.046701
0.087624
0.052935
0.051293
0.053603
0.055685
804.05
314.60
391.91
449.04
497.48
−0.034849
3.4705
1.3965
0.63635
0.25964
147.52
33.917
48.005
62.093
75.242
162.47
23.679
30.687
37.224
43.066
24.060
18.798
3.5600
1.4155
0.92982
0.70241
0.56658
20.601
37.372
54.037
70.683
87.321
0.015208
1.0195
250.00
450.00
650.00
850.00
1050.0
100.00
100.00
100.00
100.00
100.00
28.075
19.246
13.677
10.636
8.7929
0.035619
0.051959
0.073117
0.094022
0.11373
4.3002
16.560
27.132
37.076
46.995
7.8621
21.756
34.444
46.478
58.368
0.026023
0.067062
0.090445
0.10660
0.11916
0.043569
0.040841
0.043108
0.045620
0.047676
0.073521
0.066107
0.061252
0.059534
0.059512
1227.6
753.30
646.36
646.61
668.90
−0.27302
−0.11128
−0.054084
−0.13292
−0.21482
206.28
106.65
86.093
87.259
94.022
287.05
83.996
58.868
54.445
55.058
450.00
650.00
850.00
1050.0
500.00
500.00
500.00
500.00
28.922
25.661
23.144
21.126
0.034576
0.038969
0.043208
0.047334
13.014
23.302
33.551
43.903
30.302
42.786
55.155
67.570
0.050604
0.073576
0.090166
0.10328
0.047702
0.048419
0.049676
0.050818
0.063434
0.061885
0.061912
0.062247
1576.4
1404.7
1320.1
1278.7
−0.38514
−0.40369
−0.41098
−0.41674
239.59
197.25
177.31
168.50
303.64
191.14
145.07
123.33
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span,
R., and Wagner, W., “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data 25(6):1509–1596, 1996.
The source for viscosity is Fenghour, A., Wakeham, W. A., and Vesovic, V., “The Viscosity of Carbon Dioxide,” J. Phys. Chem. Ref. Data 27:31–44, 1998. The source for thermal conductivity is Vesovic, V., Wakeham, W. A.,
Olchowy, G. A., Sengers, J. V., Watson, J. T. R., and Millat, J., “The Transport Properties of Carbon Dioxide,” J. Phys. Chem. Ref. Data 19:763–808, 1990.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a
given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
At pressures up to 30 MPa and temperatures up to 523 K, the estimated uncertainty ranges from 0.03% to 0.05% in density, 0.03% (in the vapor) to 1% in the speed of sound (0.5% in the liquid), and 0.15% (in the
vapor) to 1.5% (in the liquid) in heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation (to the limits of chemical stability). The
uncertainty in viscosity ranges from 0.3% in the dilute gas near room temperature to 5% at the highest pressures. The uncertainty in thermal conductivity is less than 5%.
2-203
2-204
TABLE 2-114 Thermodynamic Properties of Carbon Monoxide
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
30.330
30.064
29.773
29.478
29.180
28.878
28.573
28.262
27.947
27.626
27.300
26.967
26.627
26.280
25.924
25.559
25.184
24.798
24.399
23.987
23.560
23.114
22.649
22.161
21.646
21.099
20.513
19.878
19.179
18.390
17.464
16.288
10.850
0.032971
0.033262
0.033588
0.033924
0.034270
0.034628
0.034999
0.035383
0.035782
0.036197
0.036630
0.037082
0.037556
0.038052
0.038574
0.039125
0.039708
0.040326
0.040985
0.041689
0.042446
0.043263
0.044151
0.045124
0.046197
0.047395
0.048749
0.050307
0.052141
0.054377
0.057259
0.061393
0.092166
−0.81158
−0.70065
−0.58046
−0.46058
−0.34088
−0.22127
−0.10165
0.018099
0.13806
0.25835
0.37906
0.50030
0.62218
0.74482
0.86835
0.99289
1.1186
1.2457
1.3742
1.5045
1.6368
1.7713
1.9085
2.0487
2.1925
2.3405
2.4938
2.6536
2.8221
3.0024
3.2010
3.4328
4.2912
−0.81106
−0.69995
−0.57950
−0.45927
−0.33915
−0.21900
−0.098716
0.021834
0.14277
0.26421
0.38629
0.50915
0.63291
0.75773
0.88377
1.0112
1.1402
1.2710
1.4039
1.5390
1.6768
1.8175
1.9616
2.1097
2.2624
2.4205
2.5853
2.7583
2.9420
3.1403
3.3608
3.6210
4.6137
−0.010820
−0.0092140
−0.0075210
−0.0058785
−0.0042823
−0.0027285
−0.0012138
0.00026503
0.0017110
0.0031269
0.0045153
0.0058787
0.0072195
0.0085399
0.0098422
0.011129
0.012402
0.013663
0.014916
0.016162
0.017404
0.018646
0.019891
0.021142
0.022406
0.023688
0.024996
0.026343
0.027744
0.029230
0.030854
0.032745
0.040039
5.1252
5.1600
5.1971
5.2334
5.2688
5.3031
5.3363
5.3682
5.3988
5.4280
5.4556
5.4816
5.5058
5.5280
5.5482
5.5661
5.5816
5.5945
5.6044
5.6112
5.6145
5.6138
5.6088
5.6859
5.7343
5.7859
5.8361
5.8849
5.9320
5.9775
6.0210
6.0625
6.1019
6.1388
6.1733
6.2050
6.2338
6.2595
6.2819
6.3007
6.3157
6.3265
6.3327
6.3339
6.3295
6.3191
0.084499
0.082704
0.080887
0.079194
0.077613
0.076131
0.074739
0.073426
0.072185
0.071007
0.069885
0.068813
0.067785
0.066796
0.065840
0.064912
0.064007
0.063120
0.062248
0.061385
0.060526
0.059665
0.058797
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.035351
0.034805
0.034248
0.033724
0.033232
0.032768
0.032329
0.031915
0.031522
0.031150
0.030798
0.030463
0.030146
0.029846
0.029562
0.029294
0.029043
0.028809
0.028592
0.028395
0.028218
0.028066
0.027941
0.027850
0.027800
0.027803
0.027874
0.028038
0.028333
0.028826
0.029646
0.031097
0.060430
0.060226
0.060064
0.059961
0.059917
0.059930
0.060002
0.060132
0.060324
0.060578
0.060899
0.061291
0.061760
0.062314
0.062962
0.063716
0.064590
0.065604
0.066781
0.068153
0.069759
0.071656
0.073916
0.076648
0.080005
0.084225
0.089692
0.097070
0.10762
0.12411
0.15392
0.22603
998.20
980.50
961.22
941.89
922.49
903.01
883.44
863.76
843.95
824.00
803.89
783.60
763.12
742.41
721.45
700.22
678.68
656.78
634.50
611.77
588.54
564.73
540.25
515.01
488.86
461.63
433.11
403.00
370.88
336.15
297.82
254.03
0
−0.36906
−0.36553
−0.36074
−0.35489
−0.34794
−0.33981
−0.33041
−0.31966
−0.30742
−0.29356
−0.27794
−0.26034
−0.24056
−0.21834
−0.19335
−0.16523
−0.13353
−0.097704
−0.057078
−0.010824
0.042104
0.10304
0.17371
0.25641
0.35427
0.47167
0.61495
0.79382
1.0239
1.3325
1.7728
2.4703
6.1475
180.28
175.49
170.45
165.55
160.76
156.06
151.45
146.89
142.40
137.96
133.57
129.23
124.94
120.69
116.51
112.38
108.31
104.30
100.36
96.482
92.679
88.948
85.290
81.702
78.180
74.716
71.296
67.896
64.476
60.972
57.261
53.107
274.18
252.15
232.14
215.32
201.01
188.69
177.96
168.52
160.13
152.60
145.77
139.52
133.75
128.38
123.34
118.57
114.02
109.66
105.45
101.35
97.342
93.404
89.510
85.641
81.774
77.888
73.954
69.940
65.797
61.448
56.748
51.348
0.021089
0.021155
0.021238
0.021333
0.021441
0.021563
0.021699
0.021850
0.022017
0.022199
0.022397
0.022611
0.022842
0.023089
0.023352
0.023633
0.023931
0.024248
0.024586
0.024945
0.025329
0.025741
0.026186
0.029785
0.029947
0.030153
0.030394
0.030672
0.030993
0.031360
0.031777
0.032250
0.032783
0.033383
0.034057
0.034813
0.035661
0.036615
0.037690
0.038906
0.040288
0.041869
0.043694
0.045820
0.048326
0.051322
167.25
169.22
171.27
173.22
175.07
176.80
178.42
179.92
181.29
182.54
183.66
184.65
185.51
186.22
186.80
187.23
187.52
187.67
187.66
187.51
187.20
186.73
186.11
40.804
38.426
36.126
34.080
32.250
30.604
29.116
27.763
26.527
25.392
24.345
23.377
22.477
21.638
20.853
20.118
19.426
18.773
18.154
17.565
17.001
16.458
15.930
Cv
kJ/(mol⋅K)
Saturated Properties
68.160
70.000
72.000
74.000
76.000
78.000
80.000
82.000
84.000
86.000
88.000
90.000
92.000
94.000
96.000
98.000
100.00
102.00
104.00
106.00
108.00
110.00
112.00
114.00
116.00
118.00
120.00
122.00
124.00
126.00
128.00
130.00
132.86
0.015537
0.021053
0.028718
0.038447
0.050599
0.065559
0.083738
0.10556
0.13148
0.16196
0.19748
0.23852
0.28559
0.33919
0.39983
0.46805
0.54438
0.62934
0.72348
0.82736
0.94154
1.0666
1.2031
1.3517
1.5130
1.6877
1.8765
2.0802
2.2997
2.5360
2.7904
3.0647
3.4982
68.160
70.000
72.000
74.000
76.000
78.000
80.000
82.000
84.000
86.000
88.000
90.000
92.000
94.000
96.000
98.000
100.00
102.00
104.00
106.00
108.00
110.00
112.00
0.015537
0.021053
0.028718
0.038447
0.050599
0.065559
0.083738
0.10556
0.13148
0.16196
0.19748
0.23852
0.28559
0.33919
0.39983
0.46805
0.54438
0.62934
0.72348
0.82736
0.94154
1.0666
1.2031
0.027707
0.036656
0.048780
0.063796
0.082130
0.10424
0.13059
0.16171
0.19810
0.24036
0.28906
0.34486
0.40845
0.48058
0.56209
0.65388
0.75700
0.87260
1.0020
1.1468
1.3088
1.4903
1.6938
36.091
27.281
20.500
15.675
12.176
9.5935
7.6573
6.1841
5.0478
4.1605
3.4595
2.8997
2.4483
2.0808
1.7791
1.5293
1.3210
1.1460
0.99799
0.87198
0.76404
0.67102
0.59039
6.6865
6.8845
7.1009
7.3188
7.5382
7.7592
7.9820
8.2067
8.4335
8.6627
8.8944
9.1291
9.3672
9.6091
9.8555
10.107
10.366
10.632
10.909
11.198
11.502
11.828
12.181
4.6366
4.7768
4.9329
5.0934
5.2589
5.4300
5.6076
5.7922
5.9847
6.1860
6.3968
6.6182
6.8512
7.0969
7.3566
7.6317
7.9239
8.2350
8.5675
8.9238
9.3073
9.7221
10.173
114.00
116.00
118.00
120.00
122.00
124.00
126.00
128.00
130.00
132.86
1.3517
1.5130
1.6877
1.8765
2.0802
2.2997
2.5360
2.7904
3.0647
3.4982
100.00
200.00
300.00
400.00
500.00
0.10000
0.10000
0.10000
0.10000
0.10000
100.00
108.96
1.0000
1.0000
108.96
200.00
300.00
400.00
500.00
1.0000
1.0000
1.0000
1.0000
1.0000
100.00
200.00
300.00
400.00
500.00
5.0000
5.0000
5.0000
5.0000
5.0000
1.9228
2.1815
2.4754
2.8123
3.2027
3.6629
4.2194
4.9212
5.8832
10.850
0.52008
0.45841
0.40397
0.35558
0.31224
0.27301
0.23700
0.20320
0.16998
0.092166
5.5986
5.5827
5.5598
5.5286
5.4872
5.4324
5.3595
5.2594
5.1113
4.2912
6.3016
6.2762
6.2416
6.1959
6.1367
6.0602
5.9605
5.8264
5.6322
4.6137
0.057914
0.057008
0.056070
0.055084
0.054034
0.052892
0.051613
0.050117
0.048216
0.040039
5.7653
7.8674
9.9522
12.045
14.169
6.5785
9.5259
12.446
15.371
18.328
0.080014
0.10048
0.11231
0.12073
0.12733
0.039586
0.042829
1.1047
1.7009
1.1443
1.7437
0.71782
1.6200
2.4867
3.3334
4.1732
5.6147
7.7647
9.8936
12.005
14.140
25.864
3.4130
2.0232
1.4824
1.1786
0.038663
0.29299
0.49426
0.67458
0.84845
0.026671
0.027203
0.027794
0.028462
0.029229
0.030133
0.031233
0.032636
0.034579
0.054966
0.059493
0.065263
0.072864
0.083320
0.098585
0.12291
0.16759
0.27599
185.33
184.38
183.27
181.99
180.52
178.84
176.93
174.68
171.86
0
15.411
14.894
14.372
13.833
13.265
12.648
11.956
11.140
10.100
6.1475
12.569
13.005
13.507
14.101
14.826
15.747
16.981
18.777
21.845
10.667
11.213
11.821
12.509
13.301
14.234
15.373
16.840
18.936
0.021118
0.020812
0.020833
0.021028
0.021479
0.030153
0.029239
0.029191
0.029364
0.029807
201.29
288.05
353.12
407.29
454.00
17.820
5.3111
2.5186
1.2653
0.56244
10.075
19.227
26.605
33.106
39.272
6.9147
12.897
17.731
21.870
25.540
0.012262
0.017998
0.029062
0.028142
0.064114
0.070627
685.44
577.22
−0.14414
0.070176
112.87
90.884
6.3325
9.3847
12.380
15.338
18.313
0.060114
0.080819
0.092976
0.10149
0.10812
0.025522
0.020996
0.020895
0.021064
0.021505
0.046966
0.030510
0.029646
0.029598
0.029948
186.99
286.20
354.42
409.43
456.39
16.739
5.1924
2.4256
1.2088
0.52786
11.655
19.474
26.760
33.222
39.364
0.99666
7.2656
9.6364
11.834
14.015
1.1900
8.7305
12.108
15.207
18.258
0.011154
0.064994
0.078767
0.087691
0.094498
0.029263
0.021878
0.021174
0.021224
0.021618
0.060925
0.038000
0.031673
0.030585
0.030535
737.92
285.27
362.95
420.15
467.56
−0.21740
4.3757
2.0288
0.98413
0.39254
152.30
22.190
27.812
33.871
39.837
112.19
15.094
18.716
22.588
26.139
Single-Phase Properties
0.12298
0.060293
0.040104
0.030062
0.024045
25.261
23.349
1.3931
0.61727
0.40214
0.29999
0.23962
8.1315
16.586
24.935
33.265
41.588
113.83
95.450
9.5017
13.192
17.918
22.024
25.676
100.00
200.00
300.00
400.00
500.00
10.000
10.000
10.000
10.000
10.000
26.482
7.4298
4.0263
2.9079
2.3052
0.037761
0.13459
0.24837
0.34389
0.43381
0.88669
6.5960
9.3290
11.634
13.870
1.2643
7.9419
11.813
15.073
18.208
0.0099878
0.056188
0.072068
0.081462
0.088461
0.029539
0.022832
0.021511
0.021420
0.021755
0.058409
0.048831
0.034036
0.031689
0.031188
792.04
307.84
379.01
435.68
482.48
−0.27800
2.8854
1.5731
0.74980
0.25486
200.46
34.772
30.972
35.414
40.797
110.33
19.114
19.862
23.298
26.682
100.00
200.00
300.00
400.00
500.00
50.000
50.000
50.000
50.000
50.000
29.422
20.591
14.766
11.439
9.3865
0.033988
0.048566
0.067725
0.087418
0.10654
0.39153
4.5424
7.7949
10.518
13.024
2.0910
6.9707
11.181
14.889
18.350
0.0040257
0.038097
0.055259
0.065951
0.073681
0.031398
0.025036
0.023212
0.022620
0.022659
0.052094
0.045541
0.039083
0.035519
0.033937
1066.8
706.01
609.73
604.51
622.30
−0.43831
−0.28689
−0.21242
−0.27153
−0.36911
567.46
256.88
139.18
94.476
76.899
99.463
50.929
34.086
31.319
32.167
31.474
24.888
20.200
16.970
14.662
0.031772
0.040181
0.049505
0.058928
0.068206
0.095937
3.9022
7.0625
9.8487
12.449
3.2732
7.9203
12.013
15.741
19.269
−0.00053857
0.031951
0.048608
0.059353
0.067230
0.033037
0.026437
0.024358
0.023555
0.023434
0.050530
0.043352
0.038799
0.036051
0.034683
1282.4
987.69
866.60
822.33
808.91
−0.47725
−0.50923
−0.54516
−0.59581
−0.64123
100.00
200.00
300.00
400.00
500.00
100.00
100.00
100.00
100.00
100.00
1005.7
536.84
331.69
229.18
173.58
90.560
73.380
54.648
45.748
42.504
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. The source for viscosity and thermal conductivity is Version 9.08 of the
NIST14 database.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The equation of state is valid from the triple point to 500 K with pressures to 100 MPa. At higher pressures, the deviations from the equation increase rapidly, and it is not recommended to use the equation above
100 MPa. The uncertainties in the equation are 0.3% in density (approaching 1% near the critical point), 0.2% in vapor pressure, and 2% in heat capacities. For viscosity, estimated uncertainty is 2%. For thermal
conductivity, estimated uncertainty, except near the critical region, is 4–6%.
2-205
2-206
PHYSICAL AnD CHEMICAL DATA
FIG. 2-4
Temperature-entropy diagram for carbon monoxide. Pressure P, in atmospheres; density r, in grams per cubic centimeter; enthalpy H,
in joules per gram. (From J.G. Hust and R.B. Stewart, NBS Tech. Note 202, 1963.)
TABLE 2-115
Thermodynamic Properties of Ethanol
Temperature
K
Pressure
MPa
250.00
265.00
280.00
295.00
310.00
325.00
340.00
355.00
370.00
385.00
400.00
415.00
430.00
445.00
460.00
475.00
490.00
505.00
513.90
0.00027007
0.00089527
0.0025823
0.0066146
0.015298
0.032394
0.063544
0.11663
0.20205
0.33279
0.52446
0.79509
1.1649
1.6559
2.2916
3.0963
4.0954
5.3159
6.1480
250.00
265.00
280.00
295.00
310.00
325.00
340.00
355.00
370.00
385.00
400.00
415.00
430.00
445.00
460.00
475.00
490.00
505.00
513.90
0.00027007
0.00089527
0.0025823
0.0066146
0.015298
0.032394
0.063544
0.11663
0.20205
0.33279
0.52446
0.79509
1.1649
1.6559
2.2916
3.0963
4.0954
5.3159
6.1480
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
6.9274
8.3792
9.9424
11.630
13.445
15.385
17.444
19.615
21.892
24.268
26.740
29.307
31.970
34.737
37.629
40.684
44.002
47.926
53.880
6.9275
8.3793
9.9426
11.631
13.446
15.387
17.448
19.622
21.905
24.290
26.775
29.362
32.054
34.862
37.810
40.943
44.374
48.480
54.906
0.037330
0.042968
0.048704
0.054574
0.060574
0.066684
0.072875
0.079123
0.085403
0.091699
0.098000
0.10430
0.11061
0.11695
0.12335
0.12991
0.13684
0.14485
0.15723
49.039
49.932
50.851
51.792
52.749
53.717
54.684
55.640
56.573
57.469
58.312
59.087
59.774
60.348
60.777
61.004
60.916
60.144
53.880
51.116
52.134
53.174
54.234
55.307
56.383
57.450
58.494
59.500
60.451
61.329
62.115
62.785
63.312
63.654
63.747
63.453
62.328
54.906
0.21409
0.20808
0.20310
0.19899
0.19561
0.19282
0.19053
0.18862
0.18701
0.18562
0.18438
0.18322
0.18208
0.18088
0.17954
0.17792
0.17578
0.17228
0.15723
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.076657
0.083798
0.091653
0.099433
0.10670
0.11322
0.11893
0.12381
0.12792
0.13130
0.13405
0.13625
0.13798
0.13934
0.14041
0.14134
0.14234
0.14382
0.093612
0.10028
0.10829
0.11678
0.12524
0.13340
0.14115
0.14847
0.15543
0.16215
0.16883
0.17576
0.18341
0.19262
0.20504
0.22469
0.26508
0.41790
1325.0
1260.8
1202.8
1149.2
1098.1
1048.0
997.94
947.31
895.56
842.31
787.16
729.67
669.25
605.07
535.80
459.19
371.03
264.74
0
−0.44553
−0.41423
−0.37872
−0.34323
−0.30910
−0.27615
−0.24356
−0.21011
−0.17428
−0.13410
−0.086812
−0.028333
0.047976
0.15384
0.31228
0.57597
1.0976
2.5369
8.6373
178.12
173.58
169.56
165.87
162.38
159.01
155.69
152.39
149.09
145.78
142.47
139.18
135.93
132.78
129.85
127.41
126.33
129.43
3140.9
2182.0
1564.4
1152.5
869.40
669.49
524.87
417.88
337.04
274.76
225.91
186.93
155.35
129.37
107.62
88.972
72.213
55.104
0.058885
0.060795
0.062753
0.064753
0.066816
0.068988
0.071336
0.073932
0.076838
0.080106
0.083774
0.087876
0.092450
0.097544
0.10323
0.10966
0.11709
0.12644
0.067215
0.069146
0.071149
0.073238
0.075464
0.077921
0.080736
0.084059
0.088058
0.092930
0.098936
0.10646
0.11610
0.12898
0.14727
0.17612
0.23200
0.42053
226.86
233.03
238.89
244.41
249.49
254.02
257.88
260.92
263.02
264.03
263.82
262.27
259.21
254.44
247.61
238.10
224.59
203.70
0
Cv
kJ/(mol⋅K)
Saturated Properties
17.911
17.642
17.376
17.106
16.828
16.537
16.231
15.905
15.557
15.181
14.774
14.331
13.843
13.298
12.676
11.941
11.007
9.5842
5.9910
0.00012998
0.00040670
0.0011115
0.0027080
0.0059814
0.012150
0.022975
0.040873
0.069039
0.11160
0.17385
0.26261
0.38683
0.55876
0.79629
1.1286
1.6143
2.4339
5.9910
0.055831
0.056681
0.057551
0.058460
0.059426
0.060469
0.061610
0.062872
0.064281
0.065871
0.067684
0.069779
0.072241
0.075202
0.078889
0.083745
0.090848
0.10434
0.16692
7693.7
2458.8
899.69
369.28
167.18
82.305
43.525
24.466
14.485
8.9606
5.7521
3.8080
2.5851
1.7897
1.2558
0.88602
0.61945
0.41086
0.16692
149.30
111.11
87.283
71.858
61.180
53.164
46.697
41.226
36.486
32.353
28.756
25.644
22.967
20.681
18.747
17.136
15.831
14.728
8.6373
14.936
15.737
16.612
17.566
18.602
19.731
20.969
22.341
23.886
25.659
27.741
30.251
33.369
37.377
42.735
50.248
61.578
82.512
7.2715
7.7433
8.2114
8.6756
9.1353
9.5902
10.040
10.486
10.929
11.372
11.820
12.283
12.774
13.318
13.961
14.786
15.982
18.148
(Continued)
2-207
2-208
TABLE 2-115 Thermodynamic Properties of Ethanol (Continued )
Temperature
K
Pressure
MPa
Entropy
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
164.74
153.26
1047.2
443.11
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
17.016
15.993
0.058768
0.062527
12.219
19.033
12.225
19.040
0.056554
0.077475
0.10193
0.12261
0.11962
0.14658
1132.5
960.72
−0.33179
−0.21908
55.390
59.207
67.925
77.796
58.222
62.477
72.058
82.775
0.18909
0.20043
0.22176
0.24127
0.073221
0.080640
0.092910
0.10403
0.083127
0.089997
0.10162
0.11252
260.21
279.09
312.39
341.55
42.587
28.685
11.830
5.6356
0.058707
0.067589
0.071181
12.202
26.715
30.866
12.261
26.783
30.938
0.056497
0.097937
0.10802
0.10191
0.13400
0.13732
0.11954
0.16857
0.18015
1137.9
791.85
694.41
3.0216
3.9114
4.8846
59.504
67.014
77.311
62.526
70.925
82.195
0.18255
0.20078
0.22131
0.090516
0.096953
0.10581
0.11184
0.11008
0.11605
260.65
300.64
337.33
24.014
12.007
5.6301
0.058443
0.066842
0.097846
0.099875
12.129
26.516
46.419
46.876
12.421
26.851
46.908
47.375
0.056249
0.097435
0.14179
0.14272
0.10185
0.13359
0.14311
0.14340
0.11922
0.16658
0.32410
0.35152
1161.4
829.44
308.88
292.31
−0.33665
−0.11211
1.7596
2.0063
2.1809
1.1372
0.45852
0.87939
60.445
74.966
62.737
79.363
0.17336
0.20395
0.12389
0.11419
0.34099
0.13659
209.80
314.06
15.000
5.6703
75.676
61.725
17.454
18.972
17.203
15.147
11.521
2.8001
0.058131
0.066020
0.086800
0.35713
12.041
26.293
44.752
71.266
12.623
26.953
45.620
74.837
0.055950
0.096860
0.13830
0.19172
0.10179
0.13313
0.14031
0.12599
0.11885
0.16456
0.22204
0.18744
1189.5
872.36
464.50
273.66
−0.34096
−0.13414
0.60618
5.6926
170.07
149.80
130.15
84.190
1111.8
252.40
80.680
23.411
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Single-Phase Properties
300.00
351.05
0.10000
0.10000
351.05
400.00
500.00
600.00
0.10000
0.10000
0.10000
0.10000
300.00
400.00
423.85
1.0000
1.0000
1.0000
423.85
500.00
600.00
1.0000
1.0000
1.0000
300.00
400.00
500.00
501.39
5.0000
5.0000
5.0000
5.0000
501.39
600.00
5.0000
5.0000
300.00
400.00
500.00
600.00
10.000
10.000
10.000
10.000
0.035314
0.030577
0.024191
0.020086
17.034
14.795
14.049
0.33095
0.25567
0.20473
17.111
14.961
10.220
10.013
28.317
32.704
41.338
49.786
−0.33273
−0.089821
0.013963
21.965
26.374
37.865
52.622
165.24
142.87
137.25
32.003
39.539
53.583
167.43
146.07
127.42
128.00
10.369
11.853
14.768
17.543
1053.2
227.32
167.52
12.568
14.859
17.678
1079.6
238.82
61.882
59.510
300.00
400.00
500.00
600.00
100.00
100.00
100.00
100.00
18.389
17.030
15.408
13.601
0.054380
0.058722
0.064899
0.073523
10.984
24.075
39.356
55.055
16.422
29.947
45.846
62.407
0.051802
0.090466
0.12589
0.15608
0.10149
0.12901
0.13221
0.12575
0.11571
0.15081
0.16433
0.16553
1558.1
1348.2
1166.1
1015.1
−0.37198
−0.25352
−0.17199
−0.082822
207.54
195.29
188.35
187.31
1611.3
435.09
192.15
109.49
300.00
400.00
500.00
600.00
200.00
200.00
200.00
200.00
19.244
18.138
16.878
15.505
0.051963
0.055134
0.059250
0.064494
10.349
22.905
37.295
51.902
20.742
33.931
49.145
64.801
0.048505
0.086238
0.12014
0.14869
0.10196
0.12678
0.12868
0.12066
0.11495
0.14539
0.15623
0.15566
1830.4
1660.3
1525.6
1422.7
−0.37578
−0.28090
−0.22946
−0.19099
238.67
228.57
224.49
226.40
2085.4
591.02
269.30
148.43
The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Dillon,
H.E., and Penoncello, S.G., “A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol,” Int. J. Thermophys., 25(2):321–335, 2004. The source for viscosity is Kiselev, S. B., Ely, J. F., Abdulagatov,
I. M., and Huber, M. L., “Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols,” Ind. Eng. Chem. Res., 44:6916–6927, 2005.
The source for thermal conductivity is unpublished, 2004; however, the fit uses functional form found in Marsh, K., Perkins, R., and Ramires, M.L.V., “Measurement and Correlation of the Thermal Conductivity of
Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data, 47(4):932–940, 2002.
Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary,
the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties in the equation of state are 0.2% in density, 3% in heat capacities, 1% in speed of sound, and 0.5% in vapor pressure and saturation densities. The estimated uncertainty in the liquid phase along
the saturation boundary is approximately 3%, increasing to 10% at pressures to 100 MPa, and is estimated at 10% in the vapor phase. The estimated uncertainty in the liquid phase is approximately 5% and is estimated as 10% in the vapor phase.
THERMODYnAMIC PROPERTIES
FIG. 2-5
Enthalpy-concentration diagram for aqueous ethyl alcohol. Reference states: Enthalpies of liquid water and ethyl alcohol at 0°C are
zero. Note: In order to interpolate equilibrium compositions, a vertical may be erected from any liquid composition on the boiling line and its
intersection with the auxiliary line determined. A horizontal from this intersection will establish the equilibrium vapor composition on the
dew line. (F. Bosnjakovic, Technische Thermodynamik, T. Steinkopff, Leipzig, 1935.)
2-209
2-210
TABLE 2-116
Thermodynamic Properties of normal Hydrogen
Temperature
K
Pressure
MPa
13.957
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
31.000
32.000
33.190
13.957
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
31.000
32.000
33.190
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
0.0077031
0.0078936
0.013436
0.021534
0.032848
0.048078
0.067960
0.093249
0.12472
0.16314
0.20932
0.26406
0.32818
0.40250
0.48788
0.58524
0.69554
0.81989
0.95964
1.1168
1.3301
38.148
38.129
37.701
37.261
36.802
36.321
35.812
35.274
34.702
34.092
33.439
32.738
31.979
31.152
30.242
29.225
28.067
26.706
25.017
22.637
14.940
0.026214
0.026226
0.026524
0.026838
0.027172
0.027533
0.027923
0.028350
0.028817
0.029333
0.029905
0.030546
0.031271
0.032101
0.033067
0.034217
0.035629
0.037444
0.039973
0.044175
0.066934
−0.10434
−0.10367
−0.088896
−0.074446
−0.059414
−0.043440
−0.026375
−0.0081516
0.011274
0.031947
0.053929
0.077308
0.10222
0.12884
0.15744
0.18843
0.22245
0.26061
0.30524
0.36302
0.53004
−0.10414
−0.10346
−0.088539
−0.073868
−0.058521
−0.042116
−0.024477
−0.0055080
0.014868
0.036732
0.060188
0.085375
0.11248
0.14176
0.17357
0.20846
0.24723
0.29132
0.34360
0.41236
0.61907
−0.0059480
−0.0059000
−0.0048799
−0.0039471
−0.0030355
−0.0021219
−0.0011983
−0.00026211
0.00068790
0.0016528
0.0026344
0.0036357
0.0046610
0.0057167
0.0068122
0.0079614
0.0091865
0.010527
0.012063
0.014035
0.020012
0.0077031
0.0078936
0.013436
0.021534
0.032848
0.048078
0.067960
0.093249
0.12472
0.16314
0.20932
0.26406
0.32818
0.40250
0.48788
0.58524
0.69554
0.81989
0.95964
1.1168
1.3301
0.067540
0.069018
0.11050
0.16764
0.24349
0.34126
0.46437
0.61652
0.80187
1.0251
1.2919
1.6089
1.9848
2.4307
2.9618
3.6003
4.3810
5.3643
6.6763
8.6823
14.940
14.806
14.489
9.0494
5.9651
4.1069
2.9303
2.1535
1.6220
1.2471
0.97549
0.77406
0.62153
0.50383
0.41141
0.33763
0.27775
0.22826
0.18642
0.14978
0.11518
0.066934
0.68715
0.68764
0.69864
0.70899
0.71875
0.72783
0.73614
0.74359
0.75005
0.75541
0.75951
0.76218
0.76318
0.76224
0.75895
0.75276
0.74277
0.72747
0.70374
0.66274
0.53004
0.80120
0.80201
0.82024
0.83745
0.85365
0.86871
0.88249
0.89484
0.90558
0.91455
0.92154
0.92630
0.92853
0.92783
0.92368
0.91531
0.90154
0.88031
0.84748
0.79136
0.61907
0.058918
0.058777
0.055705
0.053010
0.050622
0.048480
0.046537
0.044755
0.043103
0.041554
0.040085
0.038674
0.037303
0.035950
0.034594
0.033206
0.031749
0.030160
0.028317
0.025879
0.020012
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.011064
0.010957
0.0096961
0.0096482
0.010003
0.010462
0.010915
0.011323
0.011677
0.011978
0.012235
0.012457
0.012655
0.012840
0.013025
0.013224
0.013460
0.013764
0.014198
0.014926
0.015654
0.015547
0.014420
0.014709
0.015557
0.016642
0.017842
0.019120
0.020476
0.021935
0.023539
0.025351
0.027465
0.030024
0.033265
0.037610
0.043909
0.054194
0.074872
0.14185
1361.1
1359.6
1318.5
1271.6
1226.6
1185.5
1147.3
1110.7
1074.7
1038.2
1000.5
960.99
919.10
874.29
826.00
773.58
716.22
652.73
581.16
497.24
0
−1.4137
−1.4230
−1.5204
−1.4695
−1.3623
−1.2409
−1.1194
−1.0003
−0.88232
−0.76268
−0.63795
−0.50414
−0.35648
−0.18882
0.0073109
0.24446
0.54283
0.93827
1.5038
2.4292
5.3208
76.293
76.650
84.106
90.079
94.784
98.405
101.10
103.01
104.24
104.87
104.98
104.60
103.79
102.53
100.83
98.654
95.935
92.547
88.221
82.176
25.463
25.310
22.215
19.784
17.815
16.182
14.799
13.607
12.565
11.641
10.811
10.057
9.3625
8.7151
8.1034
7.5160
6.9409
6.3620
5.7518
5.0391
0.013157
0.013129
0.012872
0.012907
0.012992
0.013083
0.013178
0.013280
0.013392
0.013514
0.013650
0.013802
0.013973
0.014167
0.014392
0.014655
0.014971
0.015358
0.015854
0.016535
0.021964
0.021944
0.021898
0.022199
0.022618
0.023121
0.023724
0.024449
0.025329
0.026401
0.027724
0.029376
0.031482
0.034234
0.037960
0.043253
0.051322
0.065054
0.093486
0.18606
304.61
305.17
316.15
325.05
333.00
340.22
346.75
352.59
357.75
362.25
366.11
369.34
371.95
373.96
375.38
376.19
376.39
375.97
374.91
373.31
0
Cv
kJ/(mol⋅K)
Saturated Properties
31.943
31.808
28.572
25.724
23.407
21.522
19.961
18.642
17.507
16.513
15.629
14.829
14.091
13.396
12.726
12.061
11.374
10.624
9.7362
8.5059
5.3208
10.375
10.431
11.624
12.681
13.681
14.669
15.675
16.716
17.806
18.956
20.180
21.493
22.916
24.477
26.218
28.202
30.535
33.407
37.226
43.200
0.66345
0.66695
0.74268
0.81064
0.87421
0.93555
0.99611
1.0569
1.1186
1.1819
1.2472
1.3151
1.3863
1.4619
1.5433
1.6331
1.7362
1.8628
2.0375
2.3378
Single-Phase Properties
25.000
100.00
175.00
250.00
325.00
400.00
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
25.000
31.268
1.0000
1.0000
31.268
100.00
175.00
250.00
325.00
400.00
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
25.000
100.00
175.00
250.00
325.00
400.00
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
0.50823
0.12030
0.068680
0.048077
0.036986
0.030054
1.9676
8.3127
14.560
20.800
27.037
33.273
0.81207
1.7949
3.0224
4.4642
5.9947
7.5545
1.0088
2.6261
4.4785
6.5442
8.6984
10.882
0.049309
0.079163
0.092882
0.10269
0.11022
0.11626
0.012734
0.014263
0.018150
0.020003
0.020681
0.020865
0.022519
0.022637
0.026480
0.028323
0.028998
0.029180
403.66
808.92
1026.9
1209.1
1371.7
1519.7
12.894
1.4058
0.13575
−0.22980
−0.38965
−0.47650
20.761
68.334
117.11
160.59
197.72
234.06
1.3142
4.1896
6.1845
7.9025
9.4561
10.892
0.030538
0.040861
0.089693
0.31894
0.12023
0.35980
0.0041410
0.012531
0.012580
0.014353
0.025394
0.084709
985.14
560.14
−0.51115
1.7031
106.80
86.829
9.9923
5.5759
0.14049
0.83027
1.4653
2.0926
2.7176
3.3418
0.69511
1.7679
3.0101
4.4576
5.9910
7.5525
0.83559
2.5982
4.4754
6.5501
8.7086
10.894
0.027747
0.059751
0.073667
0.083515
0.091062
0.097113
0.016014
0.014331
0.018190
0.020028
0.020699
0.020878
0.10713
0.023244
0.026659
0.028401
0.029039
0.029204
374.52
817.03
1035.8
1217.3
1379.1
1526.4
9.4548
1.3036
0.11718
−0.23428
−0.39039
−0.47605
38.524
70.413
118.31
161.46
198.43
234.65
2.0997
4.2550
6.2213
7.9283
9.4759
10.908
35.661
5.9683
3.3132
2.3268
1.7990
1.4680
0.028042
0.16755
0.30183
0.42978
0.55587
0.68120
0.046611
1.6549
2.9582
4.4292
5.9750
7.5440
0.18682
2.4927
4.4673
6.5781
8.7543
10.950
0.0021443
0.045314
0.059998
0.070022
0.077631
0.083710
0.012376
0.014583
0.018352
0.020136
0.020776
0.020937
0.020610
0.025613
0.027370
0.028723
0.029211
0.029304
1223.4
865.94
1077.3
1254.0
1412.0
1556.2
−0.90198
0.86369
0.032971
−0.25678
−0.39563
−0.47537
119.36
80.395
123.58
165.19
201.36
237.09
13.101
4.5875
6.3871
8.0420
9.5631
10.979
32.746
24.474
7.1182
1.2044
0.68243
0.47788
0.36797
0.29924
25.000
100.00
175.00
250.00
325.00
400.00
10.000
10.000
10.000
10.000
10.000
10.000
37.930
11.417
6.3697
4.5028
3.5006
2.8687
0.026364
0.087588
0.15699
0.22209
0.28567
0.34859
0.020221
1.5346
2.9000
4.3966
5.9563
7.5339
0.28386
2.4105
4.4699
6.6175
8.8130
11.020
0.00059913
0.038585
0.053931
0.064133
0.071811
0.077921
0.012222
0.014838
0.018532
0.020260
0.020867
0.021006
0.018499
0.027423
0.028063
0.029065
0.029402
0.029419
1402.1
955.43
1133.3
1300.6
1453.0
1593.1
−1.0762
0.39679
−0.068718
−0.28786
−0.40519
−0.47687
131.12
94.196
130.39
169.92
205.05
240.15
16.625
5.1692
6.6199
8.1898
9.6733
11.067
100.00
175.00
250.00
325.00
400.00
50.000
50.000
50.000
50.000
50.000
31.993
22.700
17.524
14.304
12.107
0.031257
0.044053
0.057066
0.069911
0.082595
1.1768
2.6415
4.2297
5.8539
7.4773
2.7397
4.8442
7.0830
9.3494
11.607
0.023964
0.039587
0.050225
0.058153
0.064404
0.016349
0.019545
0.020999
0.021434
0.021458
0.026254
0.029321
0.030163
0.030202
0.029985
1710.1
1632.6
1690.7
1784.8
1887.2
−0.57213
−0.46415
−0.46214
−0.48443
−0.51016
192.47
189.52
211.67
237.63
267.11
10.534
9.1377
9.7772
10.827
11.965
33.019
27.257
23.228
20.261
0.030286
0.036688
0.043051
0.049356
2.5589
4.1604
5.8083
7.4555
5.5875
7.8292
10.113
12.391
0.033643
0.044291
0.052281
0.058588
0.020316
0.021603
0.021923
0.021864
0.029140
0.030346
0.030469
0.030246
2128.4
2125.4
2170.6
2235.8
−0.52750
−0.50698
−0.51215
−0.52481
282.17
303.19
327.83
356.83
13.079
12.218
12.546
13.289
175.00
250.00
325.00
400.00
100.00
100.00
100.00
100.00
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is
Younglove, B. A., “Thermophysical Properties of Fluids. I. Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen,” J. Phys. Chem. Ref. Data, Suppl. 1, 11: 1–11, 1982. The source for viscosity
is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972. The source for thermal conductivity
is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties in density are 0.1% in the liquid phase, 0.25% in the vapor phase, and 0.2% in the supercritical region. The uncertainty in heat capacity is 3%, and the uncertainty in speed of sound is 2% in the
liquid phase and 1% elsewhere. The uncertainty in viscosity ranges from 4% to 15%. The uncertainty in thermal conductivity below 100 K is estimated to be 3% below 150 atm and up to 10% below 700 atm. For
temperatures around 100 K at low densities, the uncertainty is about 1%. Above 100 K, the uncertainty is estimated to be on the order of 10%.
2-211
2-212
TABLE 2-117
T, K
273
300
350
400
450
Saturated Hydrogen Peroxide*
P, bar
vf , m3/kg
vg , m3/kg
hf , kJ/kg
hg, kJ/kg
sf , kJ/(kg⋅K)
sg , kJ/(kg⋅K)
cpf , kJ/(kg⋅K)
µf , 10−4 Pa⋅s
kf , W/(m⋅K)
0.0004
0.0031
0.0564
0.4521
2.143
0.00068
0.00069
0.00072
0.00076
0.00081
1672
235
15.1
2.12
0.487
−5577
−5510
−5376
−5238
−5091
−4027
−3995
−3933
−3878
−3820
2.990
3.224
3.631
4.032
4.346
8.662
8.269
7.758
7.440
7.172
1.45
1.48
1.54
1.61
1.68
18.0
11.3
4.3
2.2
1.3
0.483
0.481
0.474
0.464
0.453
1.75
1.82
1.90
500
550
600
650
700
7.126
18.56
40.75
79.27
141.7
0.00088
0.00095
0.00107
0.00125
0.00171
0.155
0.0605
0.0268
0.0125
0.0048
−4945
−4794
−4635
−4463
−4195
−3777
−3745
−3731
−3746
−3860
4.656
4.941
5.209
5.485
5.682
6.992
6.846
6.720
6.582
6.339
708.5c
155.3
0.00284
0.0028
−4012
−4012
5.732
5.732
0.89
0.65
0.50
0.443
0.431
0.416
*Values reproduced or converted from a tabulation by Tsykalo and Tabachnikov in V. A. Rabinovich (ed.), Thermophysical Properties of Gases and Liquids, Standartov,
Moscow, 1968; NBS-NSF transl. TT 69-55091, 1970. The reader may be reminded that very pure hydrogen peroxide is very difficult to obtain owing to its decomposition or
instability. c = critical point. The FMC Corp., Philadelphia, PA tech. bull. 67, 1969 (100 pp.) contains an enthalpy-pressure diagram to 3000 psia, 1100 K.
TABLE 2-118
Temperature
K
Thermodynamic Properties of Hydrogen Sulfide
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
0.034345
0.034479
0.035082
0.035717
0.036390
0.037107
0.037875
0.038702
0.039599
0.040580
0.041662
0.042868
0.044230
0.045791
0.047618
0.049818
0.052573
0.056256
0.061837
0.074429
0.098135
−1.7210
−1.5628
−0.87841
−0.19759
0.48138
1.1602
1.8406
2.5245
3.2135
3.9100
4.6161
5.3348
6.0696
6.8248
7.6068
8.4246
9.2932
10.241
11.335
12.903
14.470
−1.7202
−1.5619
−0.87664
−0.19446
0.48661
1.1686
1.8534
2.5434
3.2408
3.9481
4.6685
5.4053
6.1629
6.9469
7.7650
8.6283
9.5548
10.578
11.779
13.538
15.353
16.328
16.382
16.611
16.832
17.043
17.244
17.431
17.604
17.761
17.899
18.016
18.108
18.171
18.199
18.183
18.109
17.957
17.684
17.192
16.046
14.470
17.876
17.947
18.250
18.541
18.818
19.079
19.320
19.539
19.735
19.902
20.039
20.139
20.198
20.207
20.156
20.027
19.793
19.403
18.736
17.266
15.353
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
−0.34039
−0.33923
−0.33253
−0.32287
−0.30988
−0.29305
−0.27174
−0.24509
−0.21197
−0.17084
−0.11959
−0.055218
0.026636
0.13260
0.27324
0.46655
0.74618
1.1841
1.9714
3.9324
6.3885
254.24
251.74
240.93
230.26
219.81
209.52
199.43
189.56
179.91
170.48
161.26
152.24
143.40
134.71
126.16
117.71
109.36
101.19
93.864
92.754
439.13
428.67
385.68
346.75
311.74
280.37
252.29
227.14
204.60
184.32
166.02
149.44
134.32
120.43
107.58
95.533
84.050
72.784
61.060
46.102
Saturated Properties
187.70
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
373.10
0.023259
0.027106
0.050340
0.087474
0.14366
0.22485
0.33767
0.48934
0.68751
0.94022
1.2558
1.6429
2.1103
2.6672
3.3233
4.0889
4.9755
5.9969
7.1713
8.5294
8.9987
29.116
29.003
28.505
27.998
27.480
26.949
26.403
25.838
25.253
24.642
24.002
23.327
22.609
21.838
21.000
20.073
19.021
17.776
16.172
13.436
10.190
187.70
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
373.10
0.023259
0.027106
0.050340
0.087474
0.14366
0.22485
0.33767
0.48934
0.68751
0.94022
1.2558
1.6429
2.1103
2.6672
3.3233
4.0889
4.9755
5.9969
7.1713
8.5294
8.9987
0.015024
0.017314
0.030704
0.051165
0.080932
0.12253
0.17879
0.25286
0.34834
0.46937
0.62086
0.80887
1.0411
1.3280
1.6843
2.1323
2.7096
3.4881
4.6442
6.9933
10.190
66.559
57.758
32.569
19.545
12.356
8.1613
5.5933
3.9547
2.8707
2.1305
1.6107
1.2363
0.96050
0.75300
0.59373
0.46898
0.36906
0.28669
0.21532
0.14299
0.098135
−0.0085877
−0.0077504
−0.0042394
−0.00091743
0.0022415
0.0052596
0.0081564
0.010949
0.013654
0.016285
0.018857
0.021385
0.023885
0.026373
0.028873
0.031414
0.034044
0.036848
0.040035
0.044599
0.049374
0.044390
0.044124
0.043042
0.042067
0.041188
0.040393
0.039677
0.039030
0.038449
0.037930
0.037470
0.037070
0.036732
0.036462
0.036273
0.036191
0.036265
0.036600
0.037471
0.040079
0.068835
0.068707
0.068273
0.068029
0.067975
0.068115
0.068461
0.069032
0.069859
0.070989
0.072490
0.074466
0.077082
0.080603
0.085498
0.092666
0.10410
0.12534
0.17963
0.63367
1437.8
1425.8
1373.4
1321.0
1268.4
1215.6
1162.3
1108.5
1053.9
998.54
942.08
884.34
825.04
763.84
700.23
633.51
562.59
485.59
398.86
292.76
0
0.095815
0.094930
0.091395
0.088301
0.085567
0.083129
0.080933
0.078934
0.077092
0.075375
0.073752
0.072193
0.070669
0.069149
0.067594
0.065956
0.064157
0.062064
0.059360
0.054674
0.049374
0.025347
0.025386
0.025586
0.025837
0.026142
0.026502
0.026917
0.027388
0.027914
0.028496
0.029136
0.029838
0.030608
0.031458
0.032407
0.033485
0.034746
0.036293
0.038364
0.041755
0.034000
0.034078
0.034487
0.035021
0.035698
0.036537
0.037563
0.038807
0.040312
0.042139
0.044378
0.047166
0.050723
0.055410
0.061879
0.071400
0.086837
0.11617
0.19265
0.80649
245.84
247.20
252.82
257.96
262.58
266.64
270.10
272.91
275.05
276.47
277.15
277.05
276.12
274.34
271.64
268.00
263.35
257.65
250.84
242.80
0
55.730
53.868
46.796
41.090
36.435
32.601
29.412
26.737
24.476
22.550
20.897
19.466
18.212
17.097
16.081
15.116
14.142
13.053
11.629
9.0701
6.3885
10.628
10.775
11.429
12.107
12.816
13.566
14.365
15.227
16.166
17.202
18.360
19.675
21.197
22.997
25.187
27.946
31.600
36.820
45.513
70.939
8.0025
8.1053
8.5566
9.0159
9.4844
9.9634
10.455
10.961
11.485
12.031
12.604
13.213
13.867
14.582
15.380
16.300
17.405
18.833
20.940
25.604
(Continued)
2-213
2-214
TABLE 2-118
Thermodynamic Properties of Hydrogen Sulfide (Continued )
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
28.506
27.865
0.035080
0.035888
−0.87902
−0.021243
−0.87551
−0.017654
16.888
19.164
21.830
24.642
27.626
30.789
18.615
21.640
25.146
28.794
32.611
36.607
0.035053
0.040795
−0.89011
4.0550
−0.85506
4.0958
2.0080
2.2968
3.2255
4.0993
4.9547
5.8015
17.925
18.775
21.626
24.507
27.525
30.710
19.933
21.072
24.852
28.606
32.480
36.511
0.034935
0.043749
0.052654
−0.93837
5.9433
9.3164
−0.76369
6.1620
9.5797
0.36675
0.55412
0.77288
0.96476
1.1466
17.952
20.549
23.863
27.065
30.353
19.786
23.319
27.728
31.889
36.086
Cp
kJ/(mol⋅K)
Sound speed
m/s
0.043042
0.041830
0.068269
0.067997
1373.6
1307.4
0.087559
0.099486
0.10956
0.11770
0.12465
0.13081
0.025911
0.025979
0.027268
0.028923
0.030708
0.032534
0.035183
0.034563
0.035693
0.037297
0.039059
0.040873
259.21
309.73
356.35
396.06
431.20
463.05
39.791
16.968
8.9467
5.5432
3.7250
2.6185
−0.0042980
0.016821
0.043058
0.037830
0.068210
0.071266
1377.6
986.97
−0.33351
−0.16116
0.075033
0.079019
0.089907
0.098281
0.10534
0.11155
0.028623
0.027626
0.027708
0.029100
0.030799
0.032589
0.042564
0.039427
0.037234
0.038036
0.039492
0.041157
276.67
296.60
351.09
393.73
430.30
462.94
22.188
17.369
9.0111
5.5366
3.7023
2.5947
−0.0045411
0.023458
0.034113
0.043127
0.036740
0.036269
0.067957
0.075047
0.10449
1394.7
855.61
560.70
0.064108
0.073747
0.083609
0.091196
0.097665
0.034782
0.030043
0.029940
0.031216
0.032838
0.087361
0.048271
0.041996
0.041590
0.042472
263.22
325.86
384.33
427.30
463.26
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
Single-Phase Properties
200.00
212.60
0.10000
0.10000
212.60
300.00
400.00
500.00
600.00
700.00
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
200.00
272.07
1.0000
1.0000
272.07
300.00
400.00
500.00
600.00
700.00
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
200.00
300.00
340.26
5.0000
5.0000
5.0000
340.26
400.00
500.00
600.00
700.00
5.0000
5.0000
5.0000
5.0000
5.0000
0.057900
0.040389
0.030157
0.024088
0.020059
0.017187
28.528
24.513
0.49800
0.43539
0.31003
0.24394
0.20183
0.17237
28.625
22.858
18.992
2.7266
1.8047
1.2939
1.0365
0.87211
17.271
24.759
33.160
41.515
49.853
58.182
−0.0042425
−0.000082766
−0.33258
−0.31984
−0.33745
−0.017492
0.75500
14.116
9.1749
5.4471
3.5816
2.4840
240.95
227.54
12.288
17.999
24.990
32.218
39.592
47.091
241.31
168.56
17.430
19.015
25.609
32.691
39.980
47.423
242.90
146.15
109.14
385.79
337.30
9.1366
12.954
17.172
21.094
24.714
28.082
387.91
180.39
12.147
13.337
17.465
21.319
24.893
28.227
397.26
139.57
83.760
31.710
29.786
35.063
41.773
48.924
17.437
19.070
22.459
25.773
28.935
200.00
300.00
400.00
500.00
600.00
700.00
10.000
10.000
10.000
10.000
10.000
10.000
28.741
23.238
5.0473
2.8037
2.1399
1.7663
0.034793
0.043033
0.19812
0.35667
0.46730
0.56617
−0.99643
5.7496
18.370
22.959
26.466
29.903
−0.64850
6.1800
20.351
26.526
31.139
35.564
−0.0048367
0.022795
0.062081
0.076030
0.084452
0.091275
0.043212
0.036779
0.034651
0.031080
0.031755
0.033155
0.067668
0.072377
0.10189
0.048875
0.044597
0.044212
1415.5
902.78
291.29
375.68
426.01
465.45
−0.34197
−0.077399
8.2243
5.1487
3.3812
2.3347
244.82
150.49
44.719
38.963
44.210
50.878
408.90
148.08
23.639
24.438
27.165
30.013
300.00
400.00
500.00
600.00
700.00
75.000
75.000
75.000
75.000
75.000
26.050
21.973
17.947
14.519
11.974
0.038388
0.045510
0.055720
0.068874
0.083511
4.3332
9.9713
15.404
20.474
25.148
7.2123
13.384
19.583
25.640
31.412
0.017506
0.035260
0.049092
0.060142
0.069045
0.037754
0.035381
0.034762
0.034994
0.035721
0.061705
0.061962
0.061649
0.059227
0.056291
1276.9
983.51
786.35
688.11
654.55
−0.33612
−0.18247
0.057516
0.27314
0.36585
187.18
134.39
103.90
87.712
82.684
232.59
124.22
81.074
62.531
54.563
27.794
24.751
21.937
19.449
17.335
0.035979
0.040403
0.045585
0.051416
0.057687
3.5100
8.6429
13.539
18.248
22.811
8.9069
14.703
20.377
25.960
31.464
0.013888
0.030575
0.043238
0.053420
0.061906
0.038777
0.036402
0.035779
0.036044
0.036804
0.058983
0.057226
0.056273
0.055409
0.054711
1538.4
1302.6
1132.1
1019.1
949.06
−0.40376
−0.37006
−0.31802
−0.26874
−0.23292
214.24
165.64
135.75
118.38
110.03
311.25
174.85
119.57
93.323
79.581
300.00
400.00
500.00
600.00
700.00
150.00
150.00
150.00
150.00
150.00
The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport
Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W.,
and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data 51(3): 785–850, 2006. The source for viscosity and thermal conductivity is NIST14, Version 9.08.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties in density are 0.1% in the liquid phase below the critical temperature, 0.4% in the vapor phase, 1% at supercritical temperatures up to 500 K, and 2.5% at higher temperatures. Uncertainties will
be higher near the critical point, and may be lower than 0.5% between 400 and 500 K. The uncertainty in vapor pressure is 0.25%, and the uncertainty in heat capacities is estimated to be 1%. For viscosity, estimated
uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4–6%.
THERMODYnAMIC PROPERTIES
FIG. 2-6
Enthalpy-concentration diagram for aqueous hydrogen chloride at 1 atm. Reference states: enthalpy of liquid water at 0°C
is zero; enthalpy of pure saturated HCl vapor at 1 atm (–85.03°C) is 8000 kcal/mol. Note: It should be observed that the weight basis
includes the vapor, which is particularly important in the two-phase region. Saturation values may be read at the ends of the tie lines
[C.C. Van Nuys, Trans. Am. Inst. Chem. Eng 39: 663 (1943)].
2-215
2-216
TABLE 2-119
Temperature
K
Thermodynamic Properties of Methane
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
0.035534
0.036554
0.037143
0.037768
0.038431
0.039138
0.039896
0.040714
0.041600
0.042569
0.043636
0.044825
0.046165
0.047702
0.049500
0.051667
0.054394
0.058078
0.063825
0.079902
0.098628
−1.1526
−0.64728
−0.37306
−0.096585
0.18242
0.46425
0.74927
1.0379
1.3307
1.6284
1.9317
2.2418
2.5602
2.8887
3.2304
3.5895
3.9734
4.3965
4.8955
5.7074
6.2136
−1.1522
−0.64602
−0.37097
−0.093257
0.18750
0.47174
0.75999
1.0529
1.3511
1.6557
1.9676
2.2884
2.6199
2.9647
3.3262
3.7098
4.1244
4.5873
5.1420
6.0685
6.6672
−0.011389
−0.0060856
−0.0034096
−0.00083691
0.0016441
0.0040439
0.0063722
0.0086383
0.010851
0.013020
0.015154
0.017264
0.019362
0.021462
0.023584
0.025755
0.028021
0.030467
0.033313
0.038000
0.041109
63.981
23.782
15.116
10.038
6.9171
4.9183
3.5915
2.6825
2.0424
1.5803
1.2393
0.98256
0.78568
0.63206
0.51014
0.41163
0.33038
0.26139
0.19945
0.12816
0.098628
6.8310
7.0469
7.1582
7.2654
7.3680
7.4652
7.5562
7.6403
7.7165
7.7837
7.8406
7.8856
7.9166
7.9306
7.9238
7.8898
7.8184
7.6893
7.4515
6.7850
6.2136
7.5793
7.8644
8.0104
8.1501
8.2825
8.4067
8.5215
8.6257
8.7180
8.7970
8.8608
8.9074
8.9340
8.9369
8.9109
8.8482
8.7357
8.5480
8.2217
7.3641
6.6672
0.084885
0.079019
0.076413
0.074103
0.072036
0.070168
0.068464
0.066891
0.065421
0.064029
0.062694
0.061391
0.060098
0.058789
0.057431
0.055982
0.054371
0.052471
0.049961
0.044819
0.041109
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.034776
0.033908
0.033500
0.033115
0.032749
0.032400
0.032069
0.031757
0.031469
0.031206
0.030974
0.030780
0.030631
0.030541
0.030531
0.030634
0.030920
0.031554
0.033085
0.041746
0.054029
0.054681
0.055135
0.055656
0.056253
0.056941
0.057741
0.058684
0.059809
0.061169
0.062840
0.064932
0.067613
0.071156
0.076044
0.083218
0.094816
0.11699
0.17822
1.5082
1538.6
1452.0
1403.9
1354.7
1304.6
1253.5
1201.3
1148.1
1093.6
1037.7
980.17
920.85
859.39
795.43
728.42
657.52
581.27
497.01
398.59
250.31
0
−0.48191
−0.45812
−0.44202
−0.42328
−0.40145
−0.37589
−0.34578
−0.31006
−0.26735
−0.21579
−0.15286
−0.075032
0.022798
0.14836
0.31398
0.54087
0.86918
1.3866
2.3397
5.2488
6.8877
211.24
199.67
193.03
186.18
179.21
172.15
165.04
157.91
150.78
143.65
136.54
129.43
122.32
115.19
108.01
100.73
93.324
85.799
78.733
96.970
204.52
155.78
136.86
121.34
108.39
97.432
88.031
79.868
72.699
66.333
60.620
55.437
50.682
46.266
42.105
38.115
34.196
30.193
25.773
18.982
0.025243
0.025487
0.025652
0.025842
0.026056
0.026295
0.026560
0.026854
0.027182
0.027549
0.027965
0.028439
0.028989
0.029636
0.030412
0.031374
0.032615
0.034338
0.037087
0.045796
0.033851
0.034425
0.034853
0.035378
0.036016
0.036786
0.037714
0.038836
0.040203
0.041885
0.043985
0.046657
0.050144
0.054849
0.061496
0.071527
0.088273
0.12151
0.21701
2.2590
249.13
260.09
265.31
270.01
274.17
277.76
280.76
283.13
284.86
285.93
286.31
285.97
284.88
283.01
280.30
276.66
271.99
266.04
258.03
238.55
0
47.921
37.826
33.883
30.662
28.004
25.790
23.928
22.347
20.993
19.819
18.789
17.870
17.035
16.255
15.500
14.732
13.896
12.892
11.492
8.4951
6.8877
8.8517
10.015
10.669
11.350
12.062
12.811
13.604
14.449
15.355
16.334
17.402
18.581
19.904
21.423
23.225
25.477
28.545
33.392
43.706
119.40
Cv
kJ/(mol⋅K)
Saturated Properties
90.694
100.00
105.00
110.00
115.00
120.00
125.00
130.00
135.00
140.00
145.00
150.00
155.00
160.00
165.00
170.00
175.00
180.00
185.00
190.00
190.56
0.011696
0.034376
0.056377
0.088130
0.13221
0.19143
0.26876
0.36732
0.49035
0.64118
0.82322
1.0400
1.2950
1.5921
1.9351
2.3283
2.7765
3.2852
3.8617
4.5186
4.5992
28.142
27.357
26.923
26.478
26.021
25.551
25.065
24.562
24.038
23.491
22.917
22.309
21.661
20.964
20.202
19.355
18.384
17.218
15.668
12.515
10.139
90.694
100.00
105.00
110.00
115.00
120.00
125.00
130.00
135.00
140.00
145.00
150.00
155.00
160.00
165.00
170.00
175.00
180.00
185.00
190.00
190.56
0.011696
0.034376
0.056377
0.088130
0.13221
0.19143
0.26876
0.36732
0.49035
0.64118
0.82322
1.0400
1.2950
1.5921
1.9351
2.3283
2.7765
3.2852
3.8617
4.5186
4.5992
0.015630
0.042048
0.066154
0.099622
0.14457
0.20332
0.27844
0.37278
0.48962
0.63279
0.80691
1.0177
1.2728
1.5821
1.9603
2.4294
3.0268
3.8257
5.0137
7.8027
10.139
3.6388
3.9976
4.1951
4.3964
4.6019
4.8123
5.0285
5.2517
5.4833
5.7254
5.9806
6.2526
6.5462
6.8688
7.2313
7.6515
8.1609
8.8251
9.8238
12.455
Single-Phase Properties
−0.64803
−0.012738
−0.64438
−0.0089413
7.2969
9.5570
12.175
15.151
18.673
22.795
8.1908
11.209
14.665
18.475
22.831
27.784
0.036493
0.044610
−0.65829
2.1878
1.0220
1.5537
2.4524
3.3108
4.1567
4.9971
27.586
5.4706
2.1799
1.5333
1.2013
0.99281
100.00
111.51
0.10000
0.10000
111.51
200.00
300.00
400.00
500.00
600.00
0.10000
0.10000
0.10000
0.10000
0.10000
0.10000
100.00
149.14
1.0000
1.0000
149.14
200.00
300.00
400.00
500.00
600.00
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
0.97852
0.64363
0.40776
0.30205
0.24058
0.20012
100.00
200.00
300.00
400.00
500.00
600.00
5.0000
5.0000
5.0000
5.0000
5.0000
5.0000
100.00
200.00
300.00
400.00
500.00
600.00
10.000
10.000
10.000
10.000
10.000
10.000
27.360
26.341
−0.0060931
−0.000079677
0.054672
0.055828
0.073456
0.093427
0.10741
0.11834
0.12803
0.13705
0.025904
0.025259
0.027479
0.032300
0.038196
0.044179
0.035558
0.033784
0.035869
0.040652
0.046533
0.052509
271.33
369.98
449.74
510.56
561.86
608.04
29.808
9.2893
4.3216
2.2395
1.2245
0.68722
−0.62179
2.2325
−0.0061960
0.016902
0.033950
0.030810
0.054562
0.064535
1459.6
931.21
−0.46060
−0.089695
7.8788
9.3582
12.072
15.083
18.623
22.755
8.9007
10.912
14.524
18.393
22.780
27.752
0.061614
0.073276
0.087922
0.099023
0.10879
0.11784
0.028353
0.025879
0.027621
0.032360
0.038227
0.044198
0.046147
0.036730
0.036721
0.041056
0.046766
0.052659
286.08
357.81
447.04
510.57
562.99
609.73
18.022
9.5001
4.2699
2.2001
1.1998
0.67124
18.368
23.028
35.152
50.558
68.902
89.200
0.036250
0.18279
0.45874
0.65221
0.83240
1.0072
−0.70190
7.8197
11.590
14.779
18.401
22.581
−0.52065
8.7337
13.884
18.040
22.563
27.617
−0.0066393
0.051495
0.072954
0.084897
0.094971
0.10417
0.034116
0.032029
0.028262
0.032614
0.038361
0.044277
0.054117
0.11667
0.041234
0.042903
0.047789
0.053309
1490.0
291.29
439.25
513.11
569.49
618.13
−0.46993
8.9784
3.9428
2.0089
1.0870
0.60013
204.45
40.612
38.480
52.693
70.509
90.498
165.28
10.828
12.194
14.872
17.410
19.768
27.802
16.593
4.6859
3.1002
2.3887
1.9619
0.035969
0.060268
0.21340
0.32256
0.41863
0.50971
−0.75239
5.1551
10.942
14.401
18.132
22.371
−0.39270
5.7578
13.077
17.627
22.318
27.468
−0.0071652
0.034542
0.065137
0.078246
0.088698
0.098073
0.034314
0.030129
0.028995
0.032902
0.038516
0.044371
0.053642
0.085085
0.048165
0.045220
0.049007
0.054070
1525.7
567.92
444.53
522.58
580.99
630.63
−0.47979
1.0266
3.2606
1.7355
0.94125
0.51200
209.07
84.234
44.730
55.941
72.781
92.268
174.83
29.399
13.896
15.766
18.011
20.217
27.403
22.416
8.9395
16.524
24.901
33.243
41.572
49.895
1452.6
1339.7
−0.45829
−0.41705
0.033911
0.033003
0.11186
0.060518
0.040158
0.030082
0.024055
0.020042
0.036549
0.037963
199.74
184.09
11.561
21.941
34.552
50.127
68.564
88.921
200.62
130.66
155.91
117.20
4.4579
7.8096
11.245
14.272
16.976
19.431
157.63
56.297
6.2043
8.0145
11.367
14.357
17.040
19.483
200.00
300.00
400.00
500.00
600.00
100.00
100.00
100.00
100.00
100.00
25.496
21.266
17.881
15.305
13.357
0.039222
0.047024
0.055926
0.065340
0.074869
3.0510
7.0865
11.121
15.405
20.074
6.9732
11.789
16.713
21.939
27.561
0.020596
0.040126
0.054276
0.065922
0.076160
0.032058
0.031823
0.035273
0.040312
0.045724
0.048512
0.048281
0.050523
0.054139
0.058364
1541.0
1267.5
1115.8
1044.8
1018.4
−0.51619
−0.44889
−0.37484
−0.32811
−0.30439
188.05
137.68
120.38
120.87
130.36
80.392
47.835
37.584
33.590
32.111
200.00
300.00
400.00
500.00
600.00
500.00
500.00
500.00
500.00
500.00
33.003
30.786
28.929
27.331
25.934
0.030301
0.032482
0.034567
0.036588
0.038559
2.3322
5.9505
9.7401
13.934
18.612
17.482
22.192
27.024
32.228
37.892
0.0061671
0.025271
0.039152
0.050747
0.061061
0.037832
0.037006
0.039890
0.044407
0.049344
0.047821
0.047114
0.049933
0.054280
0.059017
2664.2
2500.0
2360.3
2250.3
2168.1
−0.53926
−0.55416
−0.52806
−0.49035
−0.45514
429.60
358.93
312.36
285.41
272.14
205.24
106.90
78.768
66.669
60.413
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is
Setzmann, U., and Wagner, W., “A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data
20(6):1061–1151, 1991. The source for viscosity is Younglove, B. A., and Ely, J. F., “Thermophysical Properties of Fluids. II. Methane, Ethane, Propane, Isobutane and Normal Butane,” J. Phys. Chem. Ref. Data 16:577–798,
1987. The source for thermal conductivity is Friend, D. G., Ely, J. F., and Ingham, H., “Tables for the Thermophysical Properties of Methane,” NIST Tech. Note 1325, 1989.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties in density are 0.03% for pressures below 12 MPa and temperatures below 350 K and up to 0.07% for pressures less than 50 MPa. For the speed of sound, the uncertainty ranges from 0.03% (in the vapor
phase) to 0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of 1%. The uncertainty in viscosity is 2%, except in the critical region which is 5%. The uncertainty
in thermal conductivity of the dilute gas between 130 and 625 K is 2.5%. For temperatures below 130 K, the uncertainty is less than 10%. Excluding the dilute gas, the uncertainty is 2% between 110 and 725 K at pressures
up to 70 MPa, except near the critical point which has an uncertainty of 5% or greater. For the vapor at lower temperatures and the dense liquid near the triple point, an uncertainty of 10% is possible.
2-217
2-218
TABLE 2-120
Temperature
K
Thermodynamic Properties of Methanol
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Saturated Properties
175.61
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
375.00
390.00
405.00
420.00
435.00
450.00
465.00
480.00
495.00
510.00
513.38
1.8635E-07
3.7619E-07
3.2175E-06
1.9841E-05
9.4330E-05
0.00036348
0.0011791
0.0033166
0.0082787
0.018682
0.038692
0.074453
0.13447
0.22992
0.37483
0.58617
0.88399
1.2914
1.8349
2.5433
3.4456
4.5713
5.9794
7.7496
8.2159
175.61
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
375.00
390.00
405.00
420.00
435.00
450.00
465.00
480.00
495.00
510.00
513.38
1.8635E-07
3.7619E-07
3.2175E-06
1.9841E-05
9.4330E-05
0.00036348
0.0011791
0.0033166
0.0082787
0.018682
0.038692
0.074453
0.13447
0.22992
0.37483
0.58617
0.88399
1.2914
1.8349
2.5433
3.4456
4.5713
5.9794
7.7496
8.2159
28.230
28.096
27.629
27.163
26.703
26.250
25.802
25.360
24.922
24.484
24.041
23.590
23.124
22.638
22.123
21.571
20.973
20.315
19.579
18.741
17.759
16.553
14.880
11.689
8.7852
1.2764E-07
2.5140E-07
1.9855E-06
1.1378E-05
5.0556E-05
0.00018304
0.00056065
0.0014959
0.0035581
0.0076845
0.015300
0.028438
0.049870
0.083267
0.13344
0.20674
0.31179
0.46071
0.67055
0.96219
1.3555
1.9102
2.9050
5.1706
8.7852
0.035423
0.035592
0.036194
0.036815
0.037449
0.038096
0.038756
0.039432
0.040125
0.040844
0.041595
0.042390
0.043244
0.044174
0.045203
0.046358
0.047681
0.049226
0.051075
0.053360
0.056310
0.060411
0.067203
0.085547
0.11383
7,834,400.
3,977,700.
503,660.
87,892.
19,780.
5,463.4
1,783.7
668.48
281.05
130.13
65.359
35.164
20.052
12.009
7.4940
4.8370
3.2073
2.1706
1.4913
1.0393
0.73775
0.52352
0.34423
0.19340
0.11383
−12.440
−12.130
−11.067
−10.001
−8.9277
−7.8395
−6.7318
−5.5991
−4.4351
−3.2329
−1.9858
−0.68700
0.66961
2.0901
3.5806
5.1475
6.7983
8.5423
10.392
12.364
14.488
16.820
19.521
23.297
25.917
−12.440
−12.130
−11.067
−10.001
−8.9277
−7.8395
−6.7318
−5.5990
−4.4347
−3.2322
−1.9842
−0.68385
0.67543
2.1003
3.5975
5.1746
6.8404
8.6058
10.485
12.500
14.682
17.096
19.923
23.960
26.852
−0.049524
−0.047781
−0.042108
−0.036846
−0.031908
−0.027226
−0.022750
−0.018434
−0.014239
−0.010129
−0.0060725
−0.0020451
0.0019747
0.0060049
0.010061
0.014159
0.018314
0.022546
0.026879
0.031347
0.036009
0.040977
0.046590
0.054351
0.059911
0.056728
0.056689
0.056604
0.057072
0.057992
0.059275
0.060916
0.062917
0.065250
0.067864
0.070693
0.073674
0.076752
0.079881
0.083033
0.086189
0.089346
0.092514
0.095722
0.099032
0.10257
0.10666
0.11250
0.12653
0.070390
0.070750
0.070897
0.071215
0.072004
0.073141
0.074617
0.076487
0.078803
0.081584
0.084823
0.088505
0.092616
0.097164
0.10219
0.10776
0.11405
0.12133
0.13007
0.14120
0.15679
0.18345
0.25717
1.1088
1625.1
1590.2
1496.4
1425.3
1363.2
1304.6
1248.2
1194.1
1142.6
1093.5
1046.3
1000.2
954.32
907.64
859.31
808.48
754.41
696.47
634.17
567.09
494.36
412.12
308.94
192.83
0
28.219
28.353
28.810
29.259
29.698
30.123
30.534
30.932
31.321
31.703
32.077
32.442
32.789
33.108
33.385
33.601
33.736
33.767
33.687
33.541
33.439
33.258
32.267
29.688
25.917
29.679
29.850
30.430
31.003
31.564
32.109
32.637
33.149
33.648
34.134
34.606
35.060
35.485
35.869
36.194
36.436
36.571
36.570
36.423
36.184
35.981
35.652
34.325
31.187
26.852
0.19032
0.18544
0.17069
0.15841
0.14806
0.13923
0.13164
0.12508
0.11938
0.11442
0.11009
0.10627
0.10287
0.099808
0.096984
0.094317
0.091723
0.089128
0.086505
0.083978
0.081813
0.079634
0.075685
0.068520
0.059911
0.031874
0.032397
0.035224
0.040104
0.047248
0.056324
0.066572
0.077055
0.086920
0.095581
0.10279
0.10860
0.11331
0.11736
0.12125
0.12546
0.13033
0.13587
0.14101
0.14238
0.13589
0.12618
0.12608
0.13259
0.040287
0.040854
0.043954
0.049389
0.057480
0.067973
0.080135
0.093000
0.10564
0.11740
0.12798
0.13749
0.14644
0.15559
0.16605
0.17917
0.19663
0.21986
0.24709
0.26502
0.25879
0.27959
0.42448
1.9096
239.95
242.62
251.06
258.49
265.30
271.89
278.43
284.90
291.19
297.15
302.63
307.47
311.48
314.48
316.20
316.34
314.53
310.36
303.71
295.26
285.25
267.83
247.46
212.65
0
−0.40884
−0.40373
−0.39791
−0.39361
−0.38674
−0.37793
−0.36733
−0.35457
−0.33915
−0.32073
−0.29904
−0.27385
−0.24479
−0.21121
−0.17199
−0.12529
−0.068163
0.0042669
0.10021
0.23444
0.43762
0.79465
1.6506
4.6061
6.7425
1187400.
857090.
293110.
105090.
39363.
15552.
6557.5
2971.8
1449.9
759.96
426.34
254.84
161.53
108.02
75.802
55.467
42.002
32.587
25.532
19.860
15.568
13.904
12.099
9.5115
6.7425
Single-Phase Properties
200.00
300.00
337.30
0.10000
0.10000
0.10000
337.30
400.00
500.00
600.00
0.10000
0.10000
0.10000
0.10000
200.00
300.00
400.00
409.75
1.0000
1.0000
1.0000
1.0000
409.75
500.00
600.00
1.0000
1.0000
1.0000
200.00
300.00
400.00
484.95
5.0000
5.0000
5.0000
5.0000
484.95
500.00
600.00
5.0000
5.0000
5.0000
200.00
300.00
400.00
500.00
600.00
10.000
10.000
10.000
10.000
10.000
27.474
24.486
23.366
0.037626
0.030452
0.024157
0.020089
0.036398
0.040839
0.042798
−10.709
−3.2300
−0.030266
−0.040317
−0.010133
−0.000089518
0.056702
0.067862
0.075163
0.070943
0.081580
0.090451
1471.5
1094.1
977.93
−0.39677
−0.32081
−0.26023
32.613
36.075
40.921
46.476
35.271
39.359
45.060
51.454
0.10457
0.11581
0.12851
0.14014
0.11100
0.044972
0.051823
0.059065
0.14187
0.054208
0.060380
0.067441
309.54
349.19
387.15
420.71
−10.720
−3.2472
6.2298
7.3401
−10.684
−3.2064
6.2770
7.3883
−0.040354
−0.010176
0.016901
0.019645
0.056724
0.067848
0.088257
0.090347
0.070932
0.081541
0.11177
0.11623
1475.1
1100.0
775.46
736.51
33.758
40.335
46.300
36.586
44.303
51.178
0.090904
0.10818
0.12070
0.13203
0.056676
0.061344
0.20333
0.068069
0.070369
313.48
376.08
413.09
38.678
13.330
4.5635
0.036283
0.040592
0.046640
0.062203
−10.752
−3.3039
6.0896
17.655
−10.571
−3.1010
6.3228
17.966
−0.040517
−0.010367
0.016546
0.042725
0.056820
0.067795
0.087676
0.10826
0.070883
0.081377
0.11029
0.19836
1490.9
1125.5
818.58
381.15
−0.39825
−0.32568
−0.11504
0.98684
2.1711
1.7679
1.1389
0.46060
0.56566
0.87808
33.047
35.907
45.247
35.350
38.735
49.638
0.078574
0.085457
0.10553
0.12499
0.098975
0.072927
0.32263
0.17315
0.087489
260.06
301.43
379.21
13.826
12.155
5.1009
27.648
24.779
21.717
15.932
2.6640
0.036169
0.040357
0.046048
0.062765
0.37537
−10.791
−3.3713
5.9321
19.374
43.262
−10.430
−2.9677
6.3925
20.002
47.015
−0.040716
−0.010598
0.016141
0.046226
0.096406
0.056935
0.067746
0.087087
0.10760
0.088868
0.070820
0.081196
0.10880
0.18959
0.12122
1509.9
1155.3
865.91
424.68
343.60
−0.39966
−0.32990
−0.13884
0.83939
5.0965
−7.8460
−0.44914
8.4277
19.458
32.525
−0.043691
−0.013840
0.011565
0.036085
0.059862
0.057827
0.067889
0.082823
0.095694
0.10406
0.068992
0.079818
0.098951
0.12152
0.13787
1772.1
1515.8
1334.7
1164.1
977.50
−0.41976
−0.35799
−0.26099
−0.14407
−0.023905
10.949
19.430
29.089
40.322
−0.022106
0.0022308
0.023726
0.044161
0.070293
0.077541
0.084883
0.092281
0.080627
0.089761
0.10419
0.12017
2316.0
2194.8
2123.2
2074.1
−0.34762
−0.30897
−0.24751
−0.19279
27.491
24.514
21.193
20.772
0.35352
0.25202
0.20501
27.561
24.635
21.441
16.076
26.577
32.839
41.396
49.779
−10.713
−3.2341
−0.034546
0.036376
0.040793
0.047185
0.048143
2.8287
3.9680
4.8778
200.00
300.00
400.00
500.00
600.00
100.00
100.00
100.00
100.00
100.00
28.911
26.630
24.493
22.020
19.139
0.034588
0.037552
0.040827
0.045413
0.052250
−11.305
−4.2043
4.3449
14.917
27.300
300.00
400.00
500.00
600.00
500.00
500.00
500.00
500.00
30.547
29.154
27.670
26.003
0.032736
0.034300
0.036140
0.038457
−5.4195
2.2795
11.020
21.094
202.71
40.941
12.933
4.3382
−0.39705
−0.32177
−0.090229
−0.047179
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is de Reuck, K. M., and Craven, R. J. B., “Methanol, International Thermodynamic Tables of the Fluid State—12,” IUPAC, Blackwell Scientific Publications, London, 1993. Validated equations for the viscosity and
thermal conductivity are not currently available for this fluid.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties of the equation of state are generally 0.1% in density and 2% in the speed of sound, except in the critical region and high pressures.
2-219
2-220
TABLE 2-121 Thermodynamic Properties of nitrogen
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
−4.2230
−4.1194
−4.0071
−3.8946
−3.7819
−3.6689
−3.5556
−3.4419
−3.3278
−3.2132
−3.0980
−2.9822
−2.8657
−2.7483
−2.6301
−2.5107
−2.3902
−2.2683
−2.1449
−2.0196
−1.8923
−1.7625
−1.6298
−1.4938
−1.3537
−1.2086
−1.0571
−0.89741
−0.72635
−0.53833
−0.32093
−0.031475
0.51527
−4.2226
−4.1188
−4.0063
−3.8935
−3.7804
−3.6669
−3.5530
−3.4385
−3.3235
−3.2078
−3.0913
−2.9739
−2.8555
−2.7360
−2.6152
−2.4930
−2.3691
−2.2434
−2.1156
−1.9854
−1.8525
−1.7163
−1.5765
−1.4323
−1.2828
−1.1271
−0.96336
−0.78944
−0.60161
−0.39322
−0.14962
0.17937
0.81891
0.067951
0.069569
0.071270
0.072924
0.074535
0.076105
0.077637
0.079133
0.080597
0.082030
0.083436
0.084815
0.086172
0.087507
0.088823
0.090123
0.091408
0.092682
0.093946
0.095204
0.096459
0.097715
0.098977
0.10025
0.10154
0.10285
0.10420
0.10561
0.10710
0.10873
0.11059
0.11310
0.11807
1.2945
1.3299
1.3675
1.4042
1.4400
1.4747
1.5082
1.5404
1.5713
1.6007
1.6284
1.6544
1.6784
1.7005
1.7203
1.7377
1.7525
1.7645
1.7733
1.7788
1.7804
1.7778
1.7703
1.8147
1.8639
1.9160
1.9668
2.0162
2.0639
2.1099
2.1539
2.1957
2.2353
2.2725
2.3070
2.3386
2.3672
2.3925
2.4143
2.4324
2.4463
2.4557
2.4603
2.4595
2.4528
2.4394
0.16355
0.16161
0.15966
0.15786
0.15618
0.15461
0.15314
0.15176
0.15046
0.14923
0.14806
0.14694
0.14587
0.14485
0.14385
0.14289
0.14195
0.14103
0.14012
0.13922
0.13832
0.13742
0.13651
Cp
kJ/(mol⋅K)
Sound speed
m/s
0.032951
0.032591
0.032207
0.031831
0.031463
0.031106
0.030760
0.030427
0.030105
0.029795
0.029499
0.029215
0.028944
0.028687
0.028444
0.028215
0.028001
0.027804
0.027624
0.027464
0.027327
0.027214
0.027133
0.027088
0.027089
0.027149
0.027290
0.027545
0.027981
0.028755
0.030317
0.034680
0.056033
0.056121
0.056231
0.056360
0.056512
0.056690
0.056899
0.057142
0.057425
0.057752
0.058130
0.058566
0.059068
0.059647
0.060315
0.061088
0.061983
0.063026
0.064246
0.065684
0.067392
0.069443
0.071937
0.075021
0.078914
0.083966
0.090771
0.10044
0.11531
0.14140
0.20028
0.46831
995.28
976.36
956.04
935.83
915.66
895.49
875.28
855.00
834.61
814.07
793.36
772.44
751.28
729.84
708.09
685.99
663.50
640.57
617.14
593.17
568.58
543.30
517.24
490.29
462.32
433.19
402.67
370.43
335.85
297.68
253.32
195.48
0
−0.40419
−0.39833
−0.39135
−0.38364
−0.37508
−0.36560
−0.35506
−0.34334
−0.33029
−0.31574
−0.29951
−0.28135
−0.26099
−0.23813
−0.21237
−0.18326
−0.15025
−0.11264
−0.069613
−0.020100
0.037239
0.10414
0.18288
0.27654
0.38936
0.52741
0.69974
0.92076
1.2154
1.6317
2.2811
3.5308
6.0831
0.021007
0.021059
0.021123
0.021196
0.021278
0.021370
0.021472
0.021585
0.021709
0.021845
0.021994
0.022157
0.022334
0.022528
0.022738
0.022967
0.023217
0.023489
0.023787
0.024113
0.024471
0.024860
0.025284
0.029647
0.029788
0.029969
0.030180
0.030427
0.030712
0.031039
0.031413
0.031839
0.032323
0.032873
0.033496
0.034204
0.035008
0.035925
0.036973
0.038177
0.039568
0.041185
0.043081
0.045326
0.048012
0.051276
161.11
163.20
165.37
167.43
169.39
171.23
172.95
174.55
176.03
177.38
178.60
179.68
180.63
181.43
182.10
182.62
182.99
183.21
183.28
183.18
182.93
182.51
181.93
40.718
38.268
35.907
33.803
31.922
30.231
28.707
27.328
26.074
24.931
23.884
22.923
22.035
21.212
20.446
19.730
19.057
18.421
17.815
17.236
16.676
16.132
15.600
Cv
kJ/(mol⋅K)
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
173.24
169.51
165.49
161.47
157.47
153.46
149.47
145.48
141.50
137.55
133.61
129.66
125.72
121.77
117.83
113.89
109.95
106.02
102.08
98.144
94.208
90.272
86.337
82.404
78.472
74.544
70.626
66.728
62.883
59.196
56.121
56.435
311.59
282.07
254.55
230.85
210.32
192.43
176.75
162.94
150.71
139.82
130.07
121.31
113.38
106.18
99.602
93.568
88.004
82.847
78.042
73.543
69.306
65.292
61.464
57.786
54.224
50.740
47.290
43.824
40.270
36.509
32.310
26.935
Saturated Properties
63.151
65.000
67.000
69.000
71.000
73.000
75.000
77.000
79.000
81.000
83.000
85.000
87.000
89.000
91.000
93.000
95.000
97.000
99.000
101.00
103.00
105.00
107.00
109.00
111.00
113.00
115.00
117.00
119.00
121.00
123.00
125.00
126.19
0.012520
0.017404
0.024300
0.033213
0.044527
0.058656
0.076043
0.097152
0.12247
0.15251
0.18780
0.22886
0.27626
0.33055
0.39230
0.46210
0.54052
0.62817
0.72566
0.83358
0.95259
1.0833
1.2264
1.3826
1.5526
1.7371
1.9370
2.1533
2.3869
2.6391
2.9116
3.2069
3.3958
63.151
65.000
67.000
69.000
71.000
73.000
75.000
77.000
79.000
81.000
83.000
85.000
87.000
89.000
91.000
93.000
95.000
97.000
99.000
101.00
103.00
105.00
107.00
0.012520
0.017404
0.024300
0.033213
0.044527
0.058656
0.076043
0.097152
0.12247
0.15251
0.18780
0.22886
0.27626
0.33055
0.39230
0.46210
0.54052
0.62817
0.72566
0.83358
0.95259
1.0833
1.2264
30.957
30.685
30.387
30.085
29.779
29.468
29.153
28.832
28.506
28.175
27.837
27.492
27.139
26.779
26.409
26.030
25.640
25.238
24.822
24.390
23.941
23.471
22.978
22.457
21.902
21.306
20.658
19.943
19.134
18.187
16.997
15.210
11.184
0.024070
0.032594
0.044300
0.059031
0.077273
0.099542
0.12638
0.15838
0.19613
0.24030
0.29157
0.35069
0.41846
0.49576
0.58355
0.68291
0.79504
0.92134
1.0634
1.2231
1.4027
1.6049
1.8331
0.032303
0.032589
0.032909
0.033239
0.033581
0.033935
0.034302
0.034683
0.035080
0.035493
0.035924
0.036375
0.036847
0.037343
0.037865
0.038417
0.039002
0.039623
0.040288
0.041000
0.041769
0.042605
0.043520
0.044530
0.045658
0.046935
0.048407
0.050144
0.052262
0.054985
0.058834
0.065747
0.089414
41.546
30.680
22.573
16.940
12.941
10.046
7.9124
6.3140
5.0986
4.1614
3.4297
2.8515
2.3897
2.0171
1.7137
1.4643
1.2578
1.0854
0.94038
0.81759
0.71291
0.62309
0.54553
5.6209
5.8164
6.0298
6.2457
6.4645
6.6870
6.9138
7.1458
7.3839
7.6295
7.8837
8.1483
8.4251
8.7163
9.0247
9.3533
9.7060
10.087
10.503
10.960
11.467
12.035
12.679
4.3763
4.5123
4.6601
4.8088
4.9585
5.1096
5.2621
5.4164
5.5727
5.7313
5.8924
6.0565
6.2238
6.3948
6.5700
6.7499
6.9353
7.1270
7.3260
7.5334
7.7509
7.9804
8.2245
109.00
111.00
113.00
115.00
117.00
119.00
121.00
123.00
125.00
126.19
1.3826
1.5526
1.7371
1.9370
2.1533
2.3869
2.6391
2.9116
3.2069
3.3958
100.00
600.00
1100.0
1600.0
0.10000
0.10000
0.10000
0.10000
100.00
103.75
1.0000
1.0000
103.75
600.00
1100.0
1600.0
1.0000
1.0000
1.0000
1.0000
100.00
600.00
1100.0
1600.0
5.0000
5.0000
5.0000
5.0000
2.0916
2.3860
2.7240
3.1162
3.5786
4.1370
4.8380
5.7846
7.3244
11.184
0.47811
0.41911
0.36711
0.32091
0.27944
0.24172
0.20670
0.17287
0.13653
0.089414
1.7573
1.7377
1.7102
1.6730
1.6234
1.5572
1.4665
1.3343
1.1039
0.51527
2.4183
2.3884
2.3479
2.2946
2.2251
2.1341
2.0119
1.8376
1.5417
0.81891
0.13557
0.13461
0.13360
0.13253
0.13138
0.13009
0.12860
0.12675
0.12400
0.11807
0.025750
0.026284
0.026924
0.027721
0.028723
0.029997
0.031683
0.034185
0.039278
0.055332
0.060528
0.067435
0.077010
0.091003
0.11312
0.15295
0.24490
0.66512
181.19
180.28
179.15
177.75
176.01
173.87
171.17
167.43
160.26
0
15.075
14.546
13.996
13.409
12.767
12.045
11.203
10.148
8.6030
6.0831
13.419
14.284
15.315
16.580
18.186
20.329
23.424
28.604
41.535
8.4867
8.7716
9.0860
9.4395
9.8474
10.336
10.953
11.813
13.326
9.3806
44.840
70.075
92.344
6.9581
29.577
44.199
56.398
Single-Phase Properties
100.00
600.00
1100.0
1600.0
600.00
1100.0
1600.0
600.00
1100.0
1600.0
10.000
10.000
10.000
10.000
500.00
500.00
500.00
1000.0
1000.0
1000.0
0.12268
0.020037
0.010930
0.0075152
24.658
23.768
1.4754
0.19960
0.10899
0.074993
8.1514
49.908
91.489
133.06
0.040554
0.042073
0.67778
5.0099
9.1755
13.335
2.0396
12.573
24.284
37.272
2.8547
17.564
33.433
50.579
0.15950
0.21217
0.23131
0.24414
0.021049
0.021796
0.024932
0.026815
0.030012
0.030118
0.033248
0.035130
201.64
496.27
660.05
788.94
16.082
0.021483
−0.65654
−0.81543
−2.0907
−1.8441
−2.0501
−1.8020
0.094493
0.096928
0.027546
0.027281
0.064564
0.068113
609.42
559.22
−0.054514
0.060996
100.58
92.738
76.255
67.783
1.7800
12.554
24.277
37.270
2.4577
17.564
33.452
50.605
0.13799
0.19300
0.21216
0.22499
0.024612
0.021812
0.024938
0.026820
0.046272
0.030198
0.033267
0.035138
182.79
498.66
662.07
790.64
16.471
0.0061465
−0.65940
−0.81612
11.671
44.992
70.155
92.399
7.8351
29.626
44.221
56.411
25.436
0.98084
0.53797
0.37146
0.039314
1.0195
1.8588
2.6921
−2.2176
12.469
24.247
37.259
−2.0210
17.567
33.541
50.720
0.093188
0.17948
0.19875
0.21161
0.027713
0.021881
0.024969
0.026839
0.059868
0.030539
0.033350
0.035170
673.24
509.60
671.08
798.18
−0.17096
−0.057679
−0.67112
−0.81886
108.13
45.797
70.555
92.663
84.510
29.882
44.330
56.476
26.188
1.9183
1.0590
0.73435
0.038186
0.52130
0.94433
1.3618
−2.3398
12.368
24.211
37.246
−1.9580
17.581
33.654
50.864
0.091882
0.17355
0.19296
0.20583
0.028004
0.021965
0.025006
0.026863
0.056646
0.030926
0.033447
0.035209
734.22
523.87
682.37
807.57
−0.25658
−0.12928
−0.68394
−0.82170
115.90
46.995
71.130
93.033
93.648
30.284
44.493
56.570
27.434
21.868
18.335
0.036451
0.045729
0.054541
10.778
23.840
37.584
29.003
46.705
64.855
0.13791
0.15935
0.17295
0.026493
0.027586
0.028647
0.035336
0.035848
0.036665
1574.4
1501.4
1506.6
−0.70223
−0.72394
−0.73166
177.40
149.37
147.47
103.10
79.801
79.226
34.270
29.362
25.920
0.029180
0.034057
0.038580
11.714
25.065
38.999
40.894
59.122
77.579
0.13093
0.15303
0.16685
0.029169
0.029373
0.029977
0.036905
0.036577
0.037212
2107.2
1985.1
1942.0
−0.61888
−0.65271
−0.65439
278.97
232.49
214.36
208.00
129.86
110.35
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport
Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span, R., Lemmon,
E. W., Jacobsen, R. T., Wagner, W., and Yokozeki, A., “A Reference Quality Thermodynamic Property Formulation for Nitrogen,” J. Phys. Chem. Ref. Data 29(6):1361–1433, 2000. See also Int. J. Thermophys. 14(4):1121–1132,
1998. The source for viscosity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. The source for thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given
isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line).
Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainty in density of the equation of state is 0.02% from the triple point up to temperatures of 523 K and pressures up to 12 MPa and from temperatures of 240 to 523 K at pressures less than 30 MPa. In the range
from 270 to 350 K at pressures less than 12 MPa, the uncertainty in density is 0.01%. The uncertainty at very high pressures (>1 GPa) is 0.6% in density. The uncertainty in pressure in the critical region is estimated to be
0.02%. In the gaseous and supercritical region, the speed of sound can be calculated with a typical uncertainty of 0.005% to 0.1%. At liquid states and at high pressures, the uncertainty increases to 0.5% to 1.5%. For pressures
up to 30 MPa, the estimated uncertainty for heat capacities ranges from 0.3% at gaseous and gaslike supercritical states up to 0.8% at liquid states and at certain gaseous and supercritical states at low temperatures. The
uncertainty is 2% for pressures up to 200 MPa and larger at higher pressures. The estimated uncertainties of vapor pressure, saturated-liquid density, and saturated-vapor density are in general 0.02% for each property. The
formulation yields a reasonable extrapolation behavior up to the limits of chemical stability of nitrogen.
For viscosity, the uncertainty is 0.5% in dilute gas. Away from the dilute gas (pressures greater than 1 MPa and in the liquid), the uncertainties are as low as 1% between 270 and 300 K at pressures less than 100 MPa, and
increase outside that range. The uncertainties are around 2% at temperatures of 180 K and higher. Below this and away from the critical region, the uncertainties steadily increase to around 5% at the triple points of the
fluids. The uncertainties in the critical region are higher.
For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For the nondilute gas, the uncertainty is 2% for temperatures greater than 150 K. The uncertainty is
3% at temperatures less than the critical point and 5% in the critical region, except for states very near the critical point.
2-221
2-222
FIG. 2-7 Pressure-enthalpy diagram for nitrogen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23,
NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Span,
R., E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, “A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa.,” J. Phys.
Chem. Ref. Data 29:1361–1433, 2000.
TABLE 2-122 Thermodynamic Properties of Oxygen
Temperature
K
Pressure
MPa
Density
mol/dm3
54.361
55.000
60.000
65.000
70.000
75.000
80.000
85.000
90.000
95.000
100.00
105.00
110.00
115.00
120.00
125.00
130.00
135.00
140.00
145.00
150.00
154.58
0.00014628
0.00017857
0.00072582
0.0023349
0.0062623
0.014547
0.030123
0.056831
0.099350
0.16308
0.25400
0.37853
0.54340
0.75559
1.0223
1.3509
1.7491
2.2250
2.7878
3.4477
4.2186
5.0428
40.816
40.734
40.064
39.367
38.656
37.936
37.203
36.457
35.692
34.905
34.092
33.245
32.360
31.426
30.434
29.367
28.203
26.907
25.415
23.599
21.110
13.630
54.361
55.000
60.000
65.000
70.000
75.000
80.000
85.000
90.000
95.000
100.00
105.00
110.00
115.00
120.00
125.00
130.00
135.00
140.00
145.00
150.00
154.58
0.00014628
0.00017857
0.00072582
0.0023349
0.0062623
0.014547
0.030123
0.056831
0.099350
0.16308
0.25400
0.37853
0.54340
0.75559
1.0223
1.3509
1.7491
2.2250
2.7878
3.4477
4.2186
5.0428
0.00032370
0.00039060
0.0014561
0.0043291
0.010804
0.023509
0.045891
0.082138
0.13710
0.21627
0.32579
0.47267
0.66506
0.91283
1.2284
1.6285
2.1366
2.7893
3.6487
4.8412
6.7170
13.630
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
0.024500
0.024549
0.024960
0.025402
0.025869
0.026360
0.026879
0.027430
0.028017
0.028649
0.029333
0.030079
0.030903
0.031820
0.032858
0.034051
0.035457
0.037165
0.039347
0.042375
0.047372
0.073368
−6.1954
−6.1613
−5.8938
−5.6258
−5.3573
−5.0889
−4.8202
−4.5510
−4.2806
−4.0084
−3.7337
−3.4556
−3.1732
−2.8853
−2.5904
−2.2867
−1.9711
−1.6394
−1.2839
−0.88908
−0.41330
0.66752
−6.1954
−6.1612
−5.8938
−5.6257
−5.3572
−5.0885
−4.8194
−4.5495
−4.2778
−4.0038
−3.7263
−3.4442
−3.1564
−2.8612
−2.5568
−2.2407
−1.9091
−1.5567
−1.1742
−0.74298
−0.21346
1.0375
0.066946
0.067571
0.072225
0.076516
0.080495
0.084199
0.087667
0.090931
0.094023
0.096967
0.099787
0.10250
0.10513
0.10770
0.11022
0.11271
0.11520
0.11773
0.12035
0.12319
0.12654
0.13442
3089.2
2560.2
686.75
230.99
92.556
42.536
21.791
12.175
7.2938
4.6239
3.0695
2.1156
1.5036
1.0955
0.81405
0.61407
0.46803
0.35852
0.27407
0.20656
0.14888
0.073368
1.1195
1.1327
1.2355
1.3377
1.4393
1.5397
1.6377
1.7320
1.8209
1.9031
1.9772
2.0421
2.0966
2.1391
2.1678
2.1801
2.1722
2.1380
2.0670
1.9383
1.6938
0.66752
1.5714
1.5898
1.7339
1.8770
2.0189
2.1584
2.2941
2.4239
2.5455
2.6571
2.7569
2.8430
2.9136
2.9668
3.0000
3.0097
2.9908
2.9357
2.8311
2.6505
2.3219
1.0375
0.20982
0.20850
0.19935
0.19194
0.18587
0.18083
0.17659
0.17297
0.16984
0.16708
0.16462
0.16238
0.16032
0.15838
0.15652
0.15471
0.15289
0.15100
0.14896
0.14659
0.14345
0.13442
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.038252
0.037651
0.034835
0.033469
0.032532
0.031745
0.031030
0.030365
0.029745
0.029169
0.028636
0.028146
0.027703
0.027311
0.026976
0.026712
0.026536
0.026485
0.026634
0.027189
0.028982
0.053541
0.053489
0.053548
0.053668
0.053697
0.053719
0.053808
0.054012
0.054361
0.054880
0.055599
0.056557
0.057816
0.059469
0.061666
0.064659
0.068905
0.075327
0.086099
0.10778
0.17484
1123.4
1126.9
1127.4
1101.7
1066.3
1027.5
987.43
946.87
905.90
864.40
822.19
779.06
734.77
689.03
641.52
591.86
539.50
483.69
423.10
355.20
273.80
0
−0.37992
−0.37886
−0.37011
−0.36312
−0.35686
−0.34972
−0.34056
−0.32856
−0.31302
−0.29316
−0.26804
−0.23637
−0.19639
−0.14551
−0.079899
0.0063780
0.12309
0.28750
0.53357
0.93865
1.7389
5.0628
201.92
201.02
193.94
186.82
179.70
172.58
165.44
158.27
151.05
143.81
136.55
129.25
121.92
114.57
107.23
99.912
92.634
85.404
78.217
71.056
64.190
773.62
747.53
578.07
457.94
371.79
308.66
261.22
224.62
195.64
172.12
152.56
135.93
121.52
108.81
97.426
87.086
77.571
68.687
60.223
51.869
42.900
0.021241
0.021297
0.021815
0.022310
0.022565
0.022513
0.022239
0.021896
0.021624
0.021515
0.021605
0.021894
0.022361
0.022978
0.023726
0.024597
0.025604
0.026794
0.028269
0.030276
0.033574
0.029631
0.029698
0.030320
0.030934
0.031294
0.031336
0.031177
0.031019
0.031053
0.031420
0.032204
0.033461
0.035245
0.037647
0.040839
0.045146
0.051204
0.060349
0.075824
0.10781
0.21201
140.32
141.11
147.03
152.65
158.07
163.33
168.36
173.06
177.30
180.99
184.06
186.44
188.14
189.13
189.41
188.96
187.75
185.74
182.82
178.78
172.82
0
Cv
kJ/(mol⋅K)
Saturated Properties
507.90
480.26
284.62
156.71
87.254
52.570
35.817
27.728
23.649
21.338
19.753
18.446
17.250
16.118
15.045
14.029
13.062
12.120
11.155
10.071
8.6358
5.0628
4.4204
4.4842
4.9840
5.4863
5.9925
6.5051
7.0277
7.5654
8.1241
8.7113
9.3362
10.010
10.748
11.571
12.509
13.607
14.940
16.641
18.977
22.582
29.666
4.0962
4.1481
4.5528
4.9555
5.3557
5.7533
6.1486
6.5423
6.9355
7.3301
7.7281
8.1324
8.5467
8.9760
9.4273
9.9112
10.445
11.061
11.823
12.881
14.721
(Continued)
2-223
2-224
TABLE 2-122 Thermodynamic Properties of Oxygen (Continued )
Temperature
K
Pressure
MPa
Cp
kJ/(mol⋅K)
Sound speed
m/s
0.020885
0.021078
0.022781
0.024672
0.026045
0.029925
0.029435
0.031108
0.032992
0.034363
188.37
329.72
421.27
493.31
555.60
18.479
2.6530
0.75388
0.10517
−0.18735
0.099680
0.11003
0.028683
0.027000
0.055399
0.061476
826.85
645.19
−0.27181
−0.085501
2.9983
8.6563
14.741
21.176
27.929
0.15666
0.18598
0.20149
0.21230
0.22078
0.023665
0.021148
0.022802
0.024682
0.026051
0.040564
0.029887
0.031240
0.033052
0.034395
189.41
329.90
422.68
494.87
557.14
15.124
2.6066
0.73726
0.098376
−0.19062
12.433
26.894
41.288
54.139
66.001
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
0.12316
0.040116
0.024050
0.017177
0.013360
8.1192
24.928
41.579
58.216
74.849
2.0355
6.2338
10.604
15.357
20.438
2.8474
8.7265
14.762
21.179
27.923
0.17297
0.20531
0.22069
0.23147
0.23994
0.029276
0.032774
−3.7444
−2.6131
−3.7151
−2.5803
0.83209
2.4791
4.1649
5.8360
7.5029
2.1662
6.1772
10.576
15.340
20.426
Cv
kJ/(mol⋅K)
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
mPa⋅s
9.0852
26.485
41.046
53.966
65.867
7.7121
20.652
30.486
38.653
45.806
Single-Phase Properties
100.00
300.00
500.00
700.00
900.00
0.10000
0.10000
0.10000
0.10000
0.10000
100.00
119.62
1.0000
1.0000
119.62
300.00
500.00
700.00
900.00
1.0000
1.0000
1.0000
1.0000
1.0000
100.00
154.36
5.0000
5.0000
34.497
16.011
0.028988
0.062457
−3.7983
0.35374
−3.6533
0.66602
0.099132
0.13204
0.028935
0.038878
0.054458
3.5718
850.39
163.89
−0.28978
4.2044
140.71
75.954
160.92
29.668
154.36
300.00
500.00
700.00
900.00
5.0000
5.0000
5.0000
5.0000
5.0000
11.160
2.0616
1.1908
0.84728
0.65931
0.089610
0.48505
0.83975
1.1802
1.5167
1.0294
5.9227
10.454
15.264
20.373
1.4774
8.3480
14.653
21.165
27.956
0.13729
0.17177
0.18787
0.19881
0.20734
0.041906
0.021448
0.022894
0.024726
0.026076
4.2513
0.032003
0.031815
0.033309
0.034537
158.85
332.25
429.36
501.98
564.07
6.0016
2.3730
0.66261
0.068114
−0.20519
72.313
28.797
42.362
54.901
66.593
20.574
21.766
31.267
39.261
46.305
34.158
30.512
1.2018
0.40337
0.24010
0.17135
0.13328
137.23
107.79
153.89
98.249
9.3921
20.846
30.630
38.766
45.899
100.00
300.00
500.00
700.00
900.00
10.000
10.000
10.000
10.000
10.000
34.885
4.2056
2.3538
1.6705
1.3010
0.028665
0.23778
0.42484
0.59861
0.76866
−3.8593
5.6024
10.306
15.171
20.307
−3.5726
7.9802
14.554
21.157
27.993
0.098498
0.16499
0.18182
0.19292
0.20150
0.029235
0.021790
0.022999
0.024776
0.026104
0.053516
0.034749
0.032491
0.033613
0.034706
877.07
339.35
438.67
511.24
572.92
−0.30803
2.0332
0.56900
0.030534
−0.22339
144.82
31.466
43.708
55.839
67.321
169.49
23.153
32.074
39.873
46.804
100.00
300.00
500.00
700.00
900.00
25.000
25.000
25.000
25.000
25.000
35.884
10.393
5.6243
3.9923
3.1222
0.027867
0.096215
0.17780
0.25048
0.32028
−4.0109
4.7194
9.8920
14.907
20.117
−3.3142
7.1247
14.337
21.169
28.124
0.096845
0.15490
0.17346
0.18495
0.19369
0.030037
0.022521
0.023256
0.024901
0.026174
0.051627
0.040917
0.034167
0.034397
0.035155
945.24
390.80
472.62
541.32
600.66
−0.34532
1.0167
0.30658
−0.076019
−0.27597
155.97
41.851
47.943
58.651
69.464
194.38
29.605
34.705
41.714
48.271
100.00
300.00
500.00
700.00
900.00
75.000
75.000
75.000
75.000
75.000
38.263
21.603
13.760
10.201
8.1749
0.026135
0.046289
0.072675
0.098029
0.12233
−4.3340
3.1884
8.8798
14.192
19.571
−2.3739
6.6601
14.330
21.544
28.745
0.092788
0.14315
0.16284
0.17498
0.18403
0.031906
0.023601
0.023725
0.025126
0.026293
0.049123
0.041272
0.036534
0.035903
0.036153
1115.1
645.54
619.75
657.04
701.72
−0.39472
−0.18640
−0.20732
−0.31840
−0.40609
184.96
75.261
64.149
68.835
76.863
274.96
53.378
45.084
48.269
53.163
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Schmidt, R., and Wagner, W., “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria, 19:175–200, 1985. The source for viscosity and thermal conductivity
is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties of the equation of state are 0.1% in density, 2% in heat capacity, and 1% in the speed of sound, except in the critical region. For viscosity, the uncertainty is 1% in the dilute gas at temperatures
above 200 K, and 5% in the dilute gas at lower temperatures. The uncertainty is around 2% between 270 and 300 K, and increases to 5% outside of this region. The uncertainty may be higher in the liquid near the
triple point. The uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For thermal conductivity, the uncertainties range from 3% between 270 and 300 K to 5% elsewhere. The
uncertainties above 100 MPa are not known due to a lack of experimental data.
FIG. 2-8
Pressure-enthalpy diagram for oxygen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23,
NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of
Schmidt, R., and W. Wagner, “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria 19: 175–200, 1985.
2-225
FIG. 2-9
Enthalpy-concentration diagram for oxygen-nitrogen mixture at 1 atm. Reference states: Enthalpies of liquid oxygen and liquid nitrogen at the normal
boiling point of nitrogen are zero. (Dodge, B.F. Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1944.) Wilson, G.M., P.M. Silverberg, and M.G. Zellner,
AFAPL TDR 64-64 (AD 603151), 1964, p. 314, present extensive vapor-liquid equilibrium data for the three-component system argon-nitrogen-oxygen as well as for
binary systems including oxygen-nitrogen. Calculations for this mixture are also available with the NIST REFPROP software.
6
20
10
1.5
9
.2
.05
1.0
.6
.9
.8
.1
.5
.4
4
Ethylene
2
Methane
1.5
.3
.04
.005
.02
.004
.005
.004
.03
.07
.015
.06
.07
.05
.06
Ethane
.4
3
.1
.09
.08
.09
.08
.7
.6
.006
.006
.7
5000
6000
.01
.009
.03 .008
.007
.15
.8
6
.01
.009
.008
.007
.01
.009
.02
.04
.05
.008
.045
.015
–10
–20
09
.00
.003
.04
.06
.9
5
.001
.004
.05.015
.07
.001
.002
.005
.02
.08
.2
.5
4000
.09
1.0
5
3000
.3
.3
2
7
2000
.1
.4
1.5
00.5
.003
.01
.009
.008
.007
.006
.03
.04
.4
.5
.04
.1
.09.03
.08
.07
.02
.06
.5
3
15
8
1500
.2
.6
.004
.015
.15.05
.7
.6
2
Pressure, kPa
900
1000
4
.3
Propane
500
1
.9
.8
.7
3
5
.9
.8
Temperature, °C
30
4
.02
.05
n-Nonane
1
7
400
.3 .1
.09
.08
.07
.2
.06
.4
0
ne
8
.5
1.5
.03
.1
.09
.08
.07
.06
.005
1
.001
.004
.01
8
0
0
.0
.009
.003
.008
6
.000
.007
.006
.002
5
0
.0
.04
cta
n-O
300
5
.015
10
n-Heptane
6
10
9
40
1.5
.15
.5
.15
.4
.6
2
.02
.05
.6 .2
.7
7
250
700
800
2
8
50
600
10
.9
.8
3
.2
n-Hexane
10
9
15
60
3
20
.004
.005
.01
.009
.008
.006
.007
.006
.03
.1
.09
.08
.07
.06
.3
.003
.015
.04
.4
.4
1
.9.3
.8
.7
4
4
20
70
200
5
.15
n-Pentane
6
15
80
5 20
.05
.5
.6
1.5.5
6
.06
.2
.6
Isopentane
30
.8
2 .7
–30
–40
–50
.007
.01
n-Butane
20
100
90
150
8 30
7
9
8
7
Isobutane
25
40
150
Propylene
A
101.3
110
–60
–70
FIG. 2-10 K values (K = y/x) in light-hydrocarbon systems. (a) Low-temperature range. (b) High-temperature range. [C.L.
DePriester, Chem. Eng. Prog. Symp., Ser. 7, 49: 1 (1953); converted to SI units by D.B. Dadyburjor, Chem. Eng. Prog. 74: 4 (1978).]
2-226
THERMODYnAMIC PROPERTIES
0
25
150
200
250
300
20
FIG. 2-10
n-Nonane
n-Decane
20
30
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
.001
n-Octane
.005
n-Heptane
Methane
5000
40
n-Hexane
3000
3500
4000
50
Isopentane
n-Pentane
2500
60
Isobutane
n-Butane
2000
70
90
60
80
Propylene
Propane
1500
0
10
Ethane
600
700
800
900
1000
0
Ethylene
500
Pressure, kPa
400
11
0
2
3
5
8
4
1.5
10 76
2
9
15
3
1
30
8 5
0
0
1.5
0
0
4
5
0
1
15
.8
7
70
20
4
90
2
.6
6
10
80
1
20
60 40
3
.5
20
9
5
30
1.5
70
0
8
10
.4
15
50 0
4
7
15 8
3
2
.3
15
60
1 .5
6
7
3 1.5 .9
.4
20
40
.8
.2
5
0
6
5
10
.7
9 5
.6 .3
20
4
2
100
10
1
8
15 9
.9
.5
4
30
.1
.2
90
7
3
40
8
1.5 .8
.4
15
.08
.7
6
.15
80
7
3
.6
.06
.3
5
10 6
70
.5
1.
.05
2
.1
30
.9
9 5
20 10
.04
5
.4
2
.8
.2 .08
60
9
8
1.5 .7
.03
4
.3
.06
8
3
.15
7
.6
50
15
1.5
.05
7
.5
.02
6
20
.1
3
.04
.2 .1
.9
6
.09
.015
.4
5
40
2 1
.08 .03
.8
9
.15 .07
10 5
.7
.01
15
.3
4 2
.06
1.5
9
.6
.008
7
4
30
.1 .05 .02
8
.5
6
.006
9 .04
.0
.2
1.0
3
.015 .005
7
.08
1 5
.4
10
3
.07
.004
.9
.03
.15
6
9
6
.0
.8 4
.01
.3
8
.009 .003
.05
1
2
.7
20
5
.02 .008
.9
3
7
.1
2
.007
.04
.6
.8
.09
02
.006 .0
6
.2
8
1.5 .7
.0
.015
4
.5
3
.005 .0015
.07 .0
1.5
15
2
.6
5
.4
.15
.06
4
.01 .00
3
.5
.05
1
.02 .009
1.5
4
3 .001
8
.00
.00
.3
.9
1
.1
.04
.9
.8 .4
15 .007
10
.0
9
.0
.25
.006
.8
9
.08
.7
3
.1
2
.002
.03
.3
.7
.07
.09
.005
8
.6
.01
8
.0
.06
.6
7
.009 .004
1.5
.5
.02 .008
.15
.05
2
.5
6
.06
.007
.2
.4
.003 01
.0
.04
.015 .006
.05
5
.4
1.5
.005
1
.1
.15
.3
3
.0
.9
.09
4
.004 .002
.01
.3
.25
.08
.8
.009
.03
.008
.02
.003 .015
.1
.06
.007
3
06
.0
.015
.02
15
Temperature, °C
B
101.3
110
0
–5
(Continued)
TABLE 2-123 Composition of Selected Refrigerant Mixtures*
Composition, mass%
Mixed Product
Name
R-32
R-125
R-134a
R-143a
R-404A
R-407C
R-410A
Property
Table/Figure
2-126, Fig. 2-12
2-127, Fig. 2-13
2-128, Fig. 2-14
2-129
2-130
2-131, Fig. 2-15
2-132
R-32
R-125
R-134a
R-143a
100
100
100
23
50
44
25
50
4
52
100
52
Ozone
Depletion
Potential (ODP)†
Global Warming
Potential (GWP)‡
(100 year)
0
0
0
0
0
0
0
650
3400
1300
4300
3300
1600
2088
*All products listed here are HFCs (hydrofluorocarbons), the primary replacement for hydrochlorofluorocarbons (HCFCs) like R-22.
†
The ODP of the old CFC refrigerants R-11 and R-12 is 1.
‡
CO2 is the GWP reference: GWP of CO2 = 1.
2-227
2-228
TABLE 2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane
Temperature
K
Pressure
MPa
115.73
120.00
135.00
150.00
165.00
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
369.30
3.7947E-07
9.9588E-07
1.7187E-05
0.00015627
0.00089946
0.0037009
0.011835
0.031218
0.070909
0.14319
0.26329
0.44888
0.71966
1.0970
1.6039
2.2661
3.1130
4.1837
4.9900
115.73
120.00
135.00
150.00
165.00
180.00
195.00
210.00
225.00
240.00
255.00
270.00
285.00
300.00
315.00
330.00
345.00
360.00
369.30
3.7947E-07
9.9588E-07
1.7187E-05
0.00015627
0.00089946
0.0037009
0.011835
0.031218
0.070909
0.14319
0.26329
0.44888
0.71966
1.0970
1.6039
2.2661
3.1130
4.1837
4.9900
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Saturated Properties
19.907
19.777
19.325
18.873
18.420
17.963
17.500
17.028
16.542
16.036
15.506
14.944
14.341
13.686
12.956
12.114
11.069
9.5229
6.0582
3.9436E-07
9.9813E-07
1.5313E-05
0.00012533
0.00065634
0.0024808
0.0073561
0.018161
0.038991
0.075182
0.13342
0.22208
0.35201
0.53822
0.80363
1.1882
1.7777
2.8529
6.0582
0.050235
0.050564
0.051747
0.052985
0.054289
0.055670
0.057141
0.058726
0.060453
0.062359
0.064493
0.066919
0.069730
0.073070
0.077181
0.082547
0.090340
0.10501
0.16506
2,535,700.
1,001,900.
65,305.
7,979.0
1,523.6
403.09
135.94
55.062
25.647
13.301
7.4950
4.5029
2.8409
1.8580
1.2443
0.84159
0.56253
0.35052
0.16506
2.5595
2.9559
4.3400
5.7179
7.0951
8.4715
9.8483
11.230
12.622
14.034
15.472
16.945
18.462
20.034
21.676
23.418
25.325
27.613
30.901
2.5595
2.9559
4.3400
5.7179
7.0951
8.4717
9.8490
11.232
12.627
14.043
15.489
16.975
18.513
20.114
21.800
23.605
25.606
28.053
31.725
0.0065813
0.0099451
0.020814
0.030493
0.039243
0.047227
0.054574
0.061399
0.067804
0.073877
0.079692
0.085308
0.090782
0.096166
0.10152
0.10696
0.11267
0.11931
0.12907
0.061918
0.061567
0.060123
0.059099
0.058356
0.057679
0.057097
0.056707
0.056579
0.056737
0.057171
0.057856
0.058767
0.059887
0.061218
0.062814
0.064858
0.068488
0.092976
0.092700
0.091960
0.091824
0.091789
0.091751
0.091898
0.092431
0.093482
0.095120
0.097391
0.10037
0.10424
0.10941
0.11688
0.12929
0.15550
0.25950
1410.9
1388.4
1312.3
1239.0
1166.5
1095.0
1024.5
954.55
884.79
814.96
744.97
674.69
603.91
532.11
458.37
381.15
298.16
201.90
0
27.807
27.929
28.373
28.840
29.329
29.836
30.357
30.885
31.411
31.928
32.428
32.900
33.335
33.717
34.021
34.207
34.184
33.661
30.901
28.769
28.927
29.495
30.087
30.699
31.328
31.966
32.603
33.229
33.833
34.401
34.922
35.380
35.755
36.017
36.114
35.935
35.127
31.725
0.23305
0.22637
0.20715
0.19295
0.18230
0.17421
0.16800
0.16317
0.15937
0.15634
0.15386
0.15178
0.14996
0.14830
0.14666
0.14486
0.14261
0.13896
0.12907
0.028465
0.028872
0.030386
0.031990
0.033655
0.035388
0.037218
0.039177
0.041300
0.043615
0.046138
0.048881
0.051851
0.055064
0.058574
0.062516
0.067254
0.074178
0.036779
0.037186
0.038703
0.040316
0.042018
0.043849
0.045881
0.048204
0.050920
0.054144
0.058023
0.062763
0.068713
0.076534
0.087659
0.10579
0.14389
0.29995
119.91
121.91
128.58
134.79
140.59
145.98
150.87
155.15
158.70
161.35
162.96
163.38
162.45
159.98
155.73
149.36
140.39
127.92
0
−0.44463
−0.44526
−0.44448
−0.43872
−0.43084
−0.42063
−0.40608
−0.38505
−0.35555
−0.31561
−0.26263
−0.19248
−0.097827
0.035333
0.23608
0.57205
1.2334
3.0745
10.366
398.80
367.18
269.83
197.57
146.30
110.28
84.902
66.865
53.872
44.348
37.240
31.852
27.725
24.549
22.102
20.201
18.613
16.641
10.366
Single-Phase Properties
150.00
232.06
0.10000
0.10000
232.06
250.00
350.00
450.00
550.00
0.10000
0.10000
0.10000
0.10000
0.10000
150.00
250.00
296.57
1.0000
1.0000
1.0000
296.57
350.00
450.00
550.00
1.0000
1.0000
1.0000
1.0000
150.00
250.00
350.00
450.00
550.00
5.0000
5.0000
5.0000
5.0000
5.0000
5.7167
13.284
5.7220
13.290
0.030484
0.070699
0.059102
0.056618
0.091820
0.094177
1239.3
851.94
−0.43876
−0.33819
31.656
32.442
37.325
43.093
49.620
33.517
34.465
40.211
46.822
54.186
0.15786
0.16180
0.18105
0.19762
0.21238
0.042364
0.043860
0.053191
0.061672
0.068475
0.052366
0.053391
0.061845
0.070141
0.076877
160.06
166.39
196.16
221.08
243.30
49.032
38.154
13.439
6.7638
4.0604
0.052952
0.063648
0.072248
5.7053
14.961
19.669
5.7582
15.024
19.741
0.030408
0.077665
0.094938
0.059134
0.057020
0.059612
0.091780
0.096318
0.10807
1241.8
773.25
548.68
2.0425
2.6523
3.6110
4.5027
33.635
36.754
42.774
49.400
35.677
39.407
46.385
53.903
0.14867
0.16025
0.17776
0.19283
0.054305
0.055369
0.062289
0.068737
0.074523
0.068138
0.072300
0.077971
160.70
184.85
216.22
241.16
25.205
14.183
6.8582
4.0624
18.931
15.837
11.141
1.6422
1.1832
0.052823
0.063142
0.089759
0.60893
0.84520
5.6555
14.822
25.585
41.131
48.377
5.9197
15.138
26.034
44.175
52.603
0.030074
0.077105
0.11341
0.16067
0.17760
0.059277
0.057135
0.064765
0.065284
0.069855
0.091614
0.095206
0.14356
0.087278
0.083655
1253.0
797.37
317.33
194.56
232.93
−0.44109
−0.30700
1.0314
7.0507
3.9600
18.874
16.306
0.053734
0.049441
0.034652
0.026819
0.021901
18.885
15.711
13.841
0.48960
0.37703
0.27693
0.22209
0.052982
0.061325
18.610
20.226
28.859
37.287
45.660
−0.43921
−0.28642
0.00029448
150.00
250.00
350.00
450.00
550.00
10.000
10.000
10.000
10.000
10.000
18.987
15.982
12.008
4.2433
2.5432
0.052667
0.062569
0.083275
0.23566
0.39321
5.5953
14.663
24.782
38.423
47.019
6.1220
15.289
25.615
40.780
50.951
0.029665
0.076450
0.11098
0.14893
0.16944
0.059460
0.057274
0.063647
0.068870
0.071068
0.091420
0.094054
0.11843
0.12461
0.092204
1266.7
825.41
412.24
184.82
229.21
−0.44331
−0.32844
0.39255
5.5220
3.5059
150.00
250.00
350.00
450.00
550.00
30.000
30.000
30.000
30.000
30.000
19.198
16.469
13.518
10.241
7.3810
0.052089
0.060719
0.073976
0.097648
0.13548
5.3741
14.132
23.279
33.086
42.738
6.9367
15.953
25.499
36.016
46.802
0.028113
0.074181
0.10621
0.13259
0.15425
0.060251
0.057799
0.063170
0.069234
0.073417
0.090769
0.091018
0.10053
0.10864
0.10533
1318.0
921.00
603.47
392.35
317.51
−0.45090
−0.38542
−0.13764
0.40072
0.89994
150.00
250.00
350.00
450.00
550.00
60.000
60.000
60.000
60.000
60.000
19.480
17.029
14.650
12.381
10.405
0.051336
0.058724
0.068258
0.080770
0.096108
5.0916
13.533
22.111
31.083
40.152
8.1717
17.056
26.206
35.929
45.919
0.026007
0.071434
0.10216
0.12657
0.14662
0.061560
0.058519
0.063912
0.070220
0.075020
0.089983
0.088686
0.094730
0.099099
0.10030
1384.9
1034.6
764.59
589.21
492.11
−0.45992
−0.42947
−0.31532
−0.17799
−0.055349
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Kamei, A., Beyerlein, S. W., and Jacobsen, R. T., “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophys. 16:1155–1164, 1995. Validated equations
for the viscosity and thermal conductivity are not currently available for this fluid.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainties of the equation of state are 0.1% in density, 1% in heat capacity, and 0.3% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%.
2-229
2-230
FIG. 2-11
Pressure-enthalpy diagram for Refrigerant 22. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference
Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of
state of Kamei, A., S. W. Beyerlein, and R. T. Jacobsen, “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophysics 16:1155–1164, 1995.
TABLE 2-125
Thermodynamic Properties of R-32, Difluoromethane
Temperature
K
Pressure
MPa
136.34
140.00
150.00
160.00
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
351.26
4.8000E-05
8.3535E-05
0.00032474
0.0010410
0.0028536
0.0068782
0.014904
0.029545
0.054344
0.093819
0.15345
0.23965
0.35967
0.52157
0.73415
1.0069
1.3501
1.7749
2.2934
2.9194
3.6686
4.5614
5.6311
5.7826
136.34
140.00
150.00
160.00
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
351.26
4.8000E-05
8.3535E-05
0.00032474
0.0010410
0.0028536
0.0068782
0.014904
0.029545
0.054344
0.093819
0.15345
0.23965
0.35967
0.52157
0.73415
1.0069
1.3501
1.7749
2.2934
2.9194
3.6686
4.5614
5.6311
5.7826
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
−0.99220
−0.68946
0.13324
0.95053
1.7640
2.5753
3.3862
4.1983
5.0135
5.8337
6.6608
7.4969
8.3443
9.2056
10.084
10.983
11.908
12.866
13.867
14.930
16.088
17.428
19.453
20.836
−0.99220
−0.68946
0.13325
0.95057
1.7641
2.5756
3.3868
4.1995
5.0158
5.8377
6.6675
7.5077
8.3609
9.2303
10.120
11.034
11.979
12.963
13.998
15.107
16.328
17.760
19.977
21.546
21.981
22.076
22.335
22.593
22.850
23.103
23.350
23.588
23.816
24.032
24.234
24.421
24.590
24.738
24.860
24.952
25.006
25.011
24.950
24.797
24.503
23.943
22.380
20.836
23.115
23.239
23.581
23.921
24.258
24.589
24.910
25.219
25.513
25.788
26.042
26.272
26.474
26.643
26.775
26.862
26.894
26.858
26.735
26.491
26.068
25.316
23.365
21.546
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
−0.0054608
−0.0032696
0.0024067
0.0076815
0.012613
0.017251
0.021635
0.025800
0.029778
0.033594
0.037271
0.040830
0.044291
0.047671
0.050989
0.054264
0.057517
0.060775
0.064076
0.067477
0.071088
0.075179
0.081343
0.085769
0.055447
0.054980
0.053793
0.052740
0.051818
0.051021
0.050345
0.049783
0.049333
0.048988
0.048747
0.048604
0.048559
0.048610
0.048761
0.049019
0.049399
0.049934
0.050685
0.051776
0.053487
0.056594
0.066340
0.082847
0.082588
0.081975
0.081513
0.081215
0.081087
0.081137
0.081373
0.081803
0.082443
0.083313
0.084442
0.085874
0.087676
0.089947
0.092852
0.096659
0.10185
0.10938
0.12140
0.14404
0.20457
1.2085
1414.4
1395.1
1342.3
1289.9
1237.6
1185.7
1133.8
1082.1
1030.4
978.59
926.62
874.35
821.65
768.33
714.18
658.88
602.05
543.11
481.27
415.41
343.84
263.77
163.70
0
−0.33760
−0.33728
−0.33542
−0.33191
−0.32650
−0.31891
−0.30886
−0.29600
−0.27988
−0.25996
−0.23550
−0.20551
−0.16864
−0.12292
−0.065518
0.0079177
0.10428
0.23517
0.42163
0.70602
1.1876
2.1660
5.4955
8.0731
242.91
241.74
237.64
232.45
226.39
219.64
212.37
204.70
196.75
188.62
180.39
172.14
163.92
155.78
147.75
139.86
132.11
124.48
116.94
109.42
101.80
94.166
97.067
0.17135
0.16765
0.15872
0.15125
0.14493
0.13955
0.13492
0.13090
0.12738
0.12428
0.12151
0.11901
0.11674
0.11464
0.11268
0.11079
0.10895
0.10709
0.10516
0.10305
0.10060
0.097403
0.091024
0.085769
0.025987
0.026110
0.026507
0.027014
0.027667
0.028505
0.029560
0.030843
0.032341
0.034016
0.035821
0.037709
0.039648
0.041621
0.043631
0.045693
0.047840
0.050119
0.052598
0.055390
0.058707
0.063103
0.071998
0.034319
0.034451
0.034889
0.035477
0.036272
0.037336
0.038728
0.040483
0.042613
0.045105
0.047943
0.051127
0.054696
0.058741
0.063434
0.069063
0.076110
0.085424
0.098649
0.11948
0.15836
0.26199
1.9028
169.60
171.76
177.47
182.88
187.97
192.69
197.00
200.85
204.20
206.99
209.19
210.73
211.57
211.65
210.90
209.26
206.64
202.95
198.02
191.66
183.49
172.68
154.59
0
Entropy
kJ/(mol⋅K)
Saturated Properties
27.473
27.302
26.835
26.364
25.889
25.409
24.921
24.424
23.916
23.394
22.858
22.303
21.726
21.124
20.491
19.820
19.102
18.323
17.460
16.477
15.299
13.740
10.732
8.1501
4.2353E-05
7.1788E-05
0.00026061
0.00078411
0.0020270
0.0046295
0.0095503
0.018112
0.032028
0.053428
0.084890
0.12949
0.19093
0.27370
0.38340
0.52726
0.71503
0.96054
1.2848
1.7233
2.3442
3.3211
5.7166
8.1501
0.036399
0.036627
0.037265
0.037930
0.038626
0.039357
0.040127
0.040944
0.041814
0.042745
0.043749
0.044838
0.046028
0.047340
0.048802
0.050454
0.052350
0.054577
0.057273
0.060691
0.065364
0.072779
0.093180
0.12270
23,611.
13,930.
3,837.2
1,275.3
493.35
216.01
104.71
55.213
31.223
18.717
11.780
7.7224
5.2375
3.6537
2.6083
1.8966
1.3985
1.0411
0.77830
0.58029
0.42658
0.30111
0.17493
0.12270
881.12
769.01
541.12
391.73
291.02
221.02
170.81
133.79
106.00
84.924
68.870
56.605
47.194
39.922
34.246
29.758
26.148
23.187
20.693
18.510
16.477
14.312
10.637
8.0731
6.9492
6.9554
7.0006
7.0875
7.2166
7.3887
7.6049
7.8668
8.1765
8.5374
8.9546
9.4365
9.9965
10.656
11.449
12.431
13.691
15.376
17.748
21.309
27.173
38.601
87.141
(Continued)
2-231
2-232
TABLE 2-125
Temperature
K
Thermodynamic Properties of R-32, Difluoromethane (Continued )
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Single-Phase Properties
0.037263
0.042866
0.13226
5.9359
0.13599
5.9402
0.0024002
0.034057
0.053795
0.048953
0.081971
0.082538
1342.7
972.15
−0.33547
−0.25719
237.67
187.60
0.056727
0.055592
0.040576
0.032244
26.851
23.159
19.836
17.628
17.988
24.645
31.013
0.037243
0.043179
0.050414
24.058
24.191
26.760
29.631
0.12350
6.2265
10.962
25.821
25.989
29.224
32.733
0.16075
6.2697
11.013
0.12392
0.12467
0.13708
0.14749
0.0023417
0.035360
0.054190
0.034234
0.033681
0.035327
0.041082
0.053807
0.048867
0.049012
0.045439
0.044513
0.044188
0.049630
0.081935
0.082690
0.092777
207.30
209.39
241.95
267.64
1345.7
957.47
660.15
82.688
76.114
25.024
12.117
−0.33584
−0.25084
0.0060372
8.5859
8.7199
12.643
18.907
237.89
185.10
140.04
0.52357
0.46100
0.33917
1.9100
2.1692
2.9484
24.951
25.950
29.227
26.861
28.120
32.175
0.11084
0.11518
0.12727
0.045646
0.041298
0.042549
0.068922
0.057916
0.053538
209.31
223.83
259.50
0.037154
0.042923
0.053448
0.078078
0.085198
6.1394
12.637
18.130
0.27097
6.3541
12.905
18.520
0.0020846
0.034970
0.060001
0.077304
0.053863
0.048922
0.049679
0.059015
0.081784
0.082027
0.096911
0.28240
1358.9
978.81
586.17
224.84
0.25071
0.43051
23.524
26.928
24.777
29.080
0.095475
0.10755
0.065786
0.050835
0.39574
0.090625
166.61
218.44
150.00
221.24
0.10000
0.10000
26.836
23.329
221.24
225.00
300.00
375.00
150.00
225.00
279.77
0.10000
0.10000
0.10000
0.10000
1.0000
1.0000
1.0000
279.77
300.00
375.00
1.0000
1.0000
1.0000
150.00
225.00
300.00
344.33
5.0000
5.0000
5.0000
5.0000
344.33
375.00
5.0000
5.0000
26.915
23.298
18.710
12.808
3.9887
2.3228
29.848
23.889
11.929
−0.33741
−0.26135
0.13431
2.9944
13.148
10.800
12.406
13.334
19.059
238.83
187.71
128.72
91.412
48.235
26.239
150.00
225.00
300.00
375.00
10.000
10.000
10.000
10.000
26.993
23.461
19.196
10.448
0.037047
0.042625
0.052094
0.095714
0.038702
6.0369
12.346
21.112
0.40917
6.4632
12.867
22.069
0.0017692
0.034504
0.058997
0.085980
0.053932
0.048996
0.049538
0.057265
0.081608
0.081303
0.092105
0.21222
1375.0
1004.1
639.69
231.14
−0.33924
−0.27287
0.031716
3.5190
239.97
190.81
134.49
77.284
150.00
225.00
300.00
375.00
30.000
30.000
30.000
30.000
27.285
24.030
20.517
16.472
0.036650
0.041614
0.048739
0.060708
−0.13357
5.6813
11.542
17.786
0.96593
6.9297
13.004
19.607
0.00056834
0.032836
0.056105
0.075712
0.054209
0.049307
0.049670
0.052941
0.081027
0.079197
0.083697
0.093069
1436.1
1094.1
789.57
536.98
−0.34524
−0.30661
−0.15824
0.21392
244.02
201.89
152.78
112.94
225.00
300.00
375.00
70.000
70.000
70.000
24.916
22.090
19.309
0.040135
0.045270
0.051788
5.1400
10.583
16.127
7.9495
13.752
19.752
0.030109
0.052355
0.070195
0.049916
0.050281
0.053544
0.076915
0.078370
0.081767
1240.7
986.17
788.81
−0.34341
−0.28333
−0.18583
219.54
179.29
147.00
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Tillner-Roth, R., and Yokozeki, A., “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys. Chem.
Ref. Data 26(6):1273–1328, 1997. Validated equations for the viscosity are not currently available for this fluid. The source for thermal conductivity is unpublished; however, the fit uses the functional form found in
Marsh, K., Perkins, R., and Ramires, M. L. V., “Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data 47(4):932–940, 2002.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
For the equation of state, typical uncertainties are 0.05% for density, 0.02% for the vapor pressure, and 0.5% to 1% for the heat capacity and speed of sound in the liquid phase. In the vapor phase, the uncertainty
in the speed of sound is 0.02%. For thermal conductivity, the estimated uncertainty of the correlation is 5%, except for the dilute gas and points approaching critical where the uncertainty rises to 10%.
FIG. 2-12
Pressure-enthalpy diagram for Refrigerant 32. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference
Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of
state of Tillner-Roth, R., and A. Yokozeki, “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys.
Chem. Ref. Data 26(6): 1273–1328, 1997.
2-233
2-234
TABLE 2-126 Thermodynamic Properties of R-125, Pentafluoroethane
Temperature
K
Pressure
MPa
172.52
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
339.17
0.0029140
0.0056285
0.012328
0.024602
0.045417
0.078505
0.12833
0.20004
0.29934
0.43250
0.60624
0.82782
1.1050
1.4463
1.8610
2.3600
2.9579
3.6179
172.52
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
339.17
0.0029140
0.0056285
0.012328
0.024602
0.045417
0.078505
0.12833
0.20004
0.29934
0.43250
0.60624
0.82782
1.1050
1.4463
1.8610
2.3600
2.9579
3.6179
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
10.457
11.389
12.646
13.919
15.210
16.523
17.858
19.219
20.607
22.025
23.478
24.971
26.511
28.112
29.793
31.595
33.632
37.417
10.457
11.389
12.647
13.921
15.214
16.529
17.869
19.235
20.632
22.063
23.532
25.048
26.619
28.259
29.994
31.869
34.017
38.174
0.058837
0.064124
0.070919
0.077448
0.083750
0.089856
0.095792
0.10158
0.10725
0.11282
0.11830
0.12374
0.12916
0.13461
0.14015
0.14593
0.15231
0.16438
0.081329
0.082012
0.083102
0.084327
0.085644
0.087029
0.088472
0.089971
0.091529
0.093153
0.094843
0.096594
0.098430
0.10043
0.10274
0.10571
0.11043
0.12417
0.12500
0.12647
0.12825
0.13028
0.13254
0.13505
0.13785
0.14102
0.14468
0.14903
0.15440
0.16135
0.17099
0.18593
0.21395
0.29625
932.57
893.63
843.11
793.91
745.67
698.07
650.89
603.92
556.99
510.02
462.91
415.46
367.36
318.17
267.31
213.55
153.34
0
−0.38374
−0.37406
−0.35818
−0.33901
−0.31627
−0.28935
−0.25723
−0.21839
−0.17062
−0.11056
−0.032921
0.070972
0.21606
0.43036
0.77370
1.4029
2.9184
12.361
31.863
32.307
32.913
33.530
34.157
34.788
35.421
36.052
36.678
37.292
37.890
38.460
38.988
39.453
39.828
40.054
39.964
37.417
33.293
33.795
34.477
35.167
35.860
36.552
37.237
37.911
38.568
39.202
39.805
40.363
40.858
41.267
41.554
41.651
41.355
38.174
0.19120
0.18860
0.18582
0.18368
0.18207
0.18087
0.18000
0.17940
0.17900
0.17874
0.17857
0.17844
0.17826
0.17797
0.17744
0.17649
0.17454
0.16438
0.059815
0.061648
0.064126
0.066646
0.069223
0.071864
0.074575
0.077362
0.080230
0.083141
0.086003
0.088869
0.092050
0.095933
0.10077
0.10679
0.11481
0.068285
0.070217
0.072893
0.075712
0.078713
0.081939
0.085437
0.089271
0.093526
0.098283
0.10368
0.11025
0.11918
0.13255
0.15449
0.19725
0.32843
116.43
118.54
121.15
123.47
125.44
127.01
128.11
128.68
128.64
127.93
126.44
124.10
120.81
116.42
110.71
103.29
93.550
0
90.257
77.516
64.018
53.589
45.456
39.066
34.014
29.998
26.787
24.232
22.293
20.938
20.043
19.438
19.016
18.738
18.404
12.361
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
116.02
112.52
107.79
103.06
98.331
93.653
89.019
84.443
79.940
75.520
71.187
66.940
62.772
58.667
54.597
50.534
46.661
1152.4
957.54
768.40
631.00
527.00
445.76
380.67
327.41
283.01
245.39
213.02
184.73
159.60
136.86
115.81
95.602
74.602
Saturated Properties
14.086
13.885
13.613
13.336
13.052
12.762
12.461
12.150
11.824
11.481
11.117
10.724
10.295
9.8162
9.2637
8.5923
7.6744
4.7790
0.0020381
0.0037809
0.0078784
0.015031
0.026661
0.044514
0.070679
0.10763
0.15835
0.22645
0.31661
0.43510
0.59084
0.79742
1.0777
1.4778
2.1269
4.7790
0.070990
0.072020
0.073461
0.074988
0.076615
0.078360
0.080247
0.082305
0.084572
0.087098
0.089954
0.093245
0.097130
0.10187
0.10795
0.11638
0.13030
0.20925
490.65
264.49
126.93
66.529
37.508
22.465
14.148
9.2907
6.3153
4.4159
3.1585
2.2983
1.6925
1.2540
0.92787
0.67670
0.47016
0.20925
5.2349
5.7185
6.3724
7.0353
7.7081
8.3929
9.0929
9.8136
10.563
11.356
12.213
13.169
14.286
15.680
17.586
20.574
26.607
7.4339
7.7624
8.1999
8.6344
9.0657
9.4944
9.9221
10.353
10.791
11.246
11.732
12.266
12.884
13.638
14.635
16.104
18.766
Single-Phase Properties
200.00
224.79
0.10000
0.10000
224.79
300.00
400.00
500.00
0.10000
0.10000
0.10000
0.10000
200.00
286.46
1.0000
1.0000
286.46
300.00
400.00
500.00
1.0000
1.0000
1.0000
1.0000
200.00
300.00
400.00
500.00
5.0000
5.0000
5.0000
5.0000
13.916
17.160
13.924
17.168
0.077436
0.092721
0.084327
0.087714
0.12823
0.13371
794.34
675.42
−0.33920
−0.27468
35.092
41.155
50.746
61.864
36.881
43.613
54.054
66.012
0.18042
0.20616
0.23608
0.26271
0.073155
0.086960
0.10398
0.11764
0.083578
0.095910
0.11252
0.12607
127.60
149.16
172.25
192.24
36.498
13.603
5.6807
3.1093
0.074878
0.095673
13.888
25.960
13.963
26.055
0.077295
0.12724
0.084329
0.097767
0.12805
0.15865
799.42
384.49
−0.34145
0.15862
103.50
64.240
1.8842
2.0720
3.1466
4.0661
38.807
40.159
50.310
61.591
40.691
42.231
53.456
65.657
0.17833
0.18359
0.21585
0.24302
0.090862
0.092286
0.10520
0.11806
0.11564
0.11224
0.11626
0.12764
122.09
129.90
165.47
189.33
20.318
16.539
5.9354
3.1109
13.866
14.732
22.513
31.336
12.653
13.270
17.404
21.014
13.432
10.214
2.1222
1.3333
0.074450
0.097901
0.47120
0.75004
13.768
27.606
47.739
60.288
14.140
28.095
50.095
64.038
0.076686
0.13288
0.19593
0.22710
0.084364
0.099404
0.11164
0.12001
0.12732
0.15790
0.15240
0.13643
820.94
379.39
136.55
180.53
−0.35061
0.16755
6.6581
2.9952
105.29
62.727
27.340
33.551
671.00
155.81
22.244
23.530
13.337
12.619
0.055877
0.040689
0.030228
0.024108
13.355
10.452
0.53072
0.48261
0.31780
0.24593
0.074979
0.079245
17.897
24.576
33.082
41.479
103.09
91.425
8.7263
14.156
22.115
30.917
631.60
412.85
9.6994
13.041
17.070
20.691
638.78
168.19
200.00
300.00
400.00
500.00
10.000
10.000
10.000
10.000
13.522
10.597
5.5436
2.8438
0.073953
0.094369
0.18039
0.35165
13.626
27.096
43.724
58.555
14.366
28.039
45.528
62.072
0.075959
0.13109
0.18103
0.21813
0.084459
0.098728
0.11417
0.12198
0.12655
0.14971
0.19389
0.14925
845.71
441.85
165.42
183.47
−0.36040
−0.0032571
2.8474
2.4316
107.42
67.164
40.583
37.529
712.07
177.37
46.568
29.745
200.00
300.00
400.00
500.00
30.000
30.000
30.000
30.000
13.835
11.489
9.0272
6.8239
0.072281
0.087039
0.11078
0.14654
13.138
25.838
39.705
54.141
15.306
28.449
43.028
58.538
0.073355
0.12645
0.16830
0.20288
0.085197
0.098551
0.11217
0.12339
0.12439
0.13883
0.15193
0.15662
927.73
597.35
391.05
307.14
−0.38765
−0.23171
0.060756
0.34144
115.19
79.855
59.824
53.649
889.29
245.90
112.78
67.694
300.00
400.00
500.00
60.000
60.000
60.000
12.259
10.465
8.9121
0.081575
0.095559
0.11221
24.732
37.854
51.703
29.626
43.587
58.436
0.12196
0.16206
0.19516
0.10001
0.11339
0.12470
0.13426
0.14453
0.15193
735.32
563.68
471.23
−0.32748
−0.23451
−0.15582
93.938
75.022
67.810
338.04
173.26
113.08
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., and Jacobsen, R. T., “A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125),” J. Phys. Chem. Ref. Data 34(1):69–108, 2005. The
source for viscosity is Huber, M. L., and Laesecke, A., “Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa,” Ind. Eng. Chem. Res., 45(12):4447–4453, 2006.
The source for thermal conductivity is Perkins, R., and Huber, M. L., “Measurement and Correlation of the Thermal Conductivity of Pentafluoroethane (R125) from 190 K to 512 K at Pressures to 70 MPa,” J. Chem.
Eng. Data 51(3):898–904, 2006.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainty in density is 0.1% at temperatures from the triple point to 400 K at pressures up to 60 MPa, except in the critical region, where an uncertainty of 0.2% in pressure is generally attained. In the
limited region between 340 and 400 K and at pressures from 4 to 10 MPa, as well as for all states above 400 K, the uncertainty in density increases to 0.5%. At temperatures below 330 K and pressures below 30 MPa,
the uncertainty in density in the liquid phase may be as low as 0.04%. In the vapor and supercritical region, speed of sound data are represented within 0.05% at pressures below 1 MPa. The estimated uncertainty
for heat capacities is 0.5%, and the estimated uncertainty for the speed of sound in the liquid phase is 0.5% for T > 250 K. The estimated uncertainties of vapor pressures and saturated liquid densities calculated
using the Maxwell criterion are 0.1% for each property, and the estimated uncertainty for saturated vapor densities is 0.2%. The uncertainty in density increases as the critical point is approached, while the accompanying uncertainty in calculated pressures is 0.2%. The viscosity correlation has an estimated uncertainty of 3.0% along the saturation boundary in the liquid phase, and 0.8% in the vapor. For thermal conductivity, the estimated uncertainty of the correlation is 3%, except for the dilute gas and points approaching critical, where the uncertainty rises to 5%.
2-235
2-236
FIG. 2-13
Pressure-enthalpy diagram for Refrigerant 125.
TABLE 2-127
Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane
Temperature
K
Pressure
MPa
169.85
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
374.21
0.00038956
0.00039617
0.0011275
0.0028170
0.0063130
0.012910
0.024433
0.043287
0.072481
0.11561
0.17684
0.26082
0.37271
0.51805
0.70282
0.93340
1.2166
1.5599
1.9715
2.4611
3.0405
3.7278
4.0591
169.85
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
360.00
370.00
374.21
0.00038956
0.00039617
0.0011275
0.0028170
0.0063130
0.012910
0.024433
0.043287
0.072481
0.11561
0.17684
0.26082
0.37271
0.51805
0.70282
0.93340
1.2166
1.5599
1.9715
2.4611
3.0405
3.7278
4.0591
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
7.2907
7.3088
8.5179
9.7328
10.957
12.194
13.444
14.710
15.992
17.293
18.613
19.956
21.322
22.716
24.141
25.603
27.108
28.667
30.297
32.029
33.932
36.283
38.947
7.2907
7.3088
8.5179
9.7330
10.958
12.195
13.446
14.713
15.997
17.301
18.627
19.976
21.352
22.759
24.201
25.685
27.219
28.816
30.495
32.293
34.289
36.797
39.756
0.042100
0.042207
0.049117
0.055686
0.061966
0.067999
0.073815
0.079441
0.084899
0.090209
0.095389
0.10046
0.10543
0.11032
0.11516
0.11996
0.12475
0.12956
0.13446
0.13952
0.14496
0.15159
0.15938
0.080831
0.080824
0.080732
0.081114
0.081784
0.082633
0.083595
0.084636
0.085734
0.086879
0.088067
0.089298
0.090576
0.091908
0.093303
0.094777
0.096352
0.098067
0.10001
0.10241
0.10601
0.11372
0.12079
0.12079
0.12112
0.12193
0.12303
0.12434
0.12582
0.12746
0.12927
0.13126
0.13348
0.13597
0.13883
0.14216
0.14615
0.15108
0.15740
0.16598
0.17863
0.20012
0.24863
0.52085
32.764
32.772
33.287
33.821
34.371
34.934
35.508
36.090
36.675
37.261
37.844
38.420
38.986
39.538
40.069
40.573
41.038
41.451
41.785
41.994
41.973
41.323
38.947
34.175
34.184
34.781
35.395
36.023
36.662
37.308
37.956
38.602
39.242
39.870
40.482
41.073
41.636
42.166
42.653
43.083
43.438
43.687
43.775
43.576
42.617
39.756
0.20038
0.20029
0.19502
0.19075
0.18729
0.18451
0.18228
0.18050
0.17909
0.17797
0.17709
0.17640
0.17586
0.17542
0.17504
0.17469
0.17432
0.17387
0.17326
0.17232
0.17075
0.16731
0.15938
0.051318
0.051354
0.053742
0.056118
0.058489
0.060874
0.063296
0.065783
0.068357
0.071031
0.073812
0.076698
0.079686
0.082776
0.085974
0.089297
0.092780
0.096484
0.10052
0.10510
0.11074
0.11928
0.059719
0.059756
0.062208
0.064682
0.067201
0.069802
0.072534
0.075455
0.078618
0.082078
0.085888
0.090115
0.094850
0.10023
0.10650
0.11404
0.12355
0.13638
0.15548
0.18870
0.26594
0.70016
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
1120.0
1119.2
1068.3
1017.7
967.61
918.33
869.85
822.11
775.00
728.39
682.14
636.12
590.17
544.15
497.89
451.23
404.00
355.90
306.37
254.06
196.05
127.23
0
−0.38145
−0.38136
−0.37370
−0.36352
−0.35119
−0.33678
−0.32011
−0.30082
−0.27839
−0.25204
−0.22073
−0.18299
−0.13675
−0.079015
−0.0052732
0.091533
0.22306
0.41006
0.69376
1.1714
2.1419
5.1434
11.931
145.24
145.15
139.12
133.32
127.74
122.36
117.17
112.14
107.27
102.53
97.922
93.414
88.995
84.644
80.341
76.063
71.781
67.464
63.075
58.581
54.062
51.767
2153.6
2139.7
1479.1
1106.2
867.31
702.27
582.15
491.22
420.20
363.25
316.57
277.54
244.34
215.64
190.46
168.04
147.78
129.20
111.81
95.095
78.146
57.956
Saturated Properties
15.594
15.590
15.331
15.069
14.804
14.535
14.262
13.984
13.699
13.406
13.104
12.791
12.465
12.121
11.758
11.368
10.945
10.478
9.9483
9.3237
8.5279
7.2558
5.0171
0.00027611
0.00028055
0.00075481
0.0017896
0.0038201
0.0074704
0.013574
0.023188
0.037603
0.058360
0.087278
0.12651
0.17865
0.24685
0.33512
0.44874
0.59505
0.78498
1.0363
1.3818
1.8973
2.8805
5.0171
0.064126
0.064142
0.065228
0.066362
0.067550
0.068798
0.070116
0.071512
0.072999
0.074593
0.076311
0.078179
0.080227
0.082499
0.085050
0.087965
0.091364
0.095439
0.10052
0.10725
0.11726
0.13782
0.19932
3621.7
3564.4
1324.8
558.79
261.77
133.86
73.669
43.125
26.593
17.135
11.458
7.9043
5.5976
4.0511
2.9840
2.2285
1.6805
1.2739
0.96498
0.72368
0.52707
0.34717
0.19932
126.79
126.84
130.05
133.11
135.98
138.63
141.01
143.06
144.73
145.98
146.75
146.99
146.63
145.61
143.88
141.33
137.86
133.33
127.57
120.33
111.25
99.370
0
373.57
370.78
234.43
160.10
116.94
90.215
72.584
60.236
51.130
44.137
38.613
34.169
30.561
27.621
25.230
23.301
21.768
20.578
19.687
19.033
18.448
17.050
11.931
3.0801
3.0921
3.8934
4.6952
5.4978
6.3018
7.1080
7.9176
8.7324
9.5551
10.389
11.241
12.118
13.035
14.011
15.081
16.303
17.780
19.711
22.525
27.365
40.137
6.8294
6.8353
7.2319
7.6253
8.0147
8.3993
8.7786
9.1524
9.5209
9.8853
10.247
10.611
10.980
11.363
11.771
12.219
12.735
13.358
14.164
15.300
17.140
21.336
(Continued)
2-237
2-238
TABLE 2-127
Temperature
K
Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane (Continued )
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Entropy
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
mPa⋅s
Int. energy
kJ/mol
Enthalpy
kJ/mol
10.955
16.873
10.962
16.880
0.061955
0.088519
0.081787
0.086506
0.12301
0.13060
968.03
743.31
−0.35132
−0.26099
37.073
39.124
45.154
52.096
39.037
41.348
48.032
55.610
0.17830
0.18716
0.20860
0.22818
0.070161
0.073781
0.086248
0.098386
0.080931
0.083445
0.095065
0.10695
145.63
154.76
175.31
192.97
46.198
29.047
12.552
6.7852
0.067479
0.079009
0.088775
10.933
20.597
25.980
11.001
20.676
26.069
0.061846
0.10281
0.12117
0.081812
0.089915
0.095165
0.12291
0.13695
0.15252
972.08
619.10
439.31
−0.35256
−0.16746
0.12101
128.11
91.627
74.978
2.0729
2.5555
3.3352
40.695
44.290
51.597
42.768
46.846
54.933
0.17460
0.18694
0.20785
0.090164
0.090315
0.099891
0.11623
0.10603
0.11116
140.54
159.63
185.14
22.877
13.885
7.0297
15.374
17.989
23.806
12.343
13.936
16.917
14.880
12.804
9.8674
2.0736
0.067202
0.078103
0.10134
0.48225
10.839
20.385
31.397
48.647
11.175
20.776
31.904
51.058
0.061371
0.10203
0.13765
0.18734
0.081929
0.089864
0.10066
0.10791
0.12246
0.13495
0.17178
0.15381
989.55
651.41
320.01
148.25
−0.35768
−0.19924
0.59952
7.9048
129.56
94.015
63.012
28.574
915.11
277.35
109.32
20.974
966.05
295.02
128.79
46.711
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Single-Phase Properties
200.00
246.79
0.10000
0.10000
246.79
275.00
350.00
425.00
0.10000
0.10000
0.10000
0.10000
200.00
275.00
312.54
1.0000
1.0000
1.0000
312.54
350.00
425.00
1.0000
1.0000
1.0000
200.00
275.00
350.00
425.00
5.0000
5.0000
5.0000
5.0000
14.805
13.501
0.050898
0.044972
0.034753
0.028455
14.819
12.657
11.264
0.48242
0.39132
0.29983
0.067543
0.074068
19.647
22.236
28.775
35.143
127.78
104.04
9.2899
11.540
17.537
23.539
868.18
380.27
9.7687
10.906
13.823
16.650
876.60
262.84
162.71
200.00
275.00
350.00
425.00
10.000
10.000
10.000
10.000
14.954
12.967
10.478
6.1370
0.066874
0.077121
0.095440
0.16295
10.727
20.149
30.642
43.563
11.395
20.920
31.597
45.193
0.060796
0.10115
0.13537
0.17038
0.082085
0.089868
0.099573
0.11141
0.12196
0.13304
0.15486
0.20870
1010.3
687.36
400.60
177.89
−0.36339
−0.22964
0.21924
3.0434
131.31
96.744
68.919
44.888
200.00
275.00
350.00
425.00
30.000
30.000
30.000
30.000
15.216
13.479
11.662
9.7202
0.065720
0.074190
0.085750
0.10288
10.326
19.398
29.071
39.385
12.298
21.624
31.644
42.471
0.058683
0.098210
0.13038
0.15838
0.082769
0.090220
0.098885
0.10808
0.12047
0.12865
0.13885
0.14967
1084.1
801.47
582.52
425.63
−0.38053
−0.30014
−0.15240
0.10364
137.79
105.87
82.955
67.154
1211.0
364.87
183.26
107.03
275.00
350.00
425.00
70.000
70.000
70.000
14.181
12.797
11.494
0.070517
0.078141
0.087004
18.373
27.492
37.066
23.310
32.961
43.157
0.093839
0.12484
0.15121
0.091314
0.099542
0.10829
0.12519
0.13226
0.13963
962.41
787.10
661.39
−0.35619
−0.30093
−0.23655
119.84
99.868
86.640
521.91
277.09
181.77
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Tillner-Roth, R., and Baehr, H. D., “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 K to 455 K at Pressures up to 70
MPa,” J. Phys. Chem. Ref. Data 23:657–729, 1994. The source for viscosity is Huber, M. L., Laesecke, A., and Perkins, R. A., “Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a,” Ind. Eng. Chem. Res. 42:3163–3178, 2003. The source for thermal conductivity is Perkins, R. A., Laesecke, A., Howley, J., Ramires, M. L. V., Gurova, A. N., and Cusco, L., “Experimental
Thermal Conductivity Values for the IUPAC Round-Robin Sample of 1,1,1,2-Tetrafluoroethane (R134a),” NISTIR, 2000.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty
in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K,
the uncertainty is 8%. The uncertainty in thermal conductivity is 5%.
FIG. 2-14 Pressure-enthalpy diagram for Refrigerant 134a. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference
Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of
state of Tillner-Roth, R., and H. D. Baehr, “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) Covering Temperatures from 170 K to 455 K at Pressures
up to 70 MPa,” J. Phys. Chem. Ref. Data 23(5): 657–729, 1994.
2-239
2-240
TABLE 2-128
Temperature
K
Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
−0.43936
−0.42914
−0.41402
−0.39585
−0.37472
−0.35034
−0.32211
−0.28906
−0.24979
−0.20231
−0.14368
−0.069548
0.026895
0.15683
0.34002
0.61491
1.0681
1.9469
4.3897
12.397
Saturated Properties
161.34
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
345.86
0.0010749
0.0025084
0.0059324
0.012629
0.024624
0.044602
0.075908
0.12252
0.18902
0.28049
0.40251
0.56112
0.76276
1.0144
1.3234
1.6983
2.1483
2.6850
3.3250
3.7618
161.34
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
345.86
0.0010749
0.0025084
0.0059324
0.012629
0.024624
0.044602
0.075908
0.12252
0.18902
0.28049
0.40251
0.56112
0.76276
1.0144
1.3234
1.6983
2.1483
2.6850
3.3250
3.7618
15.832
15.583
15.291
14.994
14.692
14.384
14.069
13.745
13.410
13.062
12.698
12.314
11.904
11.461
10.975
10.426
9.7846
8.9829
7.7913
5.1285
0.00080362
0.0017832
0.0039967
0.0081006
0.015110
0.026311
0.043269
0.067850
0.10227
0.14916
0.21175
0.29409
0.40144
0.54109
0.72367
0.96617
1.2991
1.7898
2.6696
5.1285
0.063163
0.064174
0.065399
0.066693
0.068062
0.069519
0.071077
0.072753
0.074570
0.076556
0.078751
0.081208
0.084004
0.087249
0.091119
0.095914
0.10220
0.11132
0.12835
0.19499
1244.4
560.78
250.20
123.45
66.180
38.007
23.111
14.738
9.7783
6.7041
4.7225
3.4004
2.4910
1.8481
1.3818
1.0350
0.76974
0.55871
0.37458
0.19499
4.4138
5.2969
6.3240
7.3629
8.4164
9.4869
10.576
11.685
12.817
13.973
15.156
16.368
17.615
18.903
20.239
21.638
23.125
24.750
26.688
29.429
4.4138
5.2971
6.3244
7.3637
8.4181
9.4900
10.581
11.694
12.831
13.995
15.188
16.414
17.680
18.991
20.360
21.801
23.344
25.048
27.114
30.163
0.026403
0.031735
0.037606
0.043223
0.048626
0.053849
0.058915
0.063848
0.068665
0.073385
0.078027
0.082607
0.087149
0.091675
0.096221
0.10083
0.10559
0.11065
0.11659
0.12527
0.068393
0.068179
0.068405
0.068990
0.069825
0.070836
0.071969
0.073190
0.074475
0.075809
0.077186
0.078605
0.080078
0.081625
0.083293
0.085172
0.087455
0.090641
0.096654
0.10179
0.10225
0.10325
0.10460
0.10621
0.10803
0.11005
0.11227
0.11474
0.11750
0.12066
0.12435
0.12879
0.13438
0.14180
0.15244
0.16980
0.20591
0.35704
1058.1
1016.7
969.14
921.61
874.04
826.46
778.88
731.28
683.65
635.90
587.94
539.61
490.70
440.95
389.93
337.04
281.21
220.39
149.32
0
25.521
25.895
26.340
26.796
27.262
27.736
28.213
28.693
29.170
29.641
30.102
30.548
30.972
31.366
31.715
32.000
32.183
32.184
31.732
29.429
26.859
27.302
27.824
28.355
28.892
29.431
29.968
30.498
31.018
31.521
32.003
32.456
32.872
33.240
33.544
33.758
33.837
33.684
32.977
30.163
0.16552
0.16118
0.15705
0.15370
0.15100
0.14881
0.14704
0.14560
0.14444
0.14349
0.14270
0.14202
0.14141
0.14081
0.14017
0.13940
0.13838
0.13682
0.13384
0.12527
0.044397
0.046371
0.048691
0.051040
0.053424
0.055867
0.058395
0.061026
0.063766
0.066612
0.069560
0.072606
0.075756
0.079035
0.082489
0.086214
0.090400
0.095488
0.10298
0.052938
0.055037
0.057550
0.060156
0.062886
0.065796
0.068954
0.072428
0.076287
0.080611
0.085515
0.091184
0.097932
0.10632
0.11743
0.13359
0.16076
0.22018
0.47999
137.57
140.62
143.91
146.92
149.60
151.89
153.71
155.02
155.74
155.81
155.15
153.70
151.36
148.04
143.59
137.85
130.56
121.34
109.29
0
385.09
262.77
176.43
124.70
92.835
72.442
58.764
49.133
42.049
36.657
32.456
29.136
26.498
24.406
22.765
21.499
20.526
19.682
18.259
12.397
Single-Phase Properties
200.00
225.63
0.10000
0.10000
225.63
300.00
400.00
500.00
600.00
0.10000
0.10000
0.10000
0.10000
0.10000
200.00
289.48
1.0000
1.0000
289.48
300.00
400.00
500.00
600.00
1.0000
1.0000
1.0000
1.0000
1.0000
200.00
300.00
400.00
500.00
600.00
5.0000
5.0000
5.0000
5.0000
5.0000
8.4143
11.198
8.4211
11.205
0.048616
0.061709
0.069829
0.072648
0.10620
0.11128
874.45
752.07
−0.37493
−0.30416
28.483
33.380
41.260
50.551
61.004
30.268
35.833
44.566
54.698
65.987
0.14619
0.16745
0.19247
0.21503
0.23558
0.059863
0.070758
0.086121
0.099065
0.10950
0.070868
0.079793
0.094695
0.10751
0.11790
154.52
179.93
207.36
231.13
252.55
52.958
18.414
7.5341
4.1010
2.5191
0.067956
0.087067
8.3891
18.835
8.4570
18.922
0.048489
0.091441
0.069866
0.081543
0.10604
0.13406
879.27
443.55
−0.37736
0.14902
1.8765
2.0285
3.1249
4.0544
4.9391
31.346
32.269
40.778
50.244
60.781
33.223
34.298
43.903
54.298
65.720
0.14084
0.14449
0.17212
0.19527
0.21607
0.078861
0.077834
0.087343
0.099519
0.10975
0.10583
0.099455
0.098681
0.10927
0.11891
148.24
155.53
198.53
227.30
251.11
24.503
20.787
7.7199
4.0976
2.4913
14.806
11.380
2.2504
1.3639
1.0491
0.067539
0.087876
0.44436
0.73318
0.95318
8.2811
19.812
38.004
48.802
59.789
8.6188
20.251
40.225
52.468
64.554
0.047943
0.094764
0.15165
0.17903
0.20106
0.070021
0.082741
0.093496
0.10135
0.11075
0.10541
0.13222
0.13815
0.11872
0.12364
900.01
452.11
159.25
213.49
246.86
−0.38724
0.11636
8.1026
3.8903
2.2996
14.694
13.888
0.056043
0.040759
0.030247
0.024114
0.020066
14.715
11.485
0.53292
0.49298
0.32001
0.24665
0.20246
0.068054
0.072006
17.843
24.534
33.061
41.469
49.836
200.00
300.00
400.00
500.00
600.00
10.000
10.000
10.000
10.000
10.000
14.913
11.776
6.3531
3.0122
2.1596
0.067054
0.084916
0.15740
0.33199
0.46305
8.1545
19.382
33.679
46.933
58.580
8.8250
20.231
35.253
50.252
63.211
0.047292
0.093258
0.13608
0.16976
0.19339
0.070195
0.082583
0.095653
0.10303
0.11178
0.10473
0.12585
0.17697
0.13206
0.12945
924.61
514.06
196.98
211.16
248.28
−0.39776
−0.037998
2.9315
3.0876
1.9304
200.00
300.00
400.00
500.00
600.00
50.000
50.000
50.000
50.000
50.000
15.598
13.358
11.268
9.4018
7.8978
0.064113
0.074862
0.088747
0.10636
0.12662
7.3673
17.612
28.859
40.839
53.306
10.573
21.355
33.296
46.157
59.637
0.042937
0.086486
0.12077
0.14943
0.17399
0.070934
0.083360
0.096003
0.10668
0.11548
0.10170
0.11389
0.12454
0.13213
0.13720
1089.7
794.12
590.09
478.93
431.69
−0.44295
−0.33796
−0.20571
−0.077157
−0.0052131
14.343
12.767
11.435
10.314
0.069721
0.078330
0.087453
0.096952
16.500
27.298
38.923
51.227
23.472
35.131
47.668
60.923
0.081539
0.11502
0.14296
0.16711
0.084059
0.097186
0.10821
0.11716
0.11166
0.12126
0.12921
0.13566
1008.9
833.69
723.22
656.57
−0.40055
−0.35302
−0.31534
−0.28902
300.00
400.00
500.00
600.00
100.00
100.00
100.00
100.00
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., and Jacobsen, R. T., “An International Standard Formulation for the Thermodynamic Properties of 1,1,1-Trifluoroethane (HFC-143a) for Temperatures from 161 to 450 K and Pressures to 50 MPa,”
J. Phys. Chem. Ref. Data 29(4):521–552, 2000. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The estimated uncertainties of properties calculated using the equation of state are 0.1% in density, 0.5% in heat capacities, 0.02% in the speed of sound for the vapor at pressures less than 1 MPa, 0.5% in speed
of sound elsewhere, and 0.1% in vapor pressure, except in the critical region.
2-241
2-242
TABLE 2-129
Thermodynamic Properties of R-404A
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
200.00
205.00
210.00
215.00
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
305.00
310.00
315.00
320.00
325.00
330.00
335.00
340.00
345.00
345.27
0.022649
0.030989
0.041658
0.055101
0.071804
0.092293
0.11713
0.14693
0.18232
0.22397
0.27258
0.32888
0.39363
0.46763
0.55168
0.64664
0.75338
0.87280
1.0059
1.1536
1.3169
1.4970
1.6950
1.9122
2.1499
2.4096
2.6932
3.0027
3.3414
3.7150
3.7348
14.209
14.059
13.907
13.755
13.600
13.444
13.286
13.126
12.963
12.796
12.627
12.453
12.275
12.092
11.904
11.709
11.508
11.298
11.078
10.848
10.605
10.346
10.069
9.7686
9.4384
9.0688
8.6431
8.1285
7.4362
5.7429
4.9400
0.070377
0.071131
0.071905
0.072703
0.073527
0.074380
0.075265
0.076185
0.077145
0.078147
0.079197
0.080301
0.081465
0.082697
0.084006
0.085402
0.086899
0.088513
0.090266
0.092182
0.094295
0.096652
0.099314
0.10237
0.10595
0.11027
0.11570
0.12302
0.13448
0.17413
0.20243
10.353
10.948
11.544
12.144
12.746
13.353
13.963
14.578
15.199
15.824
16.456
17.094
17.738
18.390
19.049
19.717
20.394
21.081
21.780
22.490
23.215
23.956
24.717
25.500
26.310
27.157
28.054
29.026
30.147
32.108
32.875
200.00
205.00
210.00
215.00
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
305.00
0.021264
0.029285
0.039592
0.052629
0.068883
0.088879
0.11318
0.14240
0.17718
0.21817
0.26610
0.32169
0.38571
0.45896
0.54225
0.63645
0.74245
0.86115
0.99353
1.1406
1.3034
1.4830
29.920
30.185
30.451
30.718
30.987
31.256
31.525
31.795
32.063
32.330
32.596
32.859
33.119
33.375
33.626
33.872
34.111
34.342
34.563
34.773
34.968
35.147
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
10.355
10.950
11.547
12.148
12.751
13.359
13.972
14.590
15.213
15.842
16.478
17.120
17.770
18.429
19.096
19.772
20.460
21.159
21.870
22.597
23.339
24.101
24.885
25.695
26.538
27.423
28.365
29.396
30.597
32.755
33.631
0.058867
0.061803
0.064678
0.067498
0.070269
0.072995
0.075679
0.078326
0.080939
0.083520
0.086073
0.088600
0.091104
0.093589
0.096056
0.098510
0.10095
0.10339
0.10583
0.10826
0.11071
0.11317
0.11566
0.11818
0.12075
0.12341
0.12619
0.12918
0.13261
0.13874
0.14126
0.076939
0.077522
0.078116
0.078719
0.079326
0.079940
0.080558
0.081183
0.081815
0.082456
0.083107
0.083770
0.084446
0.085137
0.085846
0.086574
0.087326
0.088104
0.088914
0.089761
0.090653
0.091603
0.092625
0.093744
0.094998
0.096455
0.098241
0.10064
0.10445
0.11650
31.555
31.853
32.152
32.451
32.749
33.046
33.340
33.633
33.922
34.208
34.489
34.765
35.034
35.296
35.550
35.794
36.028
36.249
36.455
36.645
36.814
36.960
0.16521
0.16408
0.16307
0.16217
0.16138
0.16068
0.16006
0.15952
0.15903
0.15861
0.15823
0.15789
0.15759
0.15732
0.15707
0.15684
0.15661
0.15639
0.15616
0.15592
0.15566
0.15536
0.058696
0.059968
0.061245
0.062526
0.063815
0.065113
0.066424
0.067750
0.069095
0.070463
0.071855
0.073276
0.074728
0.076214
0.077737
0.079300
0.080909
0.082567
0.084282
0.086062
0.087917
0.089863
Sound speed
m/s
Joule-Thomson
K/MPa
0.11881
0.11915
0.11965
0.12028
0.12103
0.12188
0.12282
0.12386
0.12499
0.12621
0.12754
0.12899
0.13057
0.13229
0.13419
0.13630
0.13866
0.14133
0.14438
0.14793
0.15211
0.15715
0.16339
0.17139
0.18212
0.19751
0.22197
0.26871
0.40392
8.2559
859.89
831.56
804.42
778.20
752.69
727.72
703.16
678.91
654.88
631.01
607.23
583.50
559.77
535.99
512.13
488.15
464.02
439.69
415.13
390.28
365.11
339.56
313.56
287.00
259.73
231.53
201.95
170.20
134.59
89.976
0
−0.34161
−0.33384
−0.32460
−0.31394
−0.30185
−0.28830
−0.27318
−0.25636
−0.23766
−0.21683
−0.19356
−0.16749
−0.13814
−0.10493
−0.067104
−0.023728
0.026418
0.084928
0.15392
0.23626
0.33594
0.45865
0.61280
0.81141
1.0757
1.4433
1.9881
2.8807
4.6353
10.564
12.409
0.068032
0.069509
0.071021
0.072573
0.074172
0.075826
0.077546
0.079344
0.081232
0.083226
0.085343
0.087604
0.090033
0.092660
0.095524
0.098671
0.10217
0.10609
0.11056
0.11574
0.12186
0.12929
138.13
139.28
140.34
141.29
142.12
142.84
143.43
143.88
144.18
144.33
144.32
144.14
143.77
143.22
142.46
141.49
140.29
138.85
137.16
135.19
132.92
130.34
88.073
77.215
68.305
60.948
54.835
49.721
45.413
41.761
38.642
35.962
33.645
31.630
29.871
28.327
26.970
25.773
24.718
23.789
22.972
22.256
21.633
21.094
Cp
kJ/(mol⋅K)
Saturated Properties
0.013010
0.017550
0.023271
0.030378
0.039095
0.049667
0.062359
0.077463
0.095292
0.11619
0.14055
0.16879
0.20137
0.23885
0.28183
0.33102
0.38725
0.45152
0.52501
0.60922
0.70599
0.81772
76.866
56.979
42.971
32.919
25.579
20.134
16.036
12.909
10.494
8.6063
7.1149
5.9247
4.9659
4.1867
3.5483
3.0210
2.5823
2.2148
1.9047
1.6414
1.4165
1.2229
310.00
315.00
320.00
325.00
330.00
335.00
340.00
345.00
345.27
1.6806
1.8975
2.1351
2.3950
2.6789
2.9893
3.3299
3.7109
3.7348
226.65
0.10000
227.41
300.00
400.00
500.00
0.10000
0.10000
0.10000
0.10000
289.79
1.0000
290.23
300.00
400.00
500.00
1.0000
1.0000
1.0000
1.0000
300.00
400.00
500.00
5.0000
5.0000
5.0000
0.94761
1.1001
1.2815
1.5019
1.7781
2.1438
2.6882
4.2113
4.9400
1.0553
0.90903
0.78032
0.66583
0.56239
0.46645
0.37199
0.23746
0.20243
35.304
35.435
35.530
35.578
35.558
35.429
35.084
33.615
32.875
37.078
37.159
37.196
37.173
37.065
36.824
36.323
34.496
33.631
0.074669
13.554
13.561
31.386
36.596
45.121
55.103
0.090189
0.15501
0.15459
0.15408
0.15343
0.15257
0.15136
0.14946
0.14379
0.14126
0.091922
0.094123
0.096513
0.099162
0.10220
0.10585
0.11074
0.12022
0.13856
0.15062
0.16713
0.19141
0.23111
0.30867
0.53035
8.6291
127.41
124.10
120.38
116.21
111.51
106.19
100.03
90.307
0
20.630
20.234
19.889
19.571
19.233
18.763
17.851
14.130
12.409
0.073887
0.080143
0.12218
719.55
−0.28348
33.188
39.050
48.428
59.250
0.16038
0.18269
0.20956
0.23365
0.065742
0.076875
0.092844
0.10612
0.076645
0.085907
0.10141
0.11456
143.14
166.24
191.81
213.92
47.558
16.998
6.9229
3.7455
21.750
21.840
0.10572
0.088879
0.14425
416.16
1.8916
2.0323
3.1292
4.0571
34.573
35.486
44.644
54.804
36.464
37.518
47.773
58.861
0.15615
0.15972
0.18922
0.21391
0.084363
0.083854
0.094142
0.10659
0.11078
0.10554
0.10545
0.11631
137.07
143.42
183.69
210.41
10.994
2.2256
1.3561
0.090955
0.44932
0.73741
22.770
41.867
53.389
23.225
44.113
57.076
0.10919
0.16875
0.19774
0.089725
0.10069
0.10859
0.14193
0.14547
0.12579
427.56
148.00
198.35
0.11428
7.6582
3.5826
Single-Phase Properties
13.392
0.055492
0.040750
0.030243
0.024113
11.088
0.52866
0.49205
0.31957
0.24648
18.021
24.540
33.066
41.471
0.15078
22.936
19.634
7.1401
3.7496
300.00
400.00
500.00
10.000
10.000
10.000
11.371
6.1241
2.9622
0.087944
0.16329
0.33758
22.323
37.557
51.539
23.203
39.190
54.915
0.10763
0.15323
0.18852
0.089307
0.10301
0.11046
0.13525
0.18569
0.13925
489.01
184.17
198.11
−0.035312
2.8522
2.8527
300.00
400.00
500.00
25.000
25.000
25.000
12.107
9.2730
6.6326
0.082594
0.10784
0.15077
21.419
34.286
47.758
23.484
36.982
51.527
0.10432
0.14304
0.17548
0.089393
0.10166
0.11215
0.12713
0.14227
0.14633
614.12
381.56
292.53
−0.22002
0.20064
0.65319
300.00
400.00
500.00
50.000
50.000
50.000
12.867
10.834
9.0225
0.077719
0.092300
0.11083
20.472
32.538
45.317
24.358
37.153
50.859
0.10057
0.13731
0.16786
0.090168
0.10251
0.11339
0.12262
0.13302
0.14051
753.19
559.24
455.37
−0.32391
−0.19415
−0.070101
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal
conductivity are not currently available for this fluid.
Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary,
the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and
dew point pressures are 0.5%.
2-243
2-244
TABLE 2-130
Thermodynamic Properties of R-407C
Temperature
K
Pressure
MPa
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
359.35
0.019158
0.035795
0.062640
0.10366
0.16353
0.24755
0.36157
0.51193
0.70540
0.94916
1.2507
1.6182
2.0599
2.5851
3.2038
3.9255
4.6317
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
290.00
300.00
310.00
320.00
330.00
340.00
350.00
359.35
0.011312
0.022624
0.041929
0.072846
0.11979
0.18793
0.28317
0.41203
0.58173
0.80008
1.0757
1.4179
1.8375
2.3470
2.9627
3.7100
4.6317
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
−0.31996
−0.30662
−0.28934
−0.26790
−0.24161
−0.20937
−0.16951
−0.11964
−0.056172
0.026372
0.13683
0.29038
0.51547
0.87274
1.5203
3.0499
10.947
Saturated Properties
17.036
16.697
16.352
15.999
15.637
15.264
14.877
14.472
14.045
13.591
13.102
12.567
11.969
11.278
10.435
9.2661
5.2600
0.0068643
0.013151
0.023450
0.039384
0.062913
0.096374
0.14256
0.20484
0.28739
0.39560
0.53670
0.72101
0.96439
1.2939
1.7642
2.5260
5.2600
0.058698
0.059892
0.061156
0.062503
0.063949
0.065512
0.067218
0.069099
0.071198
0.073576
0.076322
0.079573
0.083552
0.088671
0.095832
0.10792
0.19011
145.68
76.041
42.644
25.391
15.895
10.376
7.0147
4.8820
3.4796
2.5278
1.8632
1.3869
1.0369
0.77283
0.56682
0.39588
0.19011
8.8272
9.9359
11.051
12.175
13.312
14.464
15.632
16.822
18.035
19.278
20.555
21.877
23.255
24.711
26.287
28.110
32.145
8.8283
9.9380
11.055
12.182
13.323
14.480
15.657
16.857
18.085
19.348
20.651
22.006
23.427
24.940
26.594
28.534
33.025
0.050593
0.056002
0.061189
0.066188
0.071026
0.075728
0.080314
0.084805
0.089223
0.093590
0.097931
0.10228
0.10668
0.11119
0.11596
0.12137
0.13372
0.070988
0.071320
0.071817
0.072410
0.073074
0.073803
0.074597
0.075463
0.076412
0.077458
0.078624
0.079950
0.081509
0.083453
0.086157
0.090943
0.11073
0.11118
0.11203
0.11319
0.11465
0.11641
0.11853
0.12111
0.12427
0.12822
0.13331
0.14013
0.14989
0.16541
0.19551
0.28993
956.60
903.06
851.40
801.12
751.77
703.01
654.53
606.09
557.44
508.32
458.46
407.51
354.98
300.07
241.20
174.57
0
30.051
30.504
30.957
31.409
31.857
32.298
32.728
33.145
33.544
33.918
34.259
34.556
34.790
34.931
34.916
34.578
32.145
31.699
32.224
32.745
33.259
33.761
34.248
34.715
35.157
35.568
35.940
36.263
36.523
36.696
36.745
36.595
36.047
33.025
0.16726
0.16412
0.16151
0.15933
0.15749
0.15593
0.15460
0.15343
0.15240
0.15144
0.15051
0.14956
0.14852
0.14727
0.14560
0.14299
0.13372
0.048920
0.050967
0.053143
0.055439
0.057839
0.060328
0.062897
0.065542
0.068266
0.071085
0.074027
0.077140
0.080507
0.084283
0.088801
0.095065
0.057805
0.060200
0.062854
0.065784
0.069010
0.072563
0.076500
0.080917
0.085971
0.091920
0.099203
0.10861
0.12170
0.14208
0.18030
0.28700
149.59
152.36
154.78
156.79
158.33
159.36
159.80
159.60
158.69
156.99
154.41
150.83
146.11
140.03
132.24
122.09
0
109.12
88.122
72.006
59.560
49.904
42.378
36.483
31.840
28.163
25.236
22.898
21.024
19.516
18.284
17.206
15.951
10.947
Single-Phase Properties
200.00
229.25
0.10000
0.10000
236.25
300.00
400.00
500.00
0.10000
0.10000
0.10000
0.10000
291.84
1.0000
297.47
300.00
400.00
500.00
1.0000
1.0000
1.0000
1.0000
300.00
400.00
500.00
5.0000
5.0000
5.0000
8.8253
12.091
8.8312
12.097
0.050583
0.065819
0.070990
0.072363
0.11072
0.11310
956.99
804.85
−0.32010
−0.26966
31.690
35.535
42.554
50.849
33.574
37.991
45.862
54.997
0.15814
0.17467
0.19722
0.21756
0.056928
0.063341
0.076588
0.088895
0.067764
0.072378
0.085147
0.097330
157.81
179.00
205.99
229.27
53.242
20.041
7.7925
4.0471
0.074050
19.510
19.584
0.094388
0.077662
0.12906
499.23
2.0105
2.0465
3.1425
4.0637
34.177
34.384
42.101
50.576
36.187
36.431
45.244
54.639
0.15075
0.15156
0.17694
0.19786
0.073268
0.072744
0.078067
0.089416
0.097199
0.095419
0.089213
0.099001
155.15
156.77
198.26
225.88
13.412
2.1880
1.3504
0.074559
0.45703
0.74050
20.240
39.458
49.289
20.613
41.743
52.992
0.096862
0.15675
0.18193
0.078093
0.086188
0.091753
0.12762
0.12964
0.10811
507.10
161.10
213.00
0.027202
8.5257
3.9036
17.038
16.026
0.053062
0.040722
0.030231
0.024109
13.504
0.49738
0.48865
0.31821
0.24608
0.058692
0.062399
18.846
24.557
33.079
41.479
0.044233
23.442
22.566
7.9701
4.0390
300.00
400.00
500.00
10.000
10.000
10.000
13.740
7.1029
2.9957
0.072780
0.14079
0.33381
19.898
34.426
47.547
20.626
35.834
50.885
0.095679
0.13888
0.17282
0.077756
0.090433
0.094263
0.12301
0.20031
0.12254
558.94
184.71
207.67
−0.063246
3.3408
3.3327
300.00
400.00
500.00
25.000
25.000
25.000
14.443
10.899
7.3363
0.069238
0.091752
0.13631
19.146
30.990
43.479
20.877
33.284
46.886
0.092972
0.12855
0.15889
0.077634
0.087056
0.096319
0.11624
0.13223
0.13592
672.43
399.92
289.22
−0.19834
0.28513
0.97116
300.00
400.00
500.00
50.000
50.000
50.000
15.220
12.648
10.260
0.065703
0.079064
0.097468
18.302
29.255
40.787
21.587
33.209
45.660
0.089730
0.12310
0.15086
0.078160
0.087179
0.096753
0.11176
0.12077
0.12761
802.78
579.57
457.54
−0.28843
−0.12975
0.047330
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal
conductivity are not currently available for this fluid.
Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary,
the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and
dew point pressures are 0.5%.
2-245
2-246
FIG. 2-15
Pressure-enthalpy diagram for Refrigerant 407C. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference
Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the mixture
model of Lemmon, E. W., and R. T. Jacobsen, “Equations of State for Mixtures of R-32, R-125, R-134a, R-143a, and R-152a,” J. Phys. Chem. Ref. Data 33: 593–620, 2004.
TABLE 2-131 Thermodynamic Properties of R-410A
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
200.00
210.00
215.00
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
305.00
310.00
315.00
320.00
325.00
330.00
335.00
340.00
344.49
0.029160
0.053727
0.071143
0.092819
0.11946
0.15182
0.19070
0.23697
0.29152
0.35531
0.42933
0.51461
0.61223
0.72330
0.84899
0.99048
1.1490
1.3260
1.5226
1.7404
1.9809
2.2456
2.5364
2.8550
3.2037
3.5848
4.0009
4.4556
4.9012
19.510
19.093
18.881
18.667
18.449
18.229
18.005
17.776
17.543
17.305
17.062
16.812
16.555
16.290
16.016
15.732
15.436
15.127
14.802
14.459
14.095
13.704
13.282
12.816
12.294
11.685
10.930
9.8413
6.3240
0.051256
0.052375
0.052962
0.053571
0.054202
0.054858
0.055542
0.056255
0.057002
0.057786
0.058611
0.059482
0.060406
0.061388
0.062439
0.063567
0.064785
0.066109
0.067559
0.069160
0.070948
0.072969
0.075293
0.078025
0.081343
0.085578
0.091491
0.10161
0.15813
7.0380
8.0188
8.5112
9.0052
9.5012
9.9997
10.501
11.006
11.514
12.026
12.543
13.065
13.593
14.127
14.669
15.218
15.776
16.344
16.924
17.516
18.123
18.747
19.392
20.064
20.772
21.531
22.376
23.414
25.988
200.00
210.00
215.00
220.00
225.00
230.00
235.00
240.00
245.00
250.00
255.00
260.00
265.00
270.00
275.00
280.00
285.00
290.00
295.00
300.00
305.00
310.00
315.00
320.00
0.029010
0.053489
0.070844
0.092447
0.11900
0.15125
0.19000
0.23611
0.29049
0.35407
0.42786
0.51287
0.61019
0.72092
0.84622
0.98729
1.1454
1.3218
1.5179
1.7351
1.9749
2.2390
2.5291
2.8472
26.495
26.835
27.002
27.167
27.329
27.488
27.645
27.798
27.947
28.092
28.232
28.367
28.496
28.619
28.733
28.839
28.935
29.019
29.090
29.144
29.178
29.189
29.170
29.112
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
7.0395
8.0217
8.5149
9.0101
9.5077
10.008
10.512
11.019
11.530
12.047
12.568
13.096
13.630
14.172
14.722
15.281
15.851
16.432
17.026
17.636
18.263
18.911
19.583
20.287
21.032
21.837
22.742
23.867
26.763
0.040995
0.045781
0.048098
0.050370
0.052600
0.054791
0.056948
0.059073
0.061169
0.063240
0.065289
0.067318
0.069331
0.071331
0.073321
0.075304
0.077284
0.079266
0.081254
0.083253
0.085270
0.087314
0.089398
0.091537
0.093762
0.096123
0.098732
0.10194
0.11022
0.062260
0.062050
0.062014
0.062020
0.062066
0.062151
0.062271
0.062426
0.062615
0.062837
0.063092
0.063380
0.063701
0.064057
0.064451
0.064884
0.065363
0.065893
0.066483
0.067147
0.067901
0.068773
0.069800
0.071046
0.072616
0.074717
0.077843
0.083650
0.097942
0.098396
0.098729
0.099138
0.099628
0.10020
0.10088
0.10165
0.10253
0.10353
0.10466
0.10594
0.10738
0.10902
0.11088
0.11300
0.11543
0.11825
0.12156
0.12550
0.13029
0.13630
0.14413
0.15493
0.17109
0.19853
0.25685
0.46832
929.01
879.84
855.20
830.52
805.81
781.06
756.26
731.41
706.48
681.45
656.31
631.02
605.55
579.88
553.95
527.72
501.14
474.14
446.66
418.60
389.87
360.33
329.82
298.10
264.83
229.46
190.98
147.49
0
−0.30179
−0.28524
−0.27544
−0.26446
−0.25217
−0.23841
−0.22300
−0.20574
−0.18637
−0.16459
−0.14006
−0.11232
−0.080861
−0.045000
−0.0039006
0.043515
0.098651
0.16337
0.24022
0.33275
0.44607
0.58788
0.77028
1.0135
1.3544
1.8665
2.7232
4.4554
9.7623
28.125
28.530
28.726
28.919
29.107
29.290
29.468
29.640
29.806
29.965
30.116
30.258
30.392
30.515
30.626
30.725
30.809
30.876
30.925
30.951
30.951
30.920
30.850
30.732
0.14644
0.14345
0.14212
0.14087
0.13972
0.13864
0.13762
0.13667
0.13577
0.13492
0.13411
0.13333
0.13259
0.13187
0.13116
0.13047
0.12978
0.12908
0.12837
0.12764
0.12688
0.12606
0.12517
0.12418
0.042482
0.044604
0.045719
0.046862
0.048026
0.049206
0.050400
0.051603
0.052814
0.054033
0.055260
0.056497
0.057747
0.059014
0.060302
0.061618
0.062969
0.064364
0.065814
0.067335
0.068945
0.070671
0.072551
0.074643
0.052236
0.055055
0.056590
0.058205
0.059899
0.061674
0.063533
0.065483
0.067535
0.069705
0.072011
0.074481
0.077148
0.080057
0.083265
0.086846
0.090901
0.095568
0.10104
0.10760
0.11566
0.12589
0.13943
0.15831
164.41
167.03
168.16
169.16
170.03
170.75
171.32
171.73
171.97
172.04
171.93
171.62
171.11
170.39
169.45
168.27
166.84
165.16
163.20
160.94
158.36
155.44
152.13
148.40
Saturated Properties
0.017797
0.031567
0.041089
0.052763
0.066925
0.083936
0.10420
0.12814
0.15625
0.18905
0.22714
0.27117
0.32190
0.38018
0.44702
0.52357
0.61123
0.71170
0.82707
0.95997
1.1138
1.2933
1.5048
1.7576
56.190
31.678
24.338
18.953
14.942
11.914
9.5972
7.8039
6.4000
5.2895
4.4026
3.6877
3.1066
2.6303
2.2371
1.9100
1.6360
1.4051
1.2091
1.0417
0.89779
0.77322
0.66456
0.56894
113.67
90.100
80.508
72.155
64.889
58.571
53.077
48.299
44.137
40.508
37.336
34.560
32.123
29.979
28.087
26.412
24.924
23.598
22.410
21.338
20.365
19.470
18.632
17.826
2-247
(Continued)
2-248
TABLE 2-131 Thermodynamic Properties of R-410A (Continued )
Temperature
K
Pressure
MPa
Density
mol/dm3
Volume
dm3/mol
Int. energy
kJ/mol
325.00
330.00
335.00
340.00
344.49
3.1955
3.5766
3.9935
4.4504
4.9012
2.0668
2.4582
2.9848
3.7974
6.3240
0.48384
0.40681
0.33503
0.26334
0.15813
29.002
28.817
28.510
27.951
25.988
221.45
0.10000
221.53
300.00
400.00
500.00
0.10000
0.10000
0.10000
0.10000
280.32
1.0000
280.42
300.00
400.00
500.00
1.0000
1.0000
1.0000
1.0000
300.00
400.00
500.00
5.0000
5.0000
5.0000
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Saturated Properties (Continued)
30.548
30.272
29.848
29.123
26.763
0.12305
0.12169
0.11995
0.11740
0.11022
0.077041
0.079915
0.083629
0.089197
0.18670
0.23464
0.33370
0.65947
144.16
139.30
133.59
126.39
0
17.018
16.153
15.123
13.641
9.7623
0.051020
0.062030
0.099271
823.36
−0.26104
69.827
19.643
7.7467
4.0758
Single-Phase Properties
18.604
0.056810
0.040605
0.030202
0.024099
0.053751
9.1541
27.217
31.028
36.670
43.331
28.977
33.491
39.981
47.480
0.14051
0.15794
0.17654
0.19323
0.047215
0.050980
0.061554
0.071249
0.058714
0.059877
0.070067
0.079663
169.44
198.35
227.37
252.59
0.063641
15.253
15.317
0.075429
0.064913
0.11314
526.05
1.8849
2.1460
3.1769
4.0808
28.848
30.151
36.304
43.106
30.733
32.297
39.481
47.187
0.13041
0.13580
0.15648
0.17364
0.061731
0.057548
0.062713
0.071665
0.087169
0.075210
0.073258
0.081012
168.16
180.65
220.92
249.79
14.870
1.9755
1.3185
0.067248
0.50621
0.75845
17.202
34.349
42.072
17.539
36.880
45.864
0.082188
0.13813
0.15821
0.066139
0.068570
0.073521
0.11773
0.097588
0.087959
472.56
192.34
239.51
0.17344
7.6786
3.7957
0.036775
5.0121
3.3106
15.713
0.53054
0.46599
0.31478
0.24505
17.603
24.628
33.111
41.495
9.1488
0.046760
26.279
20.254
7.7768
4.0343
300.00
400.00
500.00
10.000
10.000
10.000
15.342
5.7949
2.8642
0.065180
0.17257
0.34914
16.830
30.845
40.710
17.482
32.570
44.202
0.080897
0.12363
0.14982
0.065435
0.074099
0.075667
0.11125
0.16518
0.098492
533.86
182.45
233.93
300.00
400.00
500.00
25.000
25.000
25.000
16.289
11.685
7.4115
0.061392
0.085582
0.13493
16.058
26.530
37.197
17.592
28.670
40.570
0.078110
0.10987
0.13644
0.065000
0.072157
0.078574
0.10273
0.11830
0.11515
658.09
379.59
291.31
−0.14678
0.50709
1.2724
300.00
400.00
500.00
50.000
50.000
50.000
17.287
14.049
11.128
0.057845
0.071182
0.089864
15.231
24.722
34.526
18.123
28.281
39.019
0.074923
0.10409
0.12804
0.065499
0.072480
0.079657
0.097459
0.10533
0.10880
792.80
566.13
449.76
−0.26163
−0.063564
0.13566
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and
Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties
is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal
conductivity are not currently available for this fluid.
Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary,
the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and
dew point pressures are 0.5%.
TABLE 2-132
Opteon™ YF (R-1234yf)
Saturation Properties—Temperature Table
Temp
[°C]
−40
−39
−38
−37
−36
−35
−34
−33
−32
−31
−30
−29
−28
−27
−26
−25
−24
−23
−22
−21
−20
−19
−18
−17
−16
−15
−14
−13
−12
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
Pressure
[kPa]
62.367
65.454
68.661
71.992
75.450
79.039
82.761
86.620
90.620
94.764
99.056
103.500
108.098
112.856
117.775
122.861
128.117
133.548
139.155
144.945
150.921
157.086
163.444
170.001
176.759
183.724
190.898
198.287
205.895
213.726
221.783
230.072
238.597
247.363
256.373
265.632
275.144
284.915
294.948
305.249
315.821
326.670
337.800
349.216
Volume [m3/kg]
Liquid vf
Vapor vg
0.000774
0.000776
0.000777
0.000779
0.000781
0.000782
0.000784
0.000786
0.000787
0.000789
0.000791
0.000793
0.000794
0.000796
0.000798
0.000800
0.000801
0.000803
0.000805
0.000807
0.000809
0.000811
0.000813
0.000815
0.000817
0.000818
0.000820
0.000822
0.000824
0.000826
0.000829
0.000831
0.000833
0.000835
0.000837
0.000839
0.000841
0.000843
0.000846
0.000848
0.000850
0.000852
0.000855
0.000857
0.2635
0.2519
0.2409
0.2304
0.2205
0.2111
0.2022
0.1937
0.1857
0.1780
0.1708
0.1639
0.1573
0.1511
0.1451
0.1394
0.1340
0.1289
0.1240
0.1193
0.1148
0.1105
0.1065
0.1026
0.0988
0.0953
0.0919
0.0886
0.0855
0.0825
0.0796
0.0769
0.0742
0.0717
0.0693
0.0670
0.0647
0.0626
0.0605
0.0586
0.0567
0.0548
0.0531
0.0514
Density [kg/m3]
Liquid df
1291.9
1289.2
1286.5
1283.8
1281.0
1278.3
1275.6
1272.8
1270.1
1267.3
1264.5
1261.8
1259.0
1256.2
1253.4
1250.5
1247.7
1244.9
1242.0
1239.2
1236.3
1233.4
1230.5
1227.6
1224.7
1221.8
1218.8
1215.9
1212.9
1209.9
1207.0
1203.9
1200.9
1197.9
1194.9
1191.8
1188.7
1185.6
1182.5
1179.4
1176.3
1173.1
1170.0
1166.8
Enthalpy [kJ/kg]
Vapor dg
Liquid hf
Latent hfg
3.795
3.970
4.152
4.340
4.535
4.737
4.946
5.162
5.386
5.617
5.855
6.102
6.357
6.620
6.891
7.171
7.460
7.758
8.066
8.383
8.709
9.046
9.392
9.750
10.117
10.496
10.885
11.286
11.699
12.123
12.559
13.008
13.469
13.943
14.431
14.931
15.446
15.974
16.517
17.074
17.647
18.234
18.837
19.457
151.1
152.2
153.4
154.6
155.7
156.9
158.1
159.3
160.4
161.6
162.8
164.0
165.2
166.4
167.6
168.8
170.0
171.2
172.4
173.7
174.9
176.1
177.3
178.6
179.8
181.0
182.3
183.5
184.8
186.0
187.3
188.5
189.8
191.0
192.3
193.6
194.9
196.1
197.4
198.7
200.0
201.3
202.6
203.9
185.5
185.0
184.5
184.0
183.5
183.0
182.5
182.0
181.5
181.0
180.5
180.0
179.5
178.9
178.4
177.9
177.4
176.8
176.3
175.7
175.2
174.6
174.1
173.5
172.9
172.4
171.8
171.2
170.6
170.0
169.5
168.9
168.3
167.7
167.0
166.4
165.8
165.2
164.6
163.9
163.3
162.6
162.0
161.3
Entropy [kJ/kg⋅K]
Vapor hg
Liquid sf
336.6
337.3
337.9
338.6
339.3
339.9
340.6
341.3
342.0
342.6
343.3
344.0
344.7
345.3
346.0
346.7
347.4
348.0
348.7
349.4
350.1
350.7
351.4
352.1
352.7
353.4
354.1
354.7
355.4
356.1
356.7
357.4
358.0
358.7
359.4
360.0
360.7
361.3
362.0
362.6
363.3
363.9
364.6
365.2
0.807
0.812
0.817
0.822
0.827
0.832
0.837
0.842
0.847
0.852
0.857
0.861
0.866
0.871
0.876
0.881
0.886
0.891
0.895
0.900
0.905
0.910
0.915
0.919
0.924
0.929
0.934
0.939
0.943
0.948
0.953
0.958
0.962
0.967
0.972
0.976
0.981
0.986
0.991
0.995
1.000
1.005
1.009
1.014
Vapor sg
1.603
1.603
1.602
1.602
1.601
1.601
1.600
1.600
1.600
1.599
1.599
1.599
1.598
1.598
1.598
1.598
1.598
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.597
1.598
1.598
1.598
1.598
1.598
1.598
Temp [°C]
−40
−39
−38
−37
−36
−35
−34
−33
−32
−31
−30
−29
−28
−27
−26
−25
−24
−23
−22
−21
−20
−19
−18
−17
−16
−15
−14
−13
−12
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
2-249
(Continued)
2-250
TABLE 2-132 Opteon™ YF (R-1234yf) (Continued )
Saturation Properties—Temperature Table
Volume [m3/kg]
Temp [°C]
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
Pressure [kPa]
Liquid vf
Vapor vg
360.923
372.925
385.227
397.833
410.750
423.981
437.532
451.408
465.613
480.152
495.031
510.255
525.828
541.756
558.044
574.697
591.721
609.120
626.901
645.068
663.626
682.582
701.940
721.707
741.887
762.487
783.511
804.966
826.857
849.190
871.971
895.206
918.900
943.060
967.691
992.800
1018.393
1044.476
1071.055
1098.137
1125.728
1153.834
1182.462
1211.618
0.000859
0.000862
0.000864
0.000867
0.000869
0.000872
0.000874
0.000877
0.000879
0.000882
0.000884
0.000887
0.000890
0.000893
0.000895
0.000898
0.000901
0.000904
0.000907
0.000910
0.000913
0.000916
0.000919
0.000922
0.000925
0.000928
0.000932
0.000935
0.000938
0.000942
0.000945
0.000949
0.000952
0.000956
0.000960
0.000963
0.000967
0.000971
0.000975
0.000979
0.000983
0.000988
0.000992
0.000996
0.0498
0.0482
0.0467
0.0452
0.0439
0.0425
0.0412
0.0400
0.0387
0.0376
0.0365
0.0354
0.0343
0.0333
0.0323
0.0314
0.0305
0.0296
0.0288
0.0279
0.0271
0.0264
0.0256
0.0249
0.0242
0.0235
0.0229
0.0222
0.0216
0.0210
0.0204
0.0199
0.0193
0.0188
0.0183
0.0178
0.0173
0.0168
0.0164
0.0159
0.0155
0.0151
0.0147
0.0143
Density [kg/m3]
Liquid df
1163.6
1160.4
1157.2
1153.9
1150.6
1147.3
1144.0
1140.7
1137.4
1134.0
1130.6
1127.2
1123.8
1120.3
1116.9
1113.4
1109.9
1106.3
1102.8
1099.2
1095.5
1091.9
1088.2
1084.5
1080.8
1077.1
1073.3
1069.5
1065.7
1061.8
1057.9
1054.0
1050.0
1046.0
1042.0
1037.9
1033.8
1029.6
1025.5
1021.2
1017.0
1012.6
1008.3
1003.9
Enthalpy [kJ/kg]
Vapor dg
Liquid hf
Latent hfg
20.092
20.744
21.413
22.100
22.804
23.526
24.267
25.027
25.807
26.606
27.425
28.266
29.127
30.011
30.916
31.845
32.796
33.772
34.772
35.797
36.848
37.925
39.029
40.161
41.321
42.510
43.729
44.979
46.260
47.573
48.920
50.301
51.717
53.169
54.658
56.186
57.753
59.360
61.010
62.702
64.440
66.223
68.053
69.933
205.2
206.5
207.8
209.1
210.5
211.8
213.1
214.4
215.8
217.1
218.5
219.8
221.2
222.5
223.9
225.2
226.6
228.0
229.3
230.7
232.1
233.5
234.9
236.3
237.7
239.1
240.5
241.9
243.4
244.8
246.2
247.6
249.1
250.5
252.0
253.4
254.9
256.4
257.8
259.3
260.8
262.3
263.8
265.3
160.7
160.0
159.3
158.7
158.0
157.3
156.6
155.9
155.2
154.5
153.8
153.0
152.3
151.6
150.8
150.1
149.3
148.5
147.7
147.0
146.2
145.4
144.6
143.7
142.9
142.1
141.2
140.4
139.5
138.7
137.8
136.9
136.0
135.1
134.1
133.2
132.3
131.3
130.3
129.4
128.4
127.4
126.3
125.3
Entropy [kJ/kg⋅K]
Vapor hg
Liquid sf
365.9
366.5
367.2
367.8
368.4
369.1
369.7
370.3
371.0
371.6
372.2
372.8
373.4
374.1
374.7
375.3
375.9
376.5
377.1
377.7
378.3
378.9
379.5
380.0
380.6
381.2
381.8
382.3
382.9
383.4
384.0
384.5
385.1
385.6
386.1
386.7
387.2
387.7
388.2
388.7
389.2
389.7
390.1
390.6
1.019
1.023
1.028
1.033
1.037
1.042
1.047
1.051
1.056
1.061
1.065
1.070
1.075
1.079
1.084
1.088
1.093
1.098
1.102
1.107
1.112
1.116
1.121
1.125
1.130
1.135
1.139
1.144
1.148
1.153
1.158
1.162
1.167
1.171
1.176
1.181
1.185
1.190
1.194
1.199
1.204
1.208
1.213
1.217
Vapor sg
1.599
1.599
1.599
1.599
1.599
1.600
1.600
1.600
1.600
1.601
1.601
1.601
1.601
1.602
1.602
1.602
1.602
1.603
1.603
1.603
1.603
1.604
1.604
1.604
1.605
1.605
1.605
1.605
1.606
1.606
1.606
1.606
1.607
1.607
1.607
1.607
1.608
1.608
1.608
1.608
1.608
1.608
1.609
1.609
Temp [°C]
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
1241.310
1271.543
1302.325
1333.663
1365.563
1398.032
1431.079
1464.709
1498.931
1533.751
1569.178
1605.219
1641.882
1679.174
1717.104
1755.680
1794.911
1834.805
1875.370
1916.617
1958.553
2001.189
2044.535
2088.600
2133.395
2178.931
2225.219
2272.271
2320.100
2368.717
2418.137
2468.375
2519.445
0.001001
0.001005
0.001010
0.001014
0.001019
0.001024
0.001029
0.001034
0.001040
0.001045
0.001051
0.001056
0.001062
0.001068
0.001075
0.001081
0.001088
0.001094
0.001101
0.001109
0.001116
0.001124
0.001132
0.001141
0.001149
0.001159
0.001168
0.001178
0.001189
0.001199
0.001211
0.001223
0.001236
0.0139
0.0135
0.0132
0.0128
0.0125
0.0121
0.0118
0.0115
0.0112
0.0109
0.0106
0.0103
0.0100
0.0098
0.0095
0.0092
0.0090
0.0087
0.0085
0.0082
0.0080
0.0078
0.0076
0.0073
0.0071
0.0069
0.0067
0.0065
0.0063
0.0061
0.0059
0.0057
0.0055
999.4
994.9
990.4
985.8
981.1
976.4
971.6
966.7
961.8
956.8
951.7
946.6
941.3
936.0
930.6
925.1
919.5
913.7
907.9
901.9
895.8
889.6
883.2
876.7
870.0
863.1
856.1
848.8
841.4
833.7
825.7
817.5
809.0
71.863
73.846
75.884
77.978
80.130
82.343
84.619
86.961
89.371
91.852
94.407
97.040
99.754
102.552
105.438
108.418
111.496
114.676
117.964
121.367
124.891
128.544
132.332
136.266
140.355
144.611
149.044
153.671
158.505
163.566
168.874
174.454
180.333
266.8
268.3
269.9
271.4
272.9
274.5
276.0
277.6
279.2
280.7
282.3
283.9
285.5
287.1
288.8
290.4
292.1
293.7
295.4
297.1
298.8
300.5
302.2
304.0
305.7
307.5
309.3
311.1
313.0
314.8
316.7
318.6
320.5
124.3
123.2
122.1
121.0
119.9
118.8
117.7
116.5
115.3
114.1
112.9
111.7
110.4
109.1
107.8
106.5
105.1
103.7
102.3
100.9
99.4
97.9
96.3
94.8
93.1
91.5
89.8
88.0
86.2
84.3
82.4
80.4
78.4
391.1
391.5
392.0
392.4
392.8
393.3
393.7
394.1
394.5
394.9
395.2
395.6
395.9
396.3
396.6
396.9
397.2
397.5
397.7
398.0
398.2
398.4
398.6
398.7
398.9
399.0
399.1
399.1
399.2
399.2
399.1
399.0
398.9
1.222
1.227
1.231
1.236
1.241
1.245
1.250
1.254
1.259
1.264
1.269
1.273
1.278
1.283
1.287
1.292
1.297
1.302
1.307
1.311
1.316
1.321
1.326
1.331
1.336
1.341
1.346
1.351
1.356
1.361
1.366
1.372
1.377
1.609
1.609
1.609
1.609
1.609
1.609
1.609
1.610
1.610
1.610
1.609
1.609
1.609
1.609
1.609
1.609
1.609
1.609
1.608
1.608
1.608
1.607
1.607
1.606
1.606
1.605
1.605
1.604
1.603
1.602
1.601
1.600
1.599
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
(Continued)
2-251
2-252
TABLE 2-132
Opteon™ YF (R-1234yf) (Continued )
Superheated Vapor—Constant Pressure Tables
V = Volume in m3/kg
H = Enthalpy in kJ/kg
S = Entropy in kJ/kg⋅K
Saturation Properties in Light Gray
Absolute Pressure, kPa
V
90
100
101.325
110
−32.15°C
−29.78°C
−29.49°C
−27.60°C
S
V
S
V
H
S
V
H
Temp [°C]
0.1869
341.9
H
1.600
0.1693
343.5
H
1.599
0.1672
343.7
1.599
0.1548
344.9
1.598
S
Temp [°C]
−30
−25
−20
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
0.1888
0.1933
0.1978
0.2022
0.2066
0.2110
0.2153
0.2197
0.2240
0.2283
0.2325
0.2368
0.2410
0.2453
0.2495
0.2537
0.2579
0.2621
0.2663
0.2705
0.2746
0.2788
0.2830
0.2871
0.2913
0.2954
0.2996
0.3037
0.3078
0.3120
343.6
347.7
351.8
355.9
360.1
364.3
368.6
372.9
377.3
381.7
386.1
390.6
395.2
399.8
404.4
409.1
413.8
418.5
423.3
428.2
433.0
438.0
442.9
447.9
453.0
458.1
463.2
468.4
473.6
478.8
1.607
1.623
1.640
1.656
1.672
1.688
1.704
1.719
1.735
1.750
1.766
1.781
1.796
1.811
1.826
1.841
1.855
1.870
1.884
1.899
1.913
1.927
1.942
1.956
1.970
1.984
1.997
2.011
2.025
2.038
0.1732
0.1773
0.1813
0.1853
0.1893
0.1932
0.1971
0.2010
0.2049
0.2088
0.2126
0.2165
0.2203
0.2241
0.2279
0.2317
0.2355
0.2393
0.2431
0.2468
0.2506
0.2544
0.2581
0.2619
0.2656
0.2693
0.2731
0.2768
0.2805
347.4
351.5
355.6
359.9
364.1
368.4
372.7
377.1
381.5
386.0
390.5
395.0
399.6
404.2
408.9
413.6
418.4
423.2
428.0
432.9
437.9
442.8
447.8
452.9
458.0
463.1
468.3
473.5
478.7
1.615
1.631
1.647
1.664
1.680
1.695
1.711
1.727
1.742
1.758
1.773
1.788
1.803
1.818
1.833
1.847
1.862
1.877
1.891
1.905
1.920
1.934
1.948
1.962
1.976
1.990
2.003
2.017
2.031
0.1708
0.1748
0.1788
0.1828
0.1867
0.1906
0.1945
0.1983
0.2022
0.2060
0.2098
0.2136
0.2174
0.2211
0.2249
0.2286
0.2324
0.2361
0.2399
0.2436
0.2473
0.2510
0.2547
0.2584
0.2621
0.2658
0.2695
0.2731
0.2768
347.3
351.5
355.6
359.8
364.1
368.4
372.7
377.1
381.5
385.9
390.4
395.0
399.6
404.2
408.9
413.6
418.4
423.2
428.0
432.9
437.8
442.8
447.8
452.9
458.0
463.1
468.3
473.5
478.7
1.614
1.630
1.646
1.663
1.679
1.694
1.710
1.726
1.741
1.757
1.772
1.787
1.802
1.817
1.832
1.846
1.861
1.876
1.890
1.904
1.919
1.933
1.947
1.961
1.975
1.989
2.002
2.016
2.030
0.1567
0.1604
0.1642
0.1678
0.1715
0.1751
0.1787
0.1822
0.1858
0.1893
0.1929
0.1964
0.1999
0.2034
0.2068
0.2103
0.2138
0.2172
0.2207
0.2241
0.2275
0.2310
0.2344
0.2378
0.2412
0.2446
0.2480
0.2514
0.2548
347.1
351.2
355.4
359.6
363.9
368.2
372.5
376.9
381.3
385.8
390.3
394.9
399.5
404.1
408.8
413.5
418.3
423.1
427.9
432.8
437.8
442.7
447.7
452.8
457.9
463.0
468.2
473.4
478.7
1.607
1.623
1.640
1.656
1.672
1.688
1.704
1.719
1.735
1.750
1.765
1.781
1.796
1.811
1.825
1.840
1.855
1.869
1.884
1.898
1.912
1.927
1.941
1.955
1.969
1.982
1.996
2.010
2.024
−30
−25
−20
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
Absolute Pressure, kPa
V
120
130
140
150
−25.56°C
−23.65°C
−21.85°C
−20.15°C
S
V
V
H
S
V
H
Temp [°C]
0.1426
346.3
H
1.598
0.1322
347.6
H
1.598
S
0.1233
348.8
1.597
0.1155
349.9
1.597
S
Temp [°C]
−25
−20
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
0.1430
0.1464
0.1499
0.1533
0.1566
0.1600
0.1633
0.1666
0.1699
0.1731
0.1764
0.1796
0.1828
0.1861
0.1893
0.1925
0.1956
0.1988
0.2020
0.2051
0.2083
0.2114
0.2146
0.2177
0.2209
0.2240
0.2271
0.2302
0.2334
0.2365
346.8
350.9
355.1
359.4
363.6
367.9
372.3
376.7
381.1
385.6
390.1
394.7
399.3
403.9
408.6
413.4
418.1
422.9
427.8
432.7
437.6
442.6
447.6
452.7
457.8
462.9
468.1
473.3
478.6
483.9
1.600
1.616
1.633
1.649
1.665
1.681
1.697
1.712
1.728
1.743
1.759
1.774
1.789
1.804
1.819
1.833
1.848
1.863
1.877
1.892
1.906
1.920
1.934
1.948
1.962
1.976
1.990
2.003
2.017
2.031
0.1346
0.1378
0.1409
0.1441
0.1472
0.1503
0.1533
0.1564
0.1594
0.1624
0.1655
0.1684
0.1714
0.1744
0.1773
0.1803
0.1832
0.1862
0.1891
0.1920
0.1949
0.1978
0.2007
0.2037
0.2065
0.2094
0.2123
0.2152
0.2181
350.7
354.9
359.1
363.4
367.7
372.1
376.5
380.9
385.4
390.0
394.5
399.1
403.8
408.5
413.2
418.0
422.8
427.7
432.6
437.5
442.5
447.5
452.6
457.7
462.8
468.0
473.2
478.5
483.8
1.610
1.626
1.642
1.659
1.675
1.690
1.706
1.722
1.737
1.752
1.768
1.783
1.798
1.813
1.827
1.842
1.857
1.871
1.885
1.900
1.914
1.928
1.942
1.956
1.970
1.984
1.997
2.011
2.025
0.1244
0.1274
0.1304
0.1333
0.1362
0.1391
0.1420
0.1448
0.1477
0.1505
0.1533
0.1561
0.1589
0.1616
0.1644
0.1671
0.1699
0.1726
0.1753
0.1781
0.1808
0.1835
0.1862
0.1889
0.1916
0.1943
0.1970
0.1997
0.2023
350.4
354.6
358.9
363.2
367.5
371.9
376.3
380.8
385.3
389.8
394.4
399.0
403.6
408.3
413.1
417.9
422.7
427.6
432.5
437.4
442.4
447.4
452.5
457.6
462.7
467.9
473.1
478.4
483.7
1.603
1.620
1.636
1.653
1.669
1.684
1.700
1.716
1.731
1.747
1.762
1.777
1.792
1.807
1.822
1.836
1.851
1.865
1.880
1.894
1.908
1.922
1.937
1.950
1.964
1.978
1.992
2.005
2.019
0.1156
0.1184
0.1212
0.1240
0.1267
0.1294
0.1321
0.1348
0.1375
0.1401
0.1428
0.1454
0.1480
0.1506
0.1532
0.1557
0.1583
0.1609
0.1634
0.1660
0.1685
0.1711
0.1736
0.1761
0.1786
0.1812
0.1837
0.1862
0.1887
350.1
354.3
358.6
362.9
367.3
371.7
376.1
380.6
385.1
389.6
394.2
398.8
403.5
408.2
413.0
417.7
422.6
427.4
432.4
437.3
442.3
447.3
452.4
457.5
462.6
467.8
473.1
478.3
483.6
1.598
1.614
1.631
1.647
1.663
1.679
1.695
1.710
1.726
1.741
1.756
1.772
1.787
1.801
1.816
1.831
1.846
1.860
1.875
1.889
1.903
1.917
1.931
1.945
1.959
1.973
1.987
2.000
2.014
−25
−20
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
(Continued)
2-253
2-254
TABLE 2-132
Opteon™ YF (R-1234yf) (Continued )
Superheated Vapor—Constant Pressure Tables
V = Volume in m3/kg
H = Enthalpy in kJ/kg
S = Entropy in kJ/kg⋅K
Saturation Properties in Light Gray
Absolute Pressure, kPa
V
160
170
180
190
−18.54°C
−17.00°C
−15.53°C
−14.12°C
H
S
V
H
S
V
H
S
V
H
S
Temp [°C]
0.1086
351.0
1.597
0.1026
352.1
1.597
0.0972
353.0
1.597
0.0923
354.0
1.597
Temp [°C]
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
0.1105
0.1132
0.1158
0.1184
0.1210
0.1235
0.1261
0.1286
0.1311
0.1335
0.1360
0.1385
0.1409
0.1433
0.1458
0.1482
0.1506
0.1530
0.1554
0.1578
0.1602
0.1626
0.1649
0.1673
0.1697
0.1720
0.1744
0.1767
0.1791
0.1815
354.1
358.4
362.7
367.1
371.5
375.9
380.4
384.9
389.4
394.0
398.7
403.3
408.1
412.8
417.6
422.4
427.3
432.2
437.2
442.2
447.2
452.3
457.4
462.6
467.7
473.0
478.2
483.5
488.9
494.2
1.609
1.625
1.641
1.658
1.674
1.689
1.705
1.721
1.736
1.751
1.766
1.782
1.796
1.811
1.826
1.841
1.855
1.870
1.884
1.898
1.912
1.926
1.940
1.954
1.968
1.982
1.995
2.009
2.023
2.036
0.1036
0.1061
0.1086
0.1111
0.1135
0.1159
0.1183
0.1207
0.1231
0.1254
0.1277
0.1301
0.1324
0.1347
0.1370
0.1393
0.1415
0.1438
0.1461
0.1483
0.1506
0.1528
0.1551
0.1573
0.1595
0.1618
0.1640
0.1662
0.1684
0.1706
353.8
358.1
362.4
366.8
371.2
375.7
380.2
384.7
389.3
393.9
398.5
403.2
407.9
412.7
417.5
422.3
427.2
432.1
437.1
442.1
447.1
452.2
457.3
462.5
467.6
472.9
478.1
483.4
488.8
494.2
1.603
1.620
1.636
1.653
1.669
1.684
1.700
1.716
1.731
1.747
1.762
1.777
1.792
1.807
1.821
1.836
1.850
1.865
1.879
1.894
1.908
1.922
1.936
1.950
1.963
1.977
1.991
2.004
2.018
2.031
0.0974
0.0998
0.1022
0.1045
0.1069
0.1092
0.1114
0.1137
0.1160
0.1182
0.1204
0.1226
0.1248
0.1270
0.1292
0.1313
0.1335
0.1356
0.1378
0.1399
0.1420
0.1442
0.1463
0.1484
0.1505
0.1526
0.1547
0.1568
0.1589
0.1610
353.5
357.8
362.2
366.6
371.0
375.5
380.0
384.5
389.1
393.7
398.4
403.0
407.8
412.5
417.3
422.2
427.1
432.0
437.0
442.0
447.0
452.1
457.2
462.4
467.6
472.8
478.1
483.4
488.7
494.1
1.598
1.615
1.632
1.648
1.664
1.680
1.696
1.711
1.727
1.742
1.757
1.772
1.787
1.802
1.817
1.832
1.846
1.861
1.875
1.889
1.903
1.917
1.931
1.945
1.959
1.973
1.987
2.000
2.014
2.027
0.0942
0.0965
0.0987
0.1009
0.1031
0.1053
0.1074
0.1096
0.1117
0.1138
0.1159
0.1180
0.1201
0.1222
0.1242
0.1263
0.1283
0.1303
0.1324
0.1344
0.1364
0.1384
0.1405
0.1425
0.1445
0.1465
0.1485
0.1505
0.1524
357.6
362.0
366.4
370.8
375.3
379.8
384.3
388.9
393.5
398.2
402.9
407.6
412.4
417.2
422.1
427.0
431.9
436.9
441.9
446.9
452.0
457.1
462.3
467.5
472.7
478.0
483.3
488.6
494.0
1.610
1.627
1.643
1.659
1.675
1.691
1.707
1.722
1.738
1.753
1.768
1.783
1.798
1.813
1.827
1.842
1.856
1.871
1.885
1.899
1.913
1.927
1.941
1.955
1.969
1.982
1.996
2.010
2.023
−15
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
Absolute Pressure, kPa
200
210
−12.77°C
V
H
220
−11.47°C
S
V
H
230
−10.22°C
−9.01°C
S
V
H
S
V
H
S
Temp [°C]
0.0879
354.9
1.597
0.0839
355.7
1.597
0.0802
356.6
1.597
0.0769
357.4
1.597
Temp [°C]
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
0.0891
0.0913
0.0934
0.0956
0.0977
0.0997
0.1018
0.1039
0.1059
0.1079
0.1099
0.1119
0.1139
0.1159
0.1178
0.1198
0.1217
0.1237
0.1256
0.1275
0.1295
0.1314
0.1333
0.1352
0.1371
0.1390
0.1409
0.1428
0.1447
0.1466
357.3
361.7
366.1
370.6
375.1
379.6
384.2
388.7
393.4
398.0
402.7
407.5
412.3
417.1
421.9
426.8
431.8
436.7
441.7
446.8
451.9
457.0
462.2
467.4
472.6
477.9
483.2
488.5
493.9
499.3
1.606
1.623
1.639
1.655
1.671
1.687
1.703
1.718
1.733
1.749
1.764
1.779
1.794
1.809
1.823
1.838
1.852
1.867
1.881
1.895
1.909
1.923
1.937
1.951
1.965
1.979
1.992
2.006
2.019
2.032
0.0845
0.0866
0.0887
0.0907
0.0927
0.0947
0.0967
0.0987
0.1006
0.1025
0.1045
0.1064
0.1083
0.1101
0.1120
0.1139
0.1158
0.1176
0.1195
0.1213
0.1231
0.1250
0.1268
0.1286
0.1305
0.1323
0.1341
0.1359
0.1377
0.1395
357.0
361.5
365.9
370.4
374.9
379.4
384.0
388.6
393.2
397.9
402.6
407.3
412.1
417.0
421.8
426.7
431.6
436.6
441.6
446.7
451.8
456.9
462.1
467.3
472.5
477.8
483.1
488.5
493.8
499.3
1.602
1.618
1.635
1.651
1.667
1.683
1.699
1.714
1.730
1.745
1.760
1.775
1.790
1.805
1.819
1.834
1.849
1.863
1.877
1.891
1.906
1.920
1.934
1.947
1.961
1.975
1.988
2.002
2.015
2.029
0.0803
0.0824
0.0843
0.0863
0.0883
0.0902
0.0921
0.0940
0.0958
0.0977
0.0995
0.1013
0.1032
0.1050
0.1068
0.1086
0.1103
0.1121
0.1139
0.1157
0.1174
0.1192
0.1209
0.1227
0.1244
0.1261
0.1279
0.1296
0.1313
0.1331
356.8
361.2
365.7
370.1
374.7
379.2
383.8
388.4
393.0
397.7
402.4
407.2
412.0
416.8
421.7
426.6
431.5
436.5
441.5
446.6
451.7
456.8
462.0
467.2
472.4
477.7
483.0
488.4
493.8
499.2
1.597
1.614
1.631
1.647
1.663
1.679
1.695
1.710
1.726
1.741
1.756
1.771
1.786
1.801
1.816
1.830
1.845
1.859
1.874
1.888
1.902
1.916
1.930
1.944
1.958
1.971
1.985
1.998
2.012
2.025
0.0785
0.0804
0.0823
0.0842
0.0860
0.0878
0.0896
0.0914
0.0932
0.0950
0.0967
0.0985
0.1002
0.1020
0.1037
0.1054
0.1071
0.1088
0.1105
0.1122
0.1139
0.1155
0.1172
0.1189
0.1206
0.1222
0.1239
0.1255
0.1272
360.9
365.4
369.9
374.4
379.0
383.6
388.2
392.9
397.6
402.3
407.0
411.8
416.7
421.6
426.5
431.4
436.4
441.4
446.5
451.6
456.7
461.9
467.1
472.3
477.6
482.9
488.3
493.7
499.1
1.610
1.627
1.643
1.659
1.675
1.691
1.707
1.722
1.737
1.753
1.768
1.783
1.798
1.812
1.827
1.841
1.856
1.870
1.884
1.899
1.913
1.927
1.940
1.954
1.968
1.981
1.995
2.008
2.022
−10
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
(Continued)
2-255
2-256
TABLE 2-132
Opteon™ YF (R-1234yf) (Continued )
Superheated Vapor—Constant Pressure Tables
V = Volume in m3/kg
H = Enthalpy in kJ/kg
S = Entropy in kJ/kg⋅K
Saturation Properties in Light Gray
Absolute Pressure, kPa
V
240
250
260
270
−7.84°C
−6.70°C
−5.60°C
−4.54°C
S
V
H
S
H
S
Temp [°C]
0.0738
358.2
H
1.597
S
0.0710
V
358.9
H
1.597
0.0684
359.6
1.597
0.0659
V
360.3
1.597
Temp [°C]
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
0.0749
0.0768
0.0786
0.0804
0.0822
0.0840
0.0857
0.0874
0.0891
0.0908
0.0925
0.0942
0.0959
0.0976
0.0992
0.1009
0.1025
0.1041
0.1058
0.1074
0.1090
0.1106
0.1122
0.1138
0.1154
0.1170
0.1186
0.1202
0.1218
0.1234
360.7
365.2
369.7
374.2
378.8
383.4
388.0
392.7
397.4
402.1
406.9
411.7
416.5
421.4
426.3
431.3
436.3
441.3
446.4
451.5
456.6
461.8
467.0
472.3
477.5
482.9
488.2
493.6
499.0
504.5
1.606
1.623
1.639
1.656
1.672
1.687
1.703
1.719
1.734
1.749
1.764
1.779
1.794
1.809
1.824
1.838
1.852
1.867
1.881
1.895
1.909
1.923
1.937
1.951
1.965
1.978
1.992
2.005
2.019
2.032
0.0716
0.0734
0.0752
0.0769
0.0787
0.0804
0.0821
0.0837
0.0854
0.0870
0.0887
0.0903
0.0919
0.0935
0.0951
0.0967
0.0983
0.0998
0.1014
0.1030
0.1045
0.1061
0.1076
0.1092
0.1107
0.1122
0.1138
0.1153
0.1168
0.1184
360.4
364.9
369.5
374.0
378.6
383.2
387.9
392.5
397.2
402.0
406.8
411.6
416.4
421.3
426.2
431.2
436.2
441.2
446.3
451.4
456.5
461.7
466.9
472.2
477.4
482.8
488.1
493.5
499.0
504.4
1.603
1.619
1.636
1.652
1.668
1.684
1.700
1.715
1.731
1.746
1.761
1.776
1.791
1.806
1.820
1.835
1.849
1.864
1.878
1.892
1.906
1.920
1.934
1.948
1.961
1.975
1.989
2.002
2.015
2.029
0.0686
0.0703
0.0721
0.0738
0.0754
0.0771
0.0787
0.0803
0.0819
0.0835
0.0851
0.0867
0.0882
0.0898
0.0913
0.0928
0.0944
0.0959
0.0974
0.0989
0.1004
0.1019
0.1034
0.1049
0.1064
0.1078
0.1093
0.1108
0.1123
0.1137
360.2
364.7
369.2
373.8
378.4
383.0
387.7
392.4
397.1
401.8
406.6
411.4
416.3
421.2
426.1
431.1
436.1
441.1
446.2
451.3
456.4
461.6
466.8
472.1
477.4
482.7
488.0
493.4
498.9
504.3
1.599
1.616
1.632
1.649
1.665
1.681
1.696
1.712
1.727
1.743
1.758
1.773
1.788
1.802
1.817
1.832
1.846
1.861
1.875
1.889
1.903
1.917
1.931
1.945
1.958
1.972
1.986
1.999
2.012
2.026
0.0675
0.0691
0.0708
0.0724
0.0740
0.0756
0.0772
0.0787
0.0803
0.0818
0.0833
0.0848
0.0863
0.0878
0.0893
0.0907
0.0922
0.0937
0.0951
0.0966
0.0980
0.0995
0.1009
0.1023
0.1038
0.1052
0.1066
0.1080
0.1094
364.4
369.0
373.6
378.2
382.8
387.5
392.2
396.9
401.7
406.5
411.3
416.1
421.0
426.0
430.9
435.9
441.0
446.1
451.2
456.3
461.5
466.7
472.0
477.3
482.6
488.0
493.4
498.8
504.3
1.612
1.629
1.645
1.661
1.677
1.693
1.709
1.724
1.739
1.755
1.770
1.785
1.799
1.814
1.829
1.843
1.858
1.872
1.886
1.900
1.914
1.928
1.942
1.956
1.969
1.983
1.996
2.010
2.023
−5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
Absolute Pressure, kPa
V
280
290
300
310
−3.50°C
−2.49°C
−1.51°C
−0.55°C
S
V
H
S
H
S
Temp [°C]
0.0637
361.0
H
1.597
S
0.0615
V
361.7
H
1.597
0.0596
362.3
1.598
0.0577
V
362.9
1.598
Temp [°C]
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
0.0648
0.0664
0.0680
0.0696
0.0712
0.0727
0.0742
0.0757
0.0772
0.0787
0.0802
0.0816
0.0831
0.0845
0.0860
0.0874
0.0888
0.0902
0.0916
0.0930
0.0944
0.0958
0.0972
0.0986
0.1000
0.1013
0.1027
0.1041
0.1055
0.1068
364.2
368.8
373.4
378.0
382.6
387.3
392.0
396.7
401.5
406.3
411.1
416.0
420.9
425.8
430.8
435.8
440.9
445.9
451.1
456.2
461.4
466.6
471.9
477.2
482.5
487.9
493.3
498.7
504.2
509.7
1.609
1.626
1.642
1.658
1.674
1.690
1.706
1.721
1.736
1.752
1.767
1.782
1.797
1.811
1.826
1.840
1.855
1.869
1.883
1.897
1.911
1.925
1.939
1.953
1.966
1.980
1.993
2.007
2.020
2.033
0.0623
0.0639
0.0655
0.0670
0.0685
0.0700
0.0715
0.0730
0.0744
0.0758
0.0773
0.0787
0.0801
0.0815
0.0829
0.0842
0.0856
0.0870
0.0884
0.0897
0.0911
0.0924
0.0938
0.0951
0.0964
0.0978
0.0991
0.1004
0.1017
0.1031
363.9
368.5
373.2
377.8
382.4
387.1
391.8
396.6
401.4
406.2
411.0
415.9
420.8
425.7
430.7
435.7
440.8
445.8
451.0
456.1
461.3
466.5
471.8
477.1
482.4
487.8
493.2
498.6
504.1
509.6
1.606
1.622
1.639
1.655
1.671
1.687
1.703
1.718
1.734
1.749
1.764
1.779
1.794
1.808
1.823
1.838
1.852
1.866
1.880
1.894
1.909
1.922
1.936
1.950
1.964
1.977
1.991
2.004
2.017
2.031
0.0600
0.0616
0.0631
0.0646
0.0661
0.0675
0.0690
0.0704
0.0718
0.0732
0.0746
0.0759
0.0773
0.0786
0.0800
0.0813
0.0827
0.0840
0.0853
0.0866
0.0879
0.0892
0.0905
0.0918
0.0931
0.0944
0.0957
0.0970
0.0983
0.0996
363.7
368.3
372.9
377.6
382.2
386.9
391.7
396.4
401.2
406.0
410.9
415.7
420.6
425.6
430.6
435.6
440.6
445.7
450.9
456.0
461.2
466.4
471.7
477.0
482.3
487.7
493.1
498.6
504.0
509.6
1.603
1.619
1.636
1.652
1.668
1.684
1.700
1.715
1.731
1.746
1.761
1.776
1.791
1.806
1.820
1.835
1.849
1.864
1.878
1.892
1.906
1.920
1.934
1.947
1.961
1.975
1.988
2.002
2.015
2.028
0.0579
0.0594
0.0609
0.0623
0.0638
0.0652
0.0666
0.0680
0.0693
0.0707
0.0720
0.0733
0.0747
0.0760
0.0773
0.0786
0.0799
0.0812
0.0825
0.0837
0.0850
0.0863
0.0875
0.0888
0.0901
0.0913
0.0926
0.0938
0.0950
0.0963
363.4
368.1
372.7
377.4
382.0
386.8
391.5
396.2
401.0
405.9
410.7
415.6
420.5
425.5
430.5
435.5
440.5
445.6
450.7
455.9
461.1
466.3
471.6
476.9
482.3
487.6
493.0
498.5
504.0
509.5
1.600
1.616
1.633
1.649
1.665
1.681
1.697
1.713
1.728
1.743
1.758
1.773
1.788
1.803
1.818
1.832
1.847
1.861
1.875
1.889
1.903
1.917
1.931
1.945
1.958
1.972
1.986
1.999
2.012
2.026
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
2-257
2-258
PHYSICAL AnD CHEMICAL DATA
FIG. 2-16
Pressure-enthalpy diagram for Refrigerant 1234yf. Properties computed with the NIST REFPROP Database, Version 7.0
(Lemmon, E. W., M.O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic
and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology).
Provided by Chemours.
THERMODYnAMIC PROPERTIES
TABLE 2-133 Thermophysical Properties of Saturated Seawater
Temp.,
°C
Pressure,
bar
v, (m3/kg)103
cp, kJ/(kg⋅K)
µ, Ns/m2
k, W/(m⋅K)
NPr
105κ, 1/bar
0
1
2
3
4
0.005993
0.006438
0.006916
0.007427
0.007970
1.000158
1.000099
1.000057
1.000033
1.000025
4.000
4.000
4.000
4.000
4.001
0.001884
0.001827
0.001772
0.001720
0.001669
0.560
0.563
0.565
0.567
0.569
13.46
12.98
12.55
12.13
11.74
5.06
5.02
4.98
4.95
4.92
5
6
7
8
9
0.008548
0.009163
0.009816
0.010511
0.011248
1.000033
1.000057
1.000096
1.000149
1.000261
4.001
4.001
4.002
4.002
4.002
0.001620
0.001574
0.001529
0.001486
0.001445
0.571
0.574
0.576
0.578
0.580
11.35
10.97
10.62
10.29
9.97
4.89
4.86
4.83
4.80
4.78
10
11
12
13
14
0.01203
0.01286
0.01374
0.01467
0.01566
1.000298
1.000392
1.000500
1.000620
1.000727
4.003
4.003
4.003
4.004
4.004
0.001405
0.001367
0.001330
0.001294
0.001259
0.582
0.584
0.586
0.588
0.590
9.70
9.37
9.09
8.81
8.54
4.76
4.74
4.72
4.70
4.68
15
16
17
18
19
0.01671
0.01781
0.01898
0.02022
0.02153
1.000899
1.001055
1.001224
1.001404
1.001595
4.005
4.005
4.006
4.006
4.007
0.001226
0.001195
0.001165
0.001136
0.001107
0.592
0.594
0.595
0.597
0.599
8.29
8.06
7.82
7.62
7.41
4.66
4.65
4.63
4.62
4.60
20
21
22
23
24
0.02291
0.02437
0.02591
0.02753
0.02924
1.001796
1.002009
1.002232
1.002465
1.002708
4.007
4.007
4.008
4.008
4.009
0.001080
0.001054
0.001029
0.001005
0.000981
0.600
0.602
0.604
0.605
0.607
7.21
7.02
6.82
6.66
6.48
4.59
4.57
4.56
4.55
4.54
25
26
27
28
29
0.03104
0.03294
0.03494
0.03705
0.03926
1.002961
1.003224
1.003496
1.003778
1.004069
4.009
4.009
4.010
4.010
4.011
0.000958
0.000936
0.000915
0.000895
0.000875
0.608
0.609
0.611
0.612
0.614
6.31
6.16
6.01
5.86
5.72
4.53
4.52
4.51
4.50
4.49
30
0.04159
1.004369
4.011
0.000855
0.615
5.58
4.48
κ = (−1/V)(∂v/∂p)T ⋅ 105. Thus, at 0°C, the compressibility is 5.06 × 10−5/bar.
For further information see, for instance, Bromley, LeR. A., J. Chem. Eng. Data, 12, 2 (1967): 202–206; 13, 1 (1968): 60–62 and
13, 3: 399–402; 15, 2 (1970): 246–253; and A.I.Ch.E.J., 20, 2 (1974): 326–335.
Thermal conductivity data sources include Castelli, V. J., E. M. Stanley, et al., Deep Sea Res., 211 (1974): 311–318; Levy,
F. L., Int. J. Refrig., 5, 3 (1982): 155–159.
For velocity of sound, see, for instance, U.S. Naval Oceanographic Office SP 58, 1962 (50 pp.). More recent information is
contained in UNESCO technical papers. See Marine Science No. 38, 1981 (6 pp.) and No. 44, 1983 (53 pp.).
For sea ice properties, see Fukusako, S., Int. J. Thermophys., 11, 2 (1990): 353–372.
2-259
FIG. 2-17
Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states: enthalpy of liquid water at 32°F and vapor pressure is zero; partial molal enthalpy of infinitely dilute NaOH solution at 64°F and 1 atm is zero. [W.L. McCabe, Trans. Am. Inst. Chem. Eng., 31: 129 (1935).]
FIG. 2-18 Enthalpy-concentration diagram for aqueous sulfuric acid at 1 atm.
Reference states: enthalpies of pure-liquid components at 32°F and vapor pressures are zero. Note: It should be observed that the weight basis includes the
vapor, which is particularly important in the two-phase region. The upper ends
of the tie lines in this region are assumed to be pure water. (O.A. Hougen and
K.M. Watson, Chemical Process Principles, part I, Wiley, New York, 1943.)
2-260
THERMODYnAMIC PROPERTIES
TABLE 2-134
Temp.,
°F
Saturated Solid/Vapor Water*
Volume,
ft3/lb
Enthalpy,
Btu/lb
Entropy,
Btu/(lb)(°F)
Pressure,
lb/in2 abs.
Solid
Vapor
Solid
Vapor
Solid
Vapor
−160
−150
−140
−130
−120
4.949.−8
1.620.−7
4.928.−7
1.403.−6
3.757.−6
0.01722
0.01723
0.01724
0.01725
0.01726
3.607.+9
1.139.+9
3.864.+8
1.400.+8
5.386.+7
−222.05
−218.82
−215.49
−212.08
−208.58
990.38
994.80
999.21
1003.63
1008.05
−0.4907
−0.4801
−0.4695
−0.4590
−0.4485
3.5549
3.4387
3.3301
3.2284
3.1330
−110
−100
−90
−80
−70
9.517.−6
2.291.−5
5.260.−5
1.157.−4
2.443.−4
0.01728
0.01729
0.01730
0.01731
0.01732
2.189.+7
9.352.+6
4.186.+6
1.955.+6
9.501.+5
−204.98
−201.28
−197.49
−193.60
−189.61
1012.47
1016.89
1021.31
1025.73
1030.15
−0.4381
−0.4277
−0.4173
−0.4069
−0.3965
3.0434
2.9591
2.8796
2.8045
2.7336
−60
−50
−45
−40
−35
4.972.−4
9.776.−4
1.354.−3
1.861.−3
2.540.−3
0.01734
0.01735
0.01736
0.01737
0.01737
4.788.+5
2.496.+5
1.824.+5
1.343.+5
9.961.+4
−185.52
−181.34
−179.21
−177.06
−174.88
1034.58
1039.00
1041.21
1043.42
1045.63
−0.3862
−0.3758
−0.3707
−0.3655
−0.3604
2.6664
2.6028
2.5723
2.5425
2.5135
−30
−25
−20
−15
−10
3.440.−3
4.627.−3
6.181.−3
8.204.−3
1.082.−2
0.01738
0.01739
0.01739
0.01740
0.01741
7.441.+4
5.596.+4
4.237.+4
3.228.+4
2.475.+4
−172.68
−170.46
−168.21
−165.94
−163.65
1047.84
1050.05
1052.26
1054.47
1056.67
−0.3552
−0.3501
−0.3449
−0.3398
−0.3347
2.4853
2.4577
2.4308
2.4046
2.3791
−5
0
5
10
15
1.419.−2
1.849.−2
2.396.−2
3.087.−2
3.957.−2
0.01741
0.01742
0.01743
0.01744
0.01744
1.909.+4
1.481.+4
1.155.+4
9.060.+3
7.144.+3
−161.33
−158.98
−156.61
−154.22
−151.80
1058.88
1061.09
1063.29
1065.50
1067.70
−0.3295
−0.3244
−0.3193
−0.3142
−0.3090
2.3541
2.3297
2.3039
2.2827
2.2600
16
18
20
22
24
4.156.−2
4.581.−2
5.045.−2
5.552.−2
6.105.−2
0.01745
0.01745
0.01745
0.01746
0.01746
6.817.+3
6.210.+3
5.662.+3
5.166.+3
4.717.+3
−151.32
−150.34
−149.36
−148.38
−147.39
1068.14
1069.02
1069.90
1070.38
1071.66
−0.3080
−0.3060
−0.3039
−0.3019
−0.2998
2.2555
2.2466
2.2378
2.2291
2.2205
26
28
30
31
32
6.708.−2
7.365.−2
8.080.−2
8.461.−2
8.858.−2
0.01746
0.01746
0.01747
0.01747
0.01747
4.311.+3
3.943.+3
3.608.+3
3.453.+3
3.305.+3
−146.40
−145.40
−144.40
−143.90
−143.40
1072.53
1073.41
1074.29
1074.73
1075.16
−0.2978
−0.2957
−0.2937
−0.2927
−0.2916
2.2119
2.2034
2.1950
2.1908
2.1867
∗Condensed from Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1967 and 1972.
Reproduced by permission. The validity of many standard reference tables has been critically reviewed by Jancso, Pupezin, and
van Hook, J. Phys. Chem., 74 (1970):2984. Current information on the properties of solid, vapor, and liquid water properties can be
found at http://www.iapws.org. The notation 4.949.−8, 3.607.+9, etc., means 4.949 × 10−8, 3.607 × 109, etc.
2-261
2-262
TABLE 2-135 Thermodynamic Properties of Water
Temperature
K
Pressure
MPa
Density
mol/dm3
273.16
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
647.1
0.000612
0.000992
0.001920
0.003537
0.006231
0.010546
0.017213
0.027188
0.041682
0.062194
0.090535
0.12885
0.17964
0.24577
0.33045
0.43730
0.57026
0.73367
0.9322
1.1709
1.4551
1.7905
2.1831
2.6392
3.1655
3.7690
4.4569
5.2369
6.1172
7.1062
8.2132
9.448
10.821
12.345
14.033
15.901
17.969
20.265
22.064
55.497
55.501
55.440
55.315
55.139
54.919
54.662
54.371
54.049
53.698
53.321
52.918
52.490
52.038
51.563
51.064
50.541
49.994
49.421
48.824
48.199
47.545
46.861
46.145
45.393
44.603
43.770
42.889
41.954
40.956
39.885
38.725
37.456
36.048
34.451
32.577
30.210
26.729
17.874
273.16
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
0.000612
0.000992
0.001920
0.003537
0.006231
0.010546
0.017213
0.027188
0.041682
0.062194
0.090535
0.12885
0.17964
0.24577
0.33045
0.43730
0.57026
0.73367
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
0
0.51875
1.2742
2.0278
2.7808
3.5339
4.2873
5.0414
5.7964
6.5526
7.3104
8.0701
8.8320
9.5966
10.364
11.136
11.911
12.692
13.477
14.269
15.068
15.875
16.690
17.515
18.352
19.200
20.064
20.943
21.841
22.762
23.709
24.688
25.707
26.777
27.917
29.160
30.585
32.422
36.314
1.1E-05
0.51877
1.2742
2.0279
2.7810
3.5340
4.2876
5.0419
5.7972
6.5538
7.3121
8.0725
8.8354
9.6013
10.371
11.144
11.923
12.706
13.496
14.293
15.098
15.913
16.737
17.573
18.421
19.285
20.165
21.065
21.987
22.935
23.915
24.932
25.996
27.119
28.324
29.648
31.180
33.180
37.548
0
0.001876
0.004527
0.007082
0.009551
0.011941
0.014260
0.016511
0.018700
0.020830
0.022906
0.024932
0.026911
0.028847
0.030743
0.032602
0.034427
0.036222
0.037988
0.039729
0.041448
0.043147
0.044830
0.046498
0.048156
0.049807
0.051454
0.053102
0.054756
0.056422
0.058106
0.059821
0.061577
0.063396
0.065309
0.067371
0.069715
0.072737
0.079393
42.785
42.954
43.201
43.446
43.690
43.931
44.169
44.404
44.634
44.860
45.079
45.291
45.496
45.691
45.876
46.050
46.211
46.359
45.055
45.280
45.609
45.936
46.261
46.582
46.900
47.212
47.519
47.819
48.111
48.393
48.665
48.924
49.170
49.400
49.613
49.807
0.16494
0.16174
0.15741
0.15344
0.14981
0.14647
0.14339
0.14054
0.13791
0.13546
0.13317
0.13104
0.12904
0.12715
0.12537
0.12369
0.12208
0.12054
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
0.075978
0.075669
0.075095
0.074412
0.073645
0.072811
0.071927
0.071008
0.070070
0.069124
0.068180
0.067247
0.066331
0.065438
0.064570
0.063731
0.062920
0.062140
0.061390
0.060671
0.059984
0.059327
0.058702
0.058109
0.057548
0.057023
0.056536
0.056089
0.055690
0.055347
0.055071
0.054881
0.054808
0.054902
0.055258
0.056100
0.058152
0.064521
0.076023
0.075688
0.075429
0.075320
0.075294
0.075317
0.075373
0.075456
0.075567
0.075708
0.075883
0.076098
0.076357
0.076664
0.077026
0.077447
0.077934
0.078495
0.079136
0.079869
0.080706
0.081662
0.082757
0.084013
0.085464
0.087149
0.089124
0.091464
0.094275
0.097713
0.10201
0.10754
0.11491
0.12526
0.14100
0.16852
0.23108
0.46736
1402.3
1434.1
1472.1
1501.4
1523.2
1538.7
1548.7
1553.9
1554.8
1552.0
1545.8
1536.5
1524.3
1509.5
1492.2
1472.5
1450.6
1426.5
1400.4
1372.2
1342.0
1309.8
1275.7
1239.6
1201.5
1161.3
1119.1
1074.6
1027.9
978.54
926.44
871.23
812.49
749.57
681.27
604.73
513.19
400.66
0
−0.24142
−0.23515
−0.22720
−0.22024
−0.21393
−0.20804
−0.20241
−0.19690
−0.19140
−0.18581
−0.18005
−0.17404
−0.16769
−0.16092
−0.15366
−0.14581
−0.13728
−0.12794
−0.11767
−0.10631
−0.09369
−0.07959
−0.06372
−0.04578
−0.02534
−0.00189
0.025264
0.057002
0.094527
0.13949
0.19425
0.26220
0.34857
0.46172
0.61660
0.84473
1.2251
1.9542
3.7410
561.04
574.04
592.73
610.28
626.05
639.71
651.18
660.55
668.00
673.76
678.02
681.00
682.83
683.64
683.52
682.53
680.70
678.05
674.59
670.28
665.12
659.07
652.06
644.05
634.95
624.68
613.15
600.26
585.95
570.21
553.08
534.74
515.43
495.46
475.03
454.10
432.51
414.93
1791.2
1433.7
1084.0
853.84
693.54
577.02
489.49
421.97
368.77
326.10
291.36
262.69
238.77
218.60
201.43
186.68
173.91
162.77
152.98
144.31
136.58
129.64
123.37
117.66
112.42
107.57
103.05
98.792
94.746
90.857
87.074
83.342
79.600
75.773
71.759
67.382
62.244
55.247
0.025553
0.025657
0.025816
0.025982
0.026158
0.026350
0.026568
0.026821
0.027118
0.027469
0.027883
0.028372
0.028944
0.029608
0.030369
0.031230
0.032187
0.033234
0.033947
0.034073
0.034270
0.034483
0.034716
0.034980
0.035287
0.035653
0.036091
0.036617
0.037249
0.038004
0.038903
0.039963
0.041203
0.042634
0.044269
0.046114
409.00
413.92
420.99
427.89
434.63
441.18
447.54
453.68
459.58
465.22
470.57
475.61
480.32
484.67
488.65
492.22
495.39
498.12
Cv
kJ/(mol⋅K)
Saturated Properties
0.000269
0.000426
0.000797
0.001420
0.002424
0.003978
0.006304
0.009681
0.014448
0.021014
0.029859
0.041537
0.056683
0.076014
0.10034
0.13055
0.16765
0.21276
0.018019
0.018018
0.018038
0.018078
0.018136
0.018209
0.018294
0.018392
0.018502
0.018623
0.018754
0.018897
0.019051
0.019217
0.019394
0.019583
0.019786
0.020003
0.020234
0.020482
0.020748
0.021033
0.021340
0.021671
0.022030
0.022420
0.022847
0.023316
0.023836
0.024417
0.025072
0.025823
0.026698
0.027741
0.029026
0.030697
0.033101
0.037413
0.055948
3711.0
2345.4
1254.3
704.01
412.60
251.39
158.62
103.30
69.213
47.586
33.491
24.075
17.642
13.156
9.9666
7.6601
5.9649
4.7002
592.65
477.26
351.65
264.35
203.74
161.25
130.92
108.77
92.178
79.440
69.427
61.373
54.749
49.181
44.405
40.237
36.550
33.259
17.071
17.442
18.031
18.673
19.369
20.117
20.922
21.784
22.707
23.695
24.750
25.875
27.074
28.347
29.699
31.128
32.638
34.230
9.2163
9.3815
9.6414
9.9195
10.213
10.518
10.833
11.157
11.487
11.823
12.162
12.504
12.848
13.192
13.538
13.883
14.228
14.573
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
647.1
0.93220
1.1709
1.4551
1.7905
2.1831
2.6392
3.1655
3.7690
4.4569
5.2369
6.1172
7.1062
8.2132
9.4480
10.821
12.345
14.033
15.901
17.969
20.265
22.064
0.26711
0.33209
0.40925
0.50035
0.60738
0.73265
0.87884
1.0491
1.2473
1.4780
1.7471
2.0620
2.4325
2.8720
3.3994
4.0434
4.8497
5.9009
7.3737
9.8331
17.874
3.7438
3.0113
2.4435
1.9986
1.6464
1.3649
1.1379
0.95318
0.80174
0.67659
0.57238
0.48497
0.41110
0.34819
0.29417
0.24732
0.20620
0.16946
0.13562
0.10170
0.055948
55.317
53.212
0.018078
0.018793
46.492
46.609
46.708
46.788
46.848
46.885
46.898
46.883
46.838
46.758
46.641
46.478
46.264
45.988
45.636
45.188
44.613
43.855
42.801
41.095
36.314
49.982
50.134
50.263
50.367
50.442
50.487
50.500
50.475
50.411
50.302
50.142
49.925
49.641
49.278
48.819
48.242
47.506
46.550
45.238
43.156
37.548
0.11907
0.11764
0.11627
0.11493
0.11362
0.11233
0.11105
0.10979
0.10852
0.10724
0.10595
0.10462
0.10324
0.10180
0.10026
0.098600
0.096755
0.094631
0.092029
0.088324
0.079393
0.034362
0.035561
0.036821
0.038137
0.039503
0.040920
0.042391
0.043920
0.045519
0.047197
0.048968
0.050848
0.052856
0.055017
0.057361
0.059939
0.062831
0.066197
0.070465
0.077576
0.048177
0.050469
0.053005
0.055809
0.058919
0.062388
0.066289
0.070723
0.075827
0.081789
0.088873
0.097461
0.10813
0.12178
0.13994
0.16540
0.20384
0.26923
0.40819
0.94736
500.41
502.24
503.60
504.45
504.78
504.55
503.71
502.23
500.05
497.10
493.31
488.58
482.79
475.80
467.41
457.33
445.11
429.99
410.21
379.64
0
30.307
27.653
25.265
23.118
21.187
19.450
17.886
16.475
15.197
14.035
12.973
11.997
11.093
10.248
9.4499
8.6837
7.9329
7.1743
6.3669
5.3854
3.7410
35.904
37.663
39.512
41.455
43.502
45.666
47.969
50.442
53.130
56.102
59.456
63.341
67.981
73.721
81.108
91.052
105.17
126.66
163.44
250.01
−0.22024
−0.17843
610.32
678.97
67.038
47.254
19.298
10.567
6.6444
4.5167
3.2280
2.3885
1.8122
1.4006
25.053
27.008
35.861
46.367
57.964
70.385
83.466
97.085
111.15
125.58
−0.22022
−0.16113
−0.11435
610.73
684.10
673.37
29.473
19.741
10.615
6.6387
4.5077
3.2212
2.3837
1.8089
1.3982
36.427
38.799
47.636
58.735
70.983
84.000
97.573
111.57
125.89
−0.22012
−0.16222
−0.04945
0.047232
612.54
686.54
646.52
604.15
14.917
15.261
15.606
15.952
16.300
16.653
17.011
17.377
17.755
18.149
18.563
19.007
19.489
20.024
20.634
21.350
22.229
23.374
25.018
27.938
Single-Phase Properties
300
372.76
0.1
0.1
372.76
400
500
600
700
800
900
1000
1100
1200
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.032769
0.030397
0.024154
0.020086
0.017201
0.015044
0.013369
0.012030
0.010936
0.010024
2.0295
7.5214
0.007081
0.02347
0.074406
0.067921
0.075315
0.075938
45.138
45.900
48.619
51.387
54.256
57.240
60.347
63.581
66.941
70.426
48.190
49.189
52.759
56.365
60.069
63.887
67.827
71.893
76.085
80.402
0.13257
0.13516
0.14313
0.14970
0.15541
0.16050
0.16514
0.16943
0.17342
0.17718
0.02801
0.02717
0.02717
0.028103
0.029225
0.030431
0.031687
0.032963
0.034228
0.035458
0.037444
0.036170
0.035693
0.036513
0.037592
0.038778
0.040024
0.041293
0.042554
0.043781
0.018070
0.019209
0.020307
2.0263
9.5914
13.717
2.0444
9.6106
13.737
0.007077
0.028834
0.038518
0.074353
0.065422
0.061169
0.075270
0.076628
0.079348
3.5015
3.9749
4.8861
5.7547
6.6074
7.4524
8.2932
9.1313
9.9677
46.529
48.111
51.123
54.087
57.121
60.258
63.511
66.885
70.380
50.030
52.086
56.009
59.842
63.729
67.710
71.804
76.016
80.347
0.11863
0.12295
0.13011
0.13602
0.14121
0.14590
0.15021
0.15422
0.15799
0.034718
0.030084
0.029002
0.029629
0.030651
0.031821
0.033051
0.034290
0.035504
0.048846
0.041065
0.038358
0.038495
0.039301
0.040358
0.041522
0.042719
0.043905
0.018038
0.019167
0.021614
0.023175
2.0204
9.5643
17.474
20.685
2.1106
9.6601
17.582
20.801
0.007057
0.028766
0.046415
0.052622
0.074119
0.065337
0.058082
0.056215
0.075070
0.076438
0.083643
0.090740
1501.5
1543.5
471.99
490.31
548.31
598.61
643.92
685.47
724.03
760.17
794.33
826.85
12.256
13.285
17.270
21.407
25.564
29.669
33.685
37.592
41.382
45.054
2-263
1
1
1
453.03
500
600
700
800
900
1000
1100
1200
1
1
1
1
1
1
1
1
1
300
400
500
537.09
5
5
5
5
537.09
600
700
5
5
5
1.4072
1.1320
0.91269
0.71063
0.88340
1.0957
46.785
49.734
53.286
50.338
54.151
58.765
0.10762
0.11436
0.12148
0.046699
0.034611
0.031678
0.079952
0.051045
0.043318
498.04
561.07
624.59
14.362
10.407
6.5536
55.203
54.653
62.680
18.032
21.062
25.547
5
5
5
5
5
0.77805
0.68224
0.60918
0.55109
0.50355
1.2853
1.4658
1.6416
1.8146
1.9859
56.576
59.855
63.197
66.632
70.172
63.002
67.183
71.405
75.705
80.101
0.12714
0.13207
0.13652
0.14061
0.14444
0.031683
0.032430
0.033447
0.034565
0.035704
0.041848
0.041922
0.042571
0.043465
0.044458
674.39
717.57
756.57
792.63
826.45
4.4532
3.1856
2.3599
1.7924
1.3865
73.950
86.626
99.971
113.64
127.51
29.806
33.891
37.821
41.606
45.257
0.28559
0.25158
0.20466
0.17377
0.15134
0.13418
0.12058
0.10951
0.10032
55.439
52.173
46.267
43.151
1503.0
1511.3
1392.0
853.83
282.91
300
400
453.03
800
900
1000
1100
1200
55.340
52.060
49.243
30.517
32.898
41.401
49.786
58.136
66.471
74.799
83.123
91.444
99.763
2.0277
7.5196
501.02
535.74
592.58
640.55
683.48
722.85
759.50
794.01
826.77
1509.8
1520.9
1250.0
1087.8
853.67
218.80
150.24
15.021
17.051
21.329
25.550
29.687
33.718
37.630
41.420
45.088
853.00
219.84
118.27
100.01
(Continued)
2-264
TABLE 2-135
Temperature
K
Thermodynamic Properties of Water (Continued )
Pressure
MPa
Density
mol/dm3
300
400
500
584.15
10
10
10
10
55.561
52.312
46.517
38.213
584.15
600
700
800
900
1000
1100
1200
10
10
10
10
10
10
10
10
Volume
dm3/mol
Int. energy
kJ/mol
Enthalpy
kJ/mol
Entropy
kJ/(mol⋅K)
Cv
kJ/(mol⋅K)
Cp
kJ/(mol⋅K)
Sound speed
m/s
Joule-Thomson
K/MPa
Therm. cond.
mW/(m⋅K)
Viscosity
µPa⋅s
Single-Phase Properties (Continued )
3.0787
2.7628
1.9625
1.6157
1.3945
1.2345
1.1111
1.0119
0.017998
0.019116
0.021497
0.026169
2.0131
9.5311
17.389
25.105
2.1931
9.7222
17.604
25.367
0.007031
0.028682
0.046244
0.060543
0.073834
0.065233
0.058028
0.054835
0.074829
0.076208
0.082910
0.11032
1518.2
1532.7
1271.3
847.33
−0.21999
−0.16351
−0.05669
0.29540
614.81
689.57
651.64
526.83
852.28
221.13
119.55
81.795
0.32482
0.36195
0.50956
0.61893
0.71709
0.81002
0.90002
0.98820
45.852
47.183
52.145
55.851
59.334
62.798
66.314
69.910
49.100
50.802
57.241
62.040
66.505
70.898
75.314
79.792
0.10117
0.10405
0.11405
0.12046
0.12572
0.13035
0.13456
0.13846
0.055964
0.047271
0.034838
0.033089
0.033219
0.033947
0.034908
0.035954
0.128640
0.092535
0.051779
0.045603
0.044062
0.043952
0.044427
0.045164
472.51
503.34
602.20
662.61
710.98
753.03
791.02
826.16
9.9124
9.4382
6.3228
4.3529
3.1289
2.3241
1.7683
1.3695
76.543
71.110
69.301
78.476
90.516
103.50
116.73
130.00
20.267
21.036
25.704
30.054
34.176
38.111
41.882
45.506
300
400
500
600
700
800
900
1000
1100
1200
100
100
100
100
100
100
100
100
100
100
57.573
54.500
49.914
43.935
36.179
26.768
19.073
14.734
12.246
10.631
0.017369
0.018349
0.020034
0.022761
0.027640
0.037359
0.052429
0.067868
0.081656
0.094062
1.8921
9.0423
16.289
23.820
31.916
40.700
48.805
55.188
60.470
65.222
3.6290
10.877
18.292
26.097
34.680
44.435
54.048
61.975
68.635
74.628
0.006516
0.027360
0.043895
0.058109
0.071320
0.084331
0.095669
0.10404
0.11039
0.11561
0.069812
0.063582
0.057324
0.052776
0.049610
0.047143
0.043932
0.041345
0.040131
0.039810
0.071696
0.073086
0.075607
0.081104
0.091576
0.10108
0.088057
0.071678
0.062539
0.057826
1667.9
1717.3
1555.7
1300.4
1020.0
813.97
765.30
792.50
832.67
872.28
−0.21618
−0.17905
−0.12564
−0.02079
0.21155
0.65939
1.0399
1.0944
0.98401
0.83544
654.50
741.80
730.42
645.83
510.14
351.46
257.03
232.07
223.70
219.07
856.88
243.50
138.92
101.51
79.363
62.042
53.250
51.518
52.497
54.415
300
400
500
600
700
800
900
1000
1100
1200
500
500
500
500
500
500
500
500
500
500
63.750
60.862
57.695
54.316
50.847
47.385
44.018
40.814
37.834
35.124
0.015686
0.016431
0.017332
0.018411
0.019667
0.021104
0.022718
0.024501
0.026432
0.028470
1.5247
7.9635
14.264
20.481
26.606
32.615
38.492
44.233
49.839
55.312
9.3678
16.179
22.930
29.687
36.439
43.167
49.851
56.484
63.055
69.547
0.003746
0.023347
0.038412
0.050731
0.061141
0.070124
0.077998
0.084987
0.091251
0.096900
0.063403
0.059634
0.055769
0.052734
0.050315
0.048442
0.047068
0.046126
0.045537
0.045218
0.068296
0.067603
0.067522
0.067584
0.067436
0.067080
0.066596
0.066041
0.065356
0.064451
2228.6
2258.7
2200.7
2093.8
1970.5
1850.1
1743.4
1655.7
1589.3
1543.9
−0.19915
−0.19486
−0.18339
−0.16883
−0.15188
−0.13256
−0.11124
−0.08910
−0.06907
−0.05511
763.82
929.09
1096.6
1097.9
935.15
738.72
572.49
445.17
350.97
282.78
1089.4
320.18
189.08
141.83
118.47
104.70
95.388
88.418
83.021
78.952
400
500
600
700
800
900
1000
1100
1200
1000
1000
1000
1000
1000
1000
1000
1000
1000
65.942
63.253
60.572
57.937
55.384
52.937
50.611
48.415
46.349
0.015165
0.015810
0.016509
0.017260
0.018056
0.018890
0.019759
0.020655
0.021575
7.4792
13.357
19.141
24.836
30.435
35.938
41.354
46.695
51.976
22.644
29.167
35.650
42.096
48.491
54.828
61.113
67.350
73.551
0.019833
0.034391
0.046212
0.056150
0.064689
0.072155
0.078776
0.084722
0.090117
0.057934
0.055063
0.053055
0.051393
0.050059
0.049062
0.048373
0.047942
0.047713
0.065743
0.064967
0.064676
0.064219
0.063663
0.063101
0.062594
0.062176
0.061861
2718.6
2677.2
2602.3
2513.7
2423.7
2338.7
2261.5
2193.2
2133.6
−0.19303
−0.19158
−0.18789
−0.18439
−0.18105
−0.17779
−0.17459
−0.17139
−0.16808
1172.7
2199.5
3250.5
3202.2
2408.7
1610.7
1052.9
703.41
487.61
329.93
190.55
137.73
108.98
91.430
80.198
72.716
67.520
63.774
The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport
Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Wagner, W., and
Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002. The source for viscosity is International
Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, IAPWS, 1997. The source for thermal conductivity is the International Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance, IAPWS, 1998.
Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for
a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the
upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface.
The uncertainty in density of the equation of state is 0.0001% at 1 atm in the liquid phase, and 0.001% at other liquid states at pressures up to 10 MPa and temperatures to 423 K. In the vapor phase, the uncertainty is
0.05% or less. The uncertainties rise at higher temperatures and/or pressures, but are generally less than 0.1% in density except at extreme conditions. The uncertainty in pressure in the critical region is 0.1%. The uncertainty of the speed of sound is 0.15% in the vapor and 0.1% or less in the liquid, and increases near the critical region and at high temperatures and pressures. The uncertainty in isobaric heat capacity is 0.2% in the vapor
and 0.1% in the liquid, with increasing values in the critical region and at high pressures. The uncertainties of saturation conditions are 0.025% in vapor pressure, 0.0025% in saturated-liquid density, and 0.1% in saturatedvapor density. The uncertainties in the saturated densities increase substantially as the critical region is approached. For the uncertainties in the viscosity and thermal conductivity, see the IAPWS Release.
THERMODYnAMIC PROPERTIES
TABLE 2-136 Thermodynamic Properties of Water Substance along the Melting Line
T, °C
103 v f , m3/kg
h f , kJ/kg
s f , kJ/kg⋅K
cpf , kJ/kg⋅K
cmelt , kJ/kg⋅K
106α f , K−1
106K f ,T bar−1
0.0100
0.0026
−0.3618
−0.7410
−1.1249
1.00021
1.00016
0.99770
0.99523
0.99278
0
0.0719
3.5140
6.9794
10.3964
0
−0.0001
−0.0054
−0.0110
−0.0167
4.219
4.218
4.196
4.174
4.152
3.969
3.970
3.997
4.023
4.047
−67.42
−67.17
−54.92
−42.52
−30.24
50.90
50.88
50.30
49.73
49.17
200
250
300
400
500
−1.5166
−1.9151
−2.3206
−3.1532
−4.0156
0.99037
0.98798
0.98562
0.98098
0.97643
13.7648
17.0843
20.3547
26.7472
32.9403
−0.0225
−0.0285
−0.0347
−0.0474
−0.0607
4.132
4.112
4.092
4.056
4.022
4.070
4.092
4.113
4.150
4.184
−18.05
−5.93
6.12
30.09
53.97
48.63
48.11
47.59
46.61
45.68
600
800
1000
−4.909
−6.790
−8.803
0.97196
0.96326
0.95493
38.932
50.300
60.836
−0.0747
−0.1046
−0.1371
3.992
3.937
3.893
4.215
4.270
4.320
77.87
126.18
175.98
44.80
43.19
41.74
P, bar
6.117 × 10
1.01325
50
100
150
–3t
Condensed from U. Grigull, Private communication, January 18, 1995.
Materials prepared at Technical University München, Germany by U. Grigull and S. Marek. For a table as a function of temperature, see Grigull, U. and S. Marek, Warme u. Stoff., 30 (1994): 1–8.
t = the triple point (at 6.117 × 10−3 bar, 0.01°C); vf = 0.0010021 m3/kg: α f = −67.42 × 10−6/K.
Other equations for properties are given by Jones, F. E. and G. L. Harris, J. Res. N.I.S.T., 97, 3 (1992): 335–340, and by Wagner,
W. and A. Pruss, J. Phys. Chem. Ref. Data, 22, 3 (1993): 783–787. Steam tables include Walker, W. A., U.S. Naval Ordn. Lab. rept.
NOLTR NOLTR-66-217 = AD 651105 (0–1000 bar, 0–150°C), 1967 (72 pp.); Grigull, U., J. Straub, et al., Steam Tables in S.I. Units
(0.01–1000 bar, 0–1000°C), Springer-Verlag, Berlin, 1990 (133 pp.); Tseng, C. M., T. A. Hamp, et al., Atomic Energy of Canada rept.
(30 props, sat liq & vap., 1–220 bar), AECL-5910 1977 (90 pp.). For dissociation, see e.g., Knonicek, V., Rozpr. Cesko Acad Ved.,
Rada techn ved (0.01–100 bar, 1000–5000 K). 77, 1 (1967). The proceedings of the 10th international conference on the properties of steam were edited by Sytchev, V. V. and A. A. Aleksandrov, Plenum, NY, 1984; and for the 11th conference by Pichal, M. and
O. Sifner, Hemisphere, 1989 (550 pp.). Current information on the properties of solid, vapor, and liquid water properties can be
found at http://www.iapws.org.
For electrical conductivity, see e.g., Marshall, W. L., J. Chem. Eng. Data, 32 (1987): 221–226.
2-265
2-266
PHYSICAL AnD CHEMICAL DATA
TRAnSPORT PROPERTIES
Introduction The tables and nomographs in this subsection are organized roughly with mass transport properties first (surface tension, viscosity,
diffusion coefficient) followed by thermal transport properties.
Unit Conversions For this subsection, the following unit conversions
are applicable:
Diffusivity: to convert square centimeters per second to square feet per
hour, multiply by 3.8750; to convert square meters per second to square feet
per hour, multiply by 38,750.
Pressure: to convert bars to pounds-force per square inch, multiply by
14.504.
Temperature: °F = 9⁄5°C + 32; °R = 9⁄5 K.
Thermal conductivity: to convert watts per meter-kelvin to British thermal unit–feet per hour–square foot–degree Fahrenheit, multiply by 0.57779;
and to convert British thermal unit–feet per hour–square foot–degree
Fahrenheit to watts per meter-kelvin, multiply by 1.7307.
Viscosity: to convert pascal-seconds to centipoise, multiply by 1000.
Additional References An extensive coverage of the general pressure
and temperature variation of thermal conductivity is given in the monograph
by Vargaftik, N. B., L. P. Filippov, A. A. Tarzimanov and E. E. Totskiy, Thermal
Conductivity of Liquids and Gases (in Russian), Standards Press, Moscow,
1978, now published in English translation by CRC Press, Miami, Fla.
For a similar work on viscosity, see Stephan and Lucas, Viscosity of
Dense Fluids, Plenum, New York and London, 1979. Tables and polynomial
fits for refrigerants in both the gaseous and the liquid states are contained
in ASHRAE Handbook—Fundamentals, SI ed., ASHRAE, Atlanta, 2005.
Other sources for viscosity include Fischer & Porter Co. catalog 10-A-94,
“Fluid Densities and Viscosities,” 1953 (200 industrial fluids in 48 pp.) and
TABLE 2-137
MASS TRAnSPORT PROPERTIES
Surface Tension r (dyn/cm) of Various Liquids
Compound
Acetic acid
Acetone
Aniline
Benzene
Benzonitrile
Bromobenzene
n-Butane
Carbon disulfide
Carbon tetrachloride
Chlorobenzene
D. van Velzen, R. L. Cardozo et al., EURATOM Ispra, Italy rept. 4735 e, 1972
(160 pp.). Liquid viscosity, 314 cpds, is summarized in I&EC Fundtls., 11
(1972): 20–26. Five hundred forty-nine binary and ternary systems are discussed in Skubla, P., Coll. Czech. Chem. Commun., 46 (1981): 303–339.
See also Duhne, C. R., Chem. Eng. (NY), 86: 15 (July 16, 1979): 83–91 (equations and 326 liquids); and Rao, K. V. K., Chem. Eng. (NY), 90, 11 (May 30,
1983): 90–91 (nomograph, 87 liquids). For rheology, non-Newtonian behavior, see, for instance, Barnes, H., The Chem. Engr. (UK), (June 24, 1993): 17–23;
Hyman, W. A., I&EC Fundtls., 16 (1976): 215–218; and Ferguson, J., and Z.
Kemblowski, Applied Fluid Rheology, Elsevier, 1991 (325 pp.). Other sources
for thermal conductivity include Ho, C. Y., R. W. Powell et al., J. Phys. Chem.
Ref. Data, 1 (1972) and 3, suppl. 1 (1974); Childs, Ericks et al., N.B.S. Monogr.
131, 1973; Jamieson, D. T., J. B. Irving et al., Liquid Thermal Conductivity,
H.M.S.O., Edinburgh, Scotland, 1975 (220 pp.).
Other references include B. Poling, J. Prausnitz, and J. O’Connell, The
Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2000; N.B.
Vargaftik, Y.K. Vinogradov, and V.S. Yargin, Handbook of Physical Properties
of Liquids and Gases, Begell House, New York, 1996; Carl Yaws, Chemical
Properties Handbook: Physical, Thermodynamics, Environmental Transport,
Safety & Health Related Properties for Organic & Inorganic Chemicals,
McGraw-Hill, New York, 1998; and M.R. Riazi, Characterization and Properties of Petroleum Fractions, ASTM, West Conshohocken, Pa., 2005. Free web
resources include the NIST Webbook at http://webbook.nist.gov and the
KDB (Korea thermophysical properties) database at http://www.cheric.org/
research/kdb/.
T, K
σ
293
333
298
308
318
293
313
333
353
293
313
333
353
293
323
363
293
323
373
203
233
293
293
313
288
308
328
348
368
293
323
373
27.59
23.62
24.02
22.34
21.22
42.67
40.5
38.33
36.15
28.88
26.25
23.67
21.2
39.37
35.89
31.26
35.82
32.34
26.54
23.31
19.69
12.46
32.32
29.35
27.65
25.21
22.76
20.31
17.86
33.59
30.01
24.06
Compound
p-Cresol
Cyclohexane
Cyclopentane
Diethyl ether
2,3-Dimethylbutane
Ethyl acetate
Ethyl benzoate
Ethyl bromide
Ethyl mercaptan
Formamide
n-Heptane
T, K
σ
313
373
293
313
333
293
313
288
303
293
313
293
313
333
353
373
293
313
333
283
303
288
303
298
338
373
293
313
333
353
34.88
29.32
25.24
22.87
20.49
22.61
19.68
17.56
16.2
17.38
15.38
23.97
21.65
19.32
17
14.68
35.04
32.92
30.81
25.36
23.04
23.87
22.68
57.02
53.66
50.71
20.14
18.18
16.22
14.26
Compound
T, K
σ
Isobutyric acid
293
313
333
363
293
323
373
423
473
293
313
333
313
333
373
293
313
333
363
293
313
333
353
373
293
313
333
25.04
23.2
21.36
18.6
24.62
20.05
12.9
6.3
0.87
22.56
20.96
19.41
39.27
37.13
32.96
23.71
22.15
20.6
18.27
29.98
26.83
24.68
22.53
20.38
37.21
34.6
31.98
Methyl formate
Methyl alcohol
Phenol
n-Propyl alcohol
n-Propyl benzene
Pyridine
Methyl formate values from D. B. Macleod, Trans. Faradaay Soc. 19:38, 1923. All others from J. J. Jasper, J. Phys. Chem. Ref. Data 1:841, 1972.
TABLE 2-138
Cmpd. no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Vapor Viscosity of Inorganic and Organic Substances (Pa∙s)
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CF4
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
153.8227
88.0043
C1
C2
1.9703E-05
1.4230E-07
1.5640E-08
1.0939E-05
3.1005E-08
4.7754E-07
1.2025E-06
6.5230E-07
1.7154E-07
2.4910E-08
1.4250E-06
4.1855E-08
1.7531E-07
9.2121E-07
2.5082E-08
3.1340E-08
1.1184E-07
7.4266E-08
3.4647E-05
3.7790E-07
6.9022E-08
1.5600E-07
4.0138E-08
1.3874E-06
7.3534E-08
2.2320E-07
6.2597E-08
6.5411E-08
6.0259E-07
2.6960E-07
3.4387E-08
7.5626E-08
7.0728E-08
1.4031E-06
1.2114E-07
6.9744E-07
4.2898E-08
1.0500E-06
1.0060E-07
3.4205E-07
5.4539E-08
3.1378E-08
2.7856E-06
4.2200E-05
1.2566E-08
1.8178E-05
2.1480E-06
5.8204E-08
1.1127E-06
3.1370E-06
2.1709E-06
0.17646
0.7574
1.078
0.23466
0.9762
0.60273
0.4952
0.579
0.7418
0.98882
0.5039
0.9806
0.72
0.60529
0.96663
0.9676
0.8002
0.8289
0.12396
0.6005
0.84014
0.7181
0.90735
0.4434
0.93798
0.7146
0.9115
0.92914
0.5309
0.6715
0.94604
0.83521
0.84383
0.4611
0.76972
0.5462
0.91349
0.4867
0.77881
0.59764
0.88896
0.96513
0.377
0.10118
1.0939
0.17513
0.46
0.9262
0.5338
0.3742
0.45853
C3
1564.6
272.14
1209.5
23.139
327.16
291.4
410.8
138.4
108.3
30.8
176.17
83.24
7.9
152.43
91.197
3260.2
409
74.746
180
34.714
678.22
184.9
199.64
134.7
71.798
64.391
537
92.661
305.25
358.7
95.108
234.21
43.687
663.14
2840
2110.6
290
44.581
94.7
491.5
208
C4
Tmin, K
Viscosity
at Tmin
Tmax, K
Viscosity
at Tmax
149.78
353.33
289.81
200.15
178.45
229.32
192.40
185.45
286.15
189.63
80.00
195.41
235.65
83.78
403.00
278.68
442.29
395.45
260.28
321.35
257.85
458.15
243.95
342.20
265.85
429.24
154.25
179.44
136.95
164.25
134.86
220.00
196.15
183.85
158.45
87.80
134.26
167.62
199.65
185.30
157.46
133.02
147.43
176.80
267.95
161.30
194.67
161.11
68.15
250.33
89.56
4.166E-06
6.842E-06
7.053E-06
5.386E-06
4.329E-06
5.208E-06
6.468E-06
4.174E-06
7.679E-06
4.455E-06
5.508E-06
6.378E-06
5.122E-06
6.742E-06
8.274E-06
7.077E-06
1.089E-05
8.578E-06
5.104E-06
5.324E-06
5.680E-06
9.122E-06
5.151E-06
6.186E-06
1.383E-05
1.187E-05
6.182E-06
8.126E-06
3.340E-06
4.553E-06
3.559E-06
5.157E-06
4.580E-06
3.961E-06
3.772E-06
1.795E-06
3.770E-06
4.044E-06
4.216E-06
3.424E-06
3.833E-06
3.520E-06
3.329E-06
4.175E-06
5.692E-06
3.144E-06
9.749E-06
5.048E-06
4.434E-06
8.361E-06
5.132E-06
1000
1000
1000
1000
1000
1000
600
1000
1000
1000
2000
1000
1000
3273.1
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
600
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
800
1000
1000
1000
1500
800
1250
1000
1000
2.600E-05
2.093E-05
2.681E-05
2.504E-05
2.571E-05
2.314E-05
1.923E-05
2.523E-05
2.532E-05
2.306E-05
6.227E-05
3.551E-05
2.154E-05
1.205E-04
1.992E-05
2.486E-05
2.441E-05
2.087E-05
1.915E-05
1.698E-05
2.129E-05
1.886E-05
2.045E-05
1.768E-05
2.967E-05
2.623E-05
3.397E-05
4.009E-05
1.966E-05
2.457E-05
2.369E-05
2.260E-05
2.259E-05
2.207E-05
2.259E-05
2.325E-05
2.360E-05
2.229E-05
1.993E-05
1.720E-05
2.427E-05
2.466E-05
1.893E-05
2.211E-05
2.404E-05
1.959E-05
5.203E-05
2.693E-05
4.654E-05
2.789E-05
4.267E-05
2-267
(Continued)
2-268
TABLE 2-138
Cmpd. no.
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued )
Name
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
Formula
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
CAS
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
Mol. wt.
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
C1
C2
2.6000E-07
1.0650E-07
3.5554E-08
1.6960E-07
6.2860E-08
4.7100E-08
3.8802E-07
1.4427E-07
8.7371E-08
1.4305E-07
3.3699E-07
3.7385E-08
1.0881E-06
6.7700E-08
7.9581E-08
5.2312E-08
1.3326E-06
2.3619E-07
3.0260E-07
1.7578E-06
3.9150E-08
3.5018E-05
2.6400E-08
7.1748E-08
5.5065E-08
6.1192E-08
3.2720E-08
5.6914E-07
2.4999E-07
1.4125E-07
1.1379E-07
2.9444E-07
7.7147E-08
2.3340E-07
1.6030E-07
1.5913E-07
2.0135E-07
1.4321E-07
7.6787E-07
1.4906E-07
1.1989E-07
3.3628E-08
4.3184E-07
1.9480E-06
6.5492E-08
2.7228E-06
4.3934E-07
7.7484E-07
4.1380E-07
1.6910E-07
9.2797E-08
0.7423
0.7942
0.98455
0.7693
0.907
0.911
0.6367
0.7438
0.80775
0.7451
0.60751
0.98433
0.48359
0.8367
0.8376
0.89422
0.4537
0.67465
0.64991
0.4265
0.91427
0.11725
0.9487
0.7982
0.8341
0.82546
0.9302
0.50744
0.6878
0.8097
0.8502
0.728
0.79906
0.714
0.763
0.7639
0.73421
0.7785
0.5741
0.7617
0.79108
0.9426
0.6035
0.41
0.86232
0.39531
0.64867
0.57978
0.5999
0.7114
0.7819
C3
98.3
94.7
96.6
205.08
166.15
98.538
159.8
221.17
330.86
36.7
104.97
58.008
445
139
167.14
370.34
22.264
3394.6
71
109.38
79.56
77.434
39.13
273.3
0.5962
83.243
93.816
154.74
80.765
260
205
193.14
111.98
98.159
276.16
105.9
84.37
39.587
247
495.8
59.455
445.07
169.64
198.7
269.5
124
93.399
C4
Tmin, K
Viscosity
at Tmin
Tmax, K
Viscosity
at Tmax
200.00
227.95
136.75
209.63
175.43
150.35
155.97
285.39
304.19
307.93
177.14
245.25
182.48
279.69
296.60
242.00
169.67
179.28
138.13
145.59
189.64
285.00
243.51
304.55
280.05
206.89
247.56
229.15
60.00
210.15
282.85
370.10
175.30
248.39
256.15
326.14
176.19
237.49
178.01
200.00
172.71
301.15
223.35
156.85
169.20
154.56
215.00
136.95
357.05
187.65
204.81
8.900E-06
5.611E-06
4.506E-06
7.091E-06
6.820E-06
4.533E-06
4.175E-06
6.113E-06
6.687E-06
6.731E-06
3.480E-06
8.411E-06
4.797E-06
6.671E-06
6.917E-06
5.714E-06
3.778E-06
4.409E-06
3.369E-06
4.150E-06
4.238E-06
5.262E-06
3.755E-06
5.070E-06
4.715E-06
3.632E-06
4.761E-06
4.091E-06
4.137E-06
7.685E-06
1.038E-05
1.538E-05
3.278E-06
5.850E-06
6.127E-06
8.313E-06
5.487E-06
7.164E-06
5.895E-06
5.515E-06
4.742E-06
6.450E-06
5.364E-06
3.720E-06
4.046E-06
5.148E-06
8.001E-06
5.478E-06
8.016E-06
4.218E-06
4.089E-06
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
900
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
480
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
3.992E-05
2.348E-05
3.195E-05
3.143E-05
3.307E-05
2.547E-05
2.618E-05
2.108E-05
2.108E-05
2.120E-05
1.834E-05
3.355E-05
2.308E-05
1.928E-05
2.346E-05
2.381E-05
2.118E-05
2.191E-05
2.309E-05
2.441E-05
2.118E-05
1.791E-05
1.729E-05
1.604E-05
1.622E-05
1.701E-05
1.944E-05
1.488E-05
1.744E-05
3.502E-05
3.696E-05
3.895E-05
1.781E-05
2.569E-05
2.588E-05
2.611E-05
2.887E-05
2.824E-05
3.175E-05
2.599E-05
2.611E-05
2.176E-05
2.239E-05
2.212E-05
2.388E-05
2.891E-05
3.317E-05
3.547E-05
2.055E-05
2.049E-05
1.881E-05
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.4172E-08
3.9833E-08
1.9377E-06
2.7570E-07
6.8567E-07
7.8220E-07
8.4576E-07
9.9104E-07
3.2282E-08
2.6800E-06
3.5538E-06
5.0372E-07
5.2195E-08
4.7238E-08
5.2854E-07
8.6101E-08
3.9554E-08
2.7334E-07
2.8451E-08
1.2900E-07
6.3440E-08
2.9236E-07
2.5906E-07
1.0613E-07
3.2140E-06
4.9340E-07
4.2231E-07
6.3441E-08
9.2371E-08
1.6175E-07
4.1070E-07
2.1696E-06
2.0789E-06
1.3744E-07
8.6706E-08
2.8132E-07
4.3403E-08
6.7610E-07
2.5704E-08
7.9129E-08
1.3974E-07
1.0498E-07
8.5992E-08
5.5300E-07
5.1539E-07
2.6635E-05
6.3600E-07
2.1174E-07
4.0868E-06
3.9346E-08
1.5948E-05
6.8290E-08
5.0702E-08
6.4320E-07
0.91098
0.91566
0.4093
0.6841
0.52542
0.4994
0.487
0.4723
0.97742
0.3975
0.3766
0.54462
0.85584
0.90849
0.6112
0.8345
0.892597
0.7393
0.93622
0.744
0.8287
0.62458
0.67988
0.8066
0.3572
0.5924
0.58154
0.8369
0.7908
0.7163
0.57143
0.3812
0.4163
0.7557
0.83923
0.6792
0.94806
0.5804
0.94738
0.79565
0.74266
0.76988
0.8427
0.6061
0.5726
0.15779
0.6638
0.7087
0.35526
1.0027
0.21516
0.8774
0.9114
0.5854
492.69
133.2
278.82
371.6
398
436.89
534
1176.1
227.44
69.036
302.85
167.86
129.93
117.03
219.5
702.84
98.902
52.7
667
239.17
239.21
73.63
102.32
142.27
230.06
577.77
352.7
122.8
75.512
238.46
354.9
83.193
98.58
100.41
58.148
273.66
288.76
2173.5
61.6
157.42
651.07
1151.1
54.864
325.3
3590
159.95
226.10
240.91
180.96
145.19
392.70
402.94
396.58
188.44
131.65
212.72
160.00
274.18
122.93
174.88
291.67
413.79
284.95
300.03
210.15
263.57
309.58
90.35
200.00
189.60
192.15
178.20
238.45
258.15
175.15
161.84
134.71
169.41
284.29
260.15
329.00
160.65
193.55
155.15
180.00
140.00
204.15
125.26
199.25
145.65
167.55
53.48
357.88
129.95
131.35
155.15
275.60
281.45
187.55
4.497E-06
5.701E-06
6.006E-06
5.563E-06
3.211E-06
7.936E-06
7.900E-06
7.957E-06
5.405E-06
3.688E-06
4.097E-06
3.300E-06
5.089E-06
3.739E-06
4.544E-06
6.231E-06
8.569E-06
1.226E-05
5.933E-06
4.429E-06
3.511E-06
3.214E-06
2.643E-06
6.029E-06
4.632E-06
4.953E-06
3.673E-06
4.733E-06
5.344E-06
3.392E-06
3.103E-06
2.659E-06
5.714E-06
6.863E-06
7.150E-06
8.359E-06
5.356E-06
5.069E-06
3.058E-06
3.371E-06
3.219E-06
4.224E-06
3.441E-06
5.768E-06
2.994E-06
4.277E-06
4.148E-06
9.491E-06
3.832E-06
5.237E-06
5.608E-06
7.882E-06
8.658E-06
5.037E-06
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
2.388E-05
2.224E-05
2.194E-05
2.744E-05
2.021E-05
1.796E-05
1.749E-05
1.801E-05
2.762E-05
2.722E-05
2.202E-05
1.766E-05
1.804E-05
2.511E-05
2.766E-05
2.350E-05
1.884E-05
3.995E-05
1.831E-05
1.970E-05
1.593E-05
1.284E-05
2.583E-05
2.651E-05
2.274E-05
2.384E-05
1.893E-05
1.915E-05
1.975E-05
1.989E-05
1.729E-05
1.914E-05
2.726E-05
2.264E-05
2.655E-05
2.477E-05
3.032E-05
2.750E-05
1.787E-05
1.781E-05
2.150E-05
1.946E-05
2.742E-05
2.857E-05
2.088E-05
2.496E-05
5.873E-05
2.446E-05
2.880E-05
4.009E-05
3.277E-05
2.776E-05
2.749E-05
2.768E-05
2-269
(Continued)
2-270
TABLE 2-138
Cmpd. no.
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued )
Name
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
Formula
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
CAS
Mol. wt.
C1
C2
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
3.2530E-07
3.1338E-07
4.2392E-05
6.6720E-08
1.3633E-08
2.5720E-07
3.4649E-05
8.9656E-08
8.8629E-08
7.7509E-08
4.6970E-08
5.9501E-07
1.2463E-07
4.0986E-05
1.7514E-07
1.2145E-08
1.5773E-07
1.0652E-07
9.7820E-08
9.8882E-08
8.0060E-08
5.2127E-07
4.3636E-08
2.9986E-07
5.5562E-07
2.3489E-07
1.7970E-07
9.1700E-08
4.9240E-07
1.2780E-08
4.5101E-14
3.9314E-08
1.1202E-07
5.2542E-08
6.7978E-05
9.1130E-08
5.2546E-07
3.0663E-07
8.0599E-08
1.3226E-06
1.1630E-06
1.6480E-06
5.6409E-07
7.4106E-08
4.0824E-07
2.4344E-08
1.8690E-07
8.9348E-08
5.0602E-07
8.5423E-07
0.7162
0.6238
0.1011
0.82837
1.0595
0.6502
0.10705
0.78236
0.78376
0.81089
0.8932
0.52758
0.7322
0.10349
0.70737
1.0861
0.7189
0.77022
0.7772
0.7755
0.81293
0.5444
0.90747
0.62647
0.5337
0.7151
0.685
0.9273
0.6702
1.0631
3.0005
1.0134
0.7822
0.88063
0.092766
0.8222
0.59006
0.69655
0.8392
0.4885
0.4787
0.4444
0.5863
0.82436
0.5923
0.97376
0.7096
0.80197
0.55258
0.47389
C3
−9.6
692.2
3420
85.752
248.6
2900.7
100.14
100.18
69.927
57.6
274.02
395
3180.6
157.14
163.3
105.85
99.53
99.825
65.274
237.01
42.32
178.17
244.38
205.05
−0.59
157.7
340
−521.83
C4
107
6000
140
76,111
100.3
4637.3
93.57
105.67
205
77.332
504.3
316
510.66
231.9
83.086
208.22
−91.597
192
77.653
199.82
239.34
18,720
Tmin, K
Viscosity
at Tmin
Tmax, K
Viscosity
at Tmax
20.00
295.13
229.80
182.57
265.83
239.15
220.00
234.15
238.15
154.12
229.92
192.22
291.31
214.93
177.83
269.25
228.55
223.00
217.35
217.50
133.39
170.05
192.62
141.25
183.65
274.69
13.95
206.45
200.00
300.00
285.50
250.00
227.15
177.95
409.15
288.15
90.69
240.00
301.15
250.00
170.45
196.32
179.69
260.75
159.53
150.00
450.15
155.95
135.58
139.39
3.530E-06
3.254E-06
4.625E-06
3.391E-06
5.052E-06
4.440E-06
4.351E-06
4.485E-06
4.550E-06
3.169E-06
4.832E-06
3.932E-06
3.274E-06
4.523E-06
3.631E-06
5.294E-06
4.567E-06
4.650E-06
4.397E-06
4.403E-06
2.871E-06
3.567E-06
4.235E-06
2.947E-06
3.851E-06
7.460E-06
6.517E-07
1.285E-05
9.594E-06
2.576E-06
9.931E-06
1.058E-05
5.415E-06
5.037E-06
9.629E-06
7.242E-06
3.470E-06
7.523E-06
7.714E-06
6.505E-06
4.769E-06
4.781E-06
5.167E-06
5.515E-06
3.572E-06
2.621E-06
1.000E-05
3.422E-06
3.083E-06
3.263E-06
2000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1673.15
3000
800
1000
425
472.68
480
1000
1000
1000
1000
1000
1000
1000
800
800
1000
1000
1000
1000
1000
1000
1000
1000
1000
7.561E-05
1.377E-05
1.928E-05
1.878E-05
2.056E-05
1.838E-05
1.861E-05
1.812E-05
1.809E-05
1.962E-05
2.124E-05
1.787E-05
1.399E-05
2.004E-05
2.005E-05
2.201E-05
1.945E-05
1.970E-05
1.909E-05
1.907E-05
2.064E-05
1.811E-05
2.209E-05
1.928E-05
1.782E-05
4.225E-05
4.330E-05
4.512E-05
4.358E-05
4.421E-06
2.019E-05
2.050E-05
2.261E-05
2.304E-05
2.289E-05
2.440E-05
2.800E-05
3.128E-05
2.464E-05
2.125E-05
2.045E-05
2.350E-05
2.628E-05
2.034E-05
2.021E-05
2.190E-05
2.109E-05
2.111E-05
1.918E-05
1.820E-05
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
CH3NO2
N 2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
5.6844E-07
3.9342E-08
4.9950E-08
4.0748E-08
3.7330E-07
4.8806E-08
6.5281E-07
8.5736E-08
2.4000E-07
2.0000E-07
9.0798E-07
3.7026E-08
3.9771E-08
1.9770E-07
2.6098E-07
2.6552E-08
8.6219E-08
6.9755E-06
1.5035E-07
9.4257E-08
3.1573E-07
1.9250E-07
1.0826E-07
8.6077E-08
1.6370E-07
4.8890E-07
7.2131E-08
1.1164E-06
1.0546E-07
1.0871E-07
9.6050E-07
9.0981E-07
3.5642E-07
4.4941E-08
5.8223E-08
3.8926E-07
7.1455E-07
1.5779E-07
7.6460E-07
6.4318E-07
7.1900E-07
2.4391E-07
6.5592E-07
8.2005E-07
4.0700E-07
2.1150E-06
1.4670E-06
3.0465E-07
3.8518E-05
1.0344E-07
1.8105E-08
1.2000E-07
3.5879E-05
0.553
0.91086
0.89479
0.92709
0.6177
0.92549
0.5294
0.80277
0.68
0.704
0.495
0.92849
0.92242
0.7453
0.68276
0.98316
0.83591
0.3154
0.7338
0.7845
0.66404
0.7091
0.77382
0.81669
0.76706
0.6096
0.80319
0.4537
0.77106
0.78135
0.4856
0.49288
0.6327
0.90199
0.88057
0.63159
0.49832
0.73224
0.5476
0.5389
0.6659
0.702
0.6081
0.61423
0.6485
0.4642
0.5123
0.62218
0.10867
0.77301
0.99668
0.74
0.10109
227.18
44.662
256.5
310.59
100.77
210
187
355.89
131.22
133.4
72.564
1034.5
108.5
90.183
173.59
109
93.349
71.294
107.97
342.23
99.437
374.74
93.745
70.639
381
260.08
232.2
48.298
169.45
303.31
112.15
284
400.16
5.3
280
54.714
114.58
367.5
305.7
125.4
705.34
3502.7
220.47
180
3258.2
160.15
157.48
175.30
183.45
187.35
139.05
146.58
299.15
280.15
269.15
130.73
146.62
115.00
182.55
160.00
186.48
167.23
174.15
150.00
189.15
256.15
127.93
180.15
171.64
150.18
224.95
240.00
119.55
176.00
150.00
298.97
132.81
185.65
133.97
160.17
116.34
249.95
164.55
278.65
353.43
30.00
183.63
63.15
66.46
244.60
182.30
110.00
305.04
267.30
219.66
285.55
268.15
238.15
3.893E-06
3.947E-06
4.052E-06
5.112E-06
3.993E-06
4.698E-06
2.934E-06
6.232E-06
6.331E-06
6.062E-06
2.722E-06
3.800E-06
3.165E-06
5.574E-06
4.551E-06
4.534E-06
4.341E-06
5.117E-06
3.448E-06
3.901E-06
7.481E-06
3.242E-06
3.968E-06
4.065E-06
4.450E-06
5.265E-06
4.162E-06
2.366E-06
3.707E-06
3.707E-06
6.727E-06
3.423E-06
4.316E-06
3.725E-06
3.908E-06
3.196E-06
5.057E-06
3.938E-06
8.264E-06
7.125E-06
5.884E-06
3.752E-06
4.372E-06
3.964E-06
5.756E-06
8.854E-06
7.618E-06
3.231E-06
5.013E-06
3.335E-06
5.074E-06
4.499E-06
4.250E-06
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
600
1000
1000
1000
1000
1000
1000
1000
1000
1000
3273.1
1000
1970
1000
1000
1000
1500
1000
1000
1000
1000
1000
1000
2.112E-05
2.125E-05
2.312E-05
2.463E-05
2.118E-05
2.917E-05
1.930E-05
1.994E-05
2.175E-05
2.181E-05
2.046E-05
2.259E-05
2.327E-05
3.009E-05
2.573E-05
2.364E-05
2.588E-05
3.029E-05
2.157E-05
1.951E-05
2.642E-05
2.327E-05
2.076E-05
2.265E-05
2.956E-05
2.456E-05
1.685E-05
1.865E-05
1.983E-05
2.242E-05
1.312E-05
2.174E-05
2.288E-05
2.284E-05
2.434E-05
2.612E-05
1.714E-05
2.232E-05
2.616E-05
1.900E-05
1.573E-04
2.432E-05
6.432E-05
5.122E-05
2.625E-05
4.000E-05
5.737E-05
1.314E-05
1.812E-05
1.767E-05
1.769E-05
1.688E-05
1.694E-05
(Continued)
2-271
2-272
TABLE 2-138
Cmpd. no.
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued )
Name
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Formula
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
CAS
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
Mol. wt.
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
C1
C2
6.6329E-08
3.8673E-08
6.1447E-07
3.2095E-07
3.9500E-05
3.1191E-08
1.5557E-08
1.7520E-07
3.4163E-05
8.0901E-08
6.1515E-11
5.0324E-05
3.3253E-08
5.7084E-07
6.3032E-05
1.1010E-06
1.1960E-07
4.0828E-08
4.3300E-05
6.3412E-08
1.0971E-08
1.8903E-07
1.1749E-07
2.4630E-07
1.1640E-07
1.6378E-06
8.8646E-08
2.7467E-08
4.1022E-08
5.7650E-07
4.3478E-07
1.0094E-07
8.5360E-08
4.3511E-08
6.0758E-07
4.9054E-08
7.9420E-07
1.2003E-06
5.4749E-07
3.8397E-05
1.4807E-08
9.6891E-06
2.1372E-07
1.6200E-07
3.0387E-07
7.3919E-07
6.0741E-07
3.5532E-08
7.9457E-08
4.5430E-08
0.82027
0.91142
0.50705
0.61839
0.10787
0.92925
1.0299
0.6941
0.10661
0.79062
1.8808
0.077611
0.9351
0.52446
0.10487
0.5634
0.84797
0.8766
0.098676
0.84758
1.11
0.7031
0.7649
0.6653
0.7615
0.44337
0.81492
0.97555
0.90585
0.53498
0.5272
0.799
0.80872
0.908
0.53845
0.90125
0.5491
0.494
0.53893
0.10821
1.0733
0.24601
0.6894
0.7285
0.61945
0.5423
0.5863
0.95654
0.84656
0.9173
C3
C4
76.204
50.646
287.19
709.09
3390
55.092
206.8
3028
99.338
3604.6
32.426
271.76
4210.1
96.3
212.68
3090
41.718
175.9
103.78
208.7
107.94
636.11
85.198
235.2
238.27
103.1
88.273
102.73
173.45
415.8
479.78
283.52
2510.9
1537.6
178.57
117
210.35
263.73
367.29
65.878
61
–26,218
Tmin, K
Viscosity
at Tmin
Tmax, K
Viscosity
at Tmax
191.91
253.05
223.15
301.31
251.65
216.38
289.65
257.65
241.55
252.85
255.55
171.45
223.95
193.55
462.65
54.35
80.15
283.07
191.59
143.42
239.15
410.95
200.00
196.29
234.18
108.02
160.75
197.45
167.45
163.83
372.38
314.06
243.15
404.15
136.87
85.47
200.00
187.35
199.00
165.00
252.45
180.37
178.15
188.36
173.55
87.89
180.25
142.61
159.95
213.15
3.542E-06
4.995E-06
4.170E-06
3.266E-06
4.955E-06
3.677E-06
5.338E-06
4.583E-06
4.530E-06
4.611E-06
2.075E-06
3.406E-06
4.579E-06
3.757E-06
1.188E-05
3.773E-06
4.922E-06
3.288E-06
4.246E-06
3.305E-06
4.793E-06
9.111E-06
4.452E-06
4.003E-06
5.079E-06
2.813E-06
3.638E-06
4.766E-06
4.242E-06
3.621E-06
6.010E-06
7.514E-06
5.324E-06
8.072E-06
3.788E-06
2.702E-06
4.732E-06
4.471E-06
3.914E-06
4.114E-06
5.607E-06
3.652E-06
3.802E-06
4.540E-06
3.350E-06
2.093E-06
4.203E-06
4.085E-06
4.132E-06
4.832E-06
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1500
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1.781E-05
1.996E-05
1.585E-05
1.345E-05
1.896E-05
1.813E-05
1.913E-05
1.755E-05
1.771E-05
1.733E-05
2.700E-05
1.868E-05
2.057E-05
1.681E-05
2.496E-05
6.371E-05
4.184E-05
1.436E-05
2.093E-05
2.124E-05
2.346E-05
2.068E-05
2.098E-05
2.019E-05
2.023E-05
2.176E-05
2.275E-05
2.320E-05
2.141E-05
1.879E-05
1.340E-05
2.283E-05
2.093E-05
2.090E-05
2.135E-05
2.480E-05
2.490E-05
2.461E-05
1.765E-05
2.309E-05
2.457E-05
2.089E-05
2.122E-05
2.223E-05
1.812E-05
2.477E-05
2.550E-05
2.632E-05
2.583E-05
2.418E-05
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C6H4O2
F4Si
C8H8
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
1.1085E-07
2.1671E-07
6.3863E-07
5.7821E-05
6.8630E-07
5.3986E-07
3.9067E-06
3.9218E-05
7.0859E-07
5.1567E-09
3.7780E-07
5.0784E-07
8.5988E-08
8.1458E-07
1.0300E-06
8.7268E-07
2.7081E-07
3.5585E-08
2.4110E-07
1.2434E-06
7.8498E-07
6.8812E-07
1.1070E-07
8.2418E-07
3.4066E-08
2.8471E-08
3.5940E-08
5.9537E-08
1.3880E-07
6.7484E-07
2.3790E-07
3.6429E-08
1.7096E-08
6.8293E-07
8.3436E-07
9.3485E-07
0.8008
0.76757
0.5254
0.099467
0.6112
0.6349
0.3845
0.12589
0.51971
1.1561
0.6533
0.5614
0.82841
0.50257
0.5497
0.49397
0.6955
0.8987
0.6845
0.4832
0.49855
0.51063
0.746
0.4931
0.95252
0.96571
0.9052
0.81842
0.7599
0.5304
0.71517
0.95924
1.1146
0.52199
0.49713
0.47683
152.51
16.28
295.1
4409.6
217
34.5
470.1
3861.1
652.24
271.01
328.55
68.172
380.29
569.4
323.79
187.93
165.3
223
447.7
362.79
330.88
72.4
371.44
43.528
30.83
125
90.245
98
230.17
102.84
324.17
365.86
371.96
19,000
388.85
250.00
242.54
460.85
197.67
205.15
297.93
700.15
329.35
279.01
164.65
237.38
176.99
373.96
234.94
178.18
236.50
267.76
158.45
156.08
247.79
229.33
165.78
387.91
398.40
354.00
247.57
288.45
180.35
173.15
119.36
178.35
273.16
225.30
247.98
286.41
9.439E-06
1.410E-05
5.158E-06
1.007E-05
8.280E-06
9.790E-06
1.355E-05
1.373E-05
4.837E-06
3.465E-06
4.006E-06
4.592E-06
4.520E-06
7.930E-06
6.049E-06
4.008E-06
6.756E-06
3.344E-06
3.210E-06
3.689E-06
4.975E-06
4.520E-06
3.488E-06
7.958E-06
9.208E-06
7.581E-06
3.506E-06
4.677E-06
4.659E-06
4.459E-06
3.907E-06
5.260E-06
8.882E-06
4.735E-06
5.225E-06
6.037E-06
1000
500
1000
1000
1000
5000
694.19
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1073.15
1000
1000
1000
2.429E-05
2.475E-05
1.858E-05
2.125E-05
3.844E-05
1.195E-04
2.883E-05
1.925E-05
1.554E-05
1.516E-05
2.710E-05
1.847E-05
2.461E-05
1.900E-05
2.926E-05
2.000E-05
2.782E-05
1.517E-05
2.230E-05
2.418E-05
1.803E-05
1.760E-05
1.786E-05
1.812E-05
2.352E-05
2.179E-05
1.660E-05
1.558E-05
2.407E-05
2.140E-05
3.016E-05
2.749E-05
4.082E-05
1.898E-05
1.894E-05
1.836E-05
The vapor viscosity is calculated by
μ = C1T C2/(1 + C3/T + C4/T 2)
where μ is the viscosity in Pa∙s and T is the temperature in K. Viscosities are at either 1 atm or the vapor pressure, whichever is lower.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and
reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data
Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
2-273
2-274
TABLE 2-139
Eqn
Cmpd.
no.
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Viscosity of Inorganic and Organic Liquids (Pa∙s)
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
C1
−10.976
1.5525
−9.03
−20.457
−14.918
5.4711
6.224
−12.032
−28.12
−0.24126
−20.077
−6.743
−15.407
−8.8685
−12.632
7.5117
−8.4562
−12.947
−23.268
−148.6
−14.152
−11.46
−11.459
−9.9265
16.775
−20.611
−5.0539
−16.615
−10.143
17.844
−7.2471
−393.86
−390.03
−82.851
−16.323
−10.773
−10.346
−10.335
−17.488
−23.802
−10.807
−10.903
−3.4644
−6.4551
−9.817
−11.13
18.775
−10.306
−4.9735
C2
755.12
1376.4
1212.3
1638.6
1023.4
143.99
−151.8
867.34
2280.2
350.57
285.15
598.3
1518.7
204.29
2668.2
294.68
1024.4
2557.9
1880.5
8377.2
2652
1497
1334.4
1576.3
-314
1656.5
645.8
931.44
472.79
−310.2
534.82
19,042
18,609
4481.8
3141.7
591.61
522.3
521.39
1478.2
1887.2
966.74
932.82
334.5
744.7
1388
1084.1
−402.92
703.01
97.67
C3
−2.0126
−0.322
1.3834
0.5961
−2.4432
−2.6554
0.19534
2.3956
−1.5676
1.784
−0.7341
0.60172
−0.38305
C4
C5
−6.238E-22
−3.690E-27
10
10
−1.294E-22
10
1.7994
20.559
−0.0000133
2
−0.043397
0.00049694
−0.21119
−3.9763
1.4415
−0.87689
0.94366
−0.028241
−4.5058
−0.57469
59.978
60.014
11.182
−4.6625E-27
−0.049479
−0.055844
−0.000020943
10
1
1
2
−6.9171E-26
10
−2.794
−0.30635
−0.011847
−0.013184
0.91828
1.8479
−0.014851
0.023034
−1.0811
−0.67524
−0.238
−4.6854
−1.1088
Tmin, K
Viscosity at
Tmin
149.78
353.33
289.81
200.15
190
229.32
193.15
185.45
286.15
189.63
59.15
195.41
235.65
83.78
403
278.68
258.27
395.52
260.28
321.35
257.85
275.65
243.95
342.2
265.85
242.43
154.25
179.44
136.95
250
134.86
220
196.15
190
238
87.8
134.26
167.62
250
200
157.46
133.02
147.43
176.8
267.95
161.3
216.58
161.58
68.15
2.647E-03
1.728E-03
1.265E-03
7.159E-03
1.655E-03
7.616E-04
1.958E-04
1.773E-03
1.359E-03
1.340E-03
3.430E-04
5.240E-04
3.429E-03
2.950E-04
2.451E-03
7.761E-04
2.047E-03
1.534E-03
2.393E-03
5.369E-03
2.092E-02
1.886E-03
2.513E-03
1.427E-03
1.353E-03
2.842E-03
5.065E-03
1.464E-03
1.081E-03
2.547E-04
2.243E-03
2.020E+02
4.410E+04
2.602E-01
4.404E-02
1.769E-02
1.483E-03
6.810E-04
1.496E-03
1.030E-02
8.716E-03
2.287E-02
1.369E-03
3.223E-03
2.561E-03
1.217E-02
2.488E-04
2.592E-03
2.688E-04
Tmax, K
294.15
494.3
391.05
412.7
329.44
354.81
273.15
353.22
460
350.45
130
393.15
426.73
150
563.15
545
442.29
600.8
464.15
664
478.6
458.15
472.03
723.15
350
429.24
393.15
363.15
284
400
420
544
540.8
391.9
372.9
335.6
276.87
274.03
399.26
456.46
373.15
358.13
373.15
347.94
436.42
390.74
303.15
441.6
131.37
Viscosity at
Tmax
2.229E-04
2.895E-04
3.890E-04
2.874E-04
2.351E-04
2.100E-04
9.819E-05
2.181E-04
2.086E-04
2.191E-04
4.276E-05
4.858E-05
2.736E-04
3.823E-05
3.730E-04
7.106E-05
3.333E-04
1.683E-04
2.836E-04
2.614E-04
1.821E-04
2.121E-04
1.788E-04
1.076E-04
6.021E-04
3.310E-04
1.751E-04
2.060E-04
1.773E-04
4.880E-05
3.566E-05
3.441E-04
2.890E-04
3.845E-04
3.715E-04
1.222E-04
1.982E-04
2.022E-04
2.521E-04
2.359E-04
2.475E-04
2.851E-04
1.271E-04
2.570E-04
3.087E-04
2.351E-04
5.652E-05
1.643E-04
6.515E-05
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
100
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Diisopropyl amine
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
153.8227
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
−8.0738
−9.9212
−9.5412
0.15772
10.9222
−14.109
10.39
10.27183
−15.458
−914.12
−377.23
−851.12
−24.988
−11.794
−3.4968
−33.763
280.87
−44.877
−11.641
−3.2612
−4.1508
−3.524
−11.338
4.1184
−97.663
−12.305
−69.985
−15.868
−11.464
−2.3633
0.000001348
−10.457
−17.582
−10.013
10.027
−114.7
−30.6
31.63
−8.991
15.312
−13.071
−10.872
−11.269
−375.21
−17.57
10.197
−5.135
10.501
−10.072
−17.723
−1.7366
1121.1
300.5
456.62
540.5
−118.895
1049.2
−134.38
−67.2235
1086
38,855
17,909
36,686
1807.9
992.33
397.94
2497.2
−31,869
3227.7
1154.3
614.16
599.77
342.54
1304.1
629.98
4342.7
2324.1
5818.8
1434.8
1510.1
791.93
1101.1
1635.4
921.31
206
4905.4
2153.4
−1080
870.2
−41.12
940.03
1033.1
1195.3
17,177
1385.7
−63.8
667.5
−52.181
710.48
850.2
599.8
−0.4726
−1.6075
−3.305
0.5377
−3.262
−3.1664
0.654
139.11
55.565
129.13
2.0556
−1.1087
3.2236
−38.837
4.887
0.066511
−1.156
−1.0308
−1.1599
0.000092396
−2.2076
13.645
−0.055494
8.0715
0.68071
−0.012754
−1.2272
−0.00014757
−0.00004841
−0.00013329
3,994,500
2
2
2
−2.002
−0.000019319
2
−0.000020577
2
−3.6367
0.5
−1.1719E-18
7
−0.0031354
0.9932
−3.1607
16.358
2.9371
−6.114
−0.2805
−3.919
0.3733
−0.00067435
0.012736
66.66
0.85647
−3.226
−0.8553
−3.3459
−0.14677
1.0601
−1.4237
250
89.56
172.12
250
136.75
209.63
175.43
150.35
250
273.15
293.15
273.15
200
245.25
182.48
279.69
296.6
242
200
225
138.13
145.59
189.64
285
240.05
304.55
285
206.89
247.56
229.15
20.35
210.15
282.85
220.6
175.3
248.39
256.15
326.14
176.19
237.49
208.38
192.5
172.71
293.15
223.35
200
225
154.56
179.6
137
250
2.032E-03
1.408E-03
1.020E-03
1.422E-03
2.026E-03
1.970E-03
7.234E-04
2.362E-03
5.514E-04
8.438E-02
9.548E-03
9.674E-02
6.363E-03
4.317E-04
8.345E-04
1.264E-03
6.328E-02
8.960E-03
4.017E-03
1.122E-03
7.531E-03
9.601E-04
1.155E-02
2.134E-03
2.741E-03
6.798E-03
1.937E-02
4.975E-03
4.364E-03
3.786E-03
1.348E-06
5.331E-03
2.042E-03
2.919E-03
5.931E-03
2.463E-03
2.726E-03
8.543E-04
4.076E-03
1.839E-03
1.406E-03
4.051E-03
1.381E-02
8.128E-01
1.190E-03
7.359E-04
1.113E-03
1.229E-03
1.030E-03
1.832E-03
7.479E-04
455
145.1
333.72
540
423.15
353.2
416.25
423.15
308.85
564.68
558.04
563.72
400
320.12
367.94
443.04
520.08
428.58
373.15
325
405.6
318.4
431.95
481.65
494.16
543.15
503
443.75
512.35
505.6
20.35
381.15
404.51
488.8
414.15
547.16
453.57
447.21
330.45
400
373.93
361.25
369.52
589.28
329.1
373.15
365.25
343.15
283.65
343.15
357.05
2.030E-04
3.897E-04
2.822E-04
1.291E-04
8.727E-05
3.410E-04
6.726E-05
1.190E-04
2.767E-04
1.793E-05
1.514E-04
2.992E-05
2.881E-04
1.676E-04
1.278E-04
2.070E-04
1.652E-04
4.402E-04
2.877E-04
3.167E-04
1.416E-04
1.080E-04
2.440E-04
2.718E-04
1.292E-04
2.304E-04
2.727E-04
2.064E-04
1.848E-04
2.167E-04
1.348E-06
5.071E-04
5.120E-04
2.951E-04
1.989E-04
1.565E-04
3.761E-04
3.039E-04
3.407E-04
2.557E-04
2.374E-04
3.301E-04
3.495E-04
1.090E-04
2.260E-04
1.141E-04
2.354E-04
1.026E-04
2.257E-04
6.050E-05
2.193E-04
2-275
(Continued)
2-276
TABLE 2-139
Eqn
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued )
Cmpd.
no.
Name
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
Diisopropyl ether
Diisopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Formula
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
CAS
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
Mol. wt.
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
C1
−11.5
−15.097
−10.968
−10.631
0.10842
−10.93
7.2565
−10.716
−11.796
−11.344
−10.577
−10.62
−20.425
−12.08
152.9
−17.641
−37.347
−16.0542
−46.166
−12.373
−15.404
−134.91
−18.315
−7.0046
7.875
14.354
19.822
−13.563
−40.706
−12.24
−15.485
−22.11
−6.894
1.8878
−53.908
−290.36
−11.012
−8.521
−9.8417
−13.037
−11.311
−11.331
−11.452
−9.7574
−8.9215
0.7109
−11.499
C2
993
1426.9
885.49
1086.4
300.2
699.5
221.4
1140.5
1463.5
1168.9
1172.6
448.99
1515.5
1112.2
−10,183
1067.5
2835
2221.79
3086.2
2017.5
1390
6054.2
2283.5
276.38
781.98
−154.6
−0.12598
1208.6
3035
1836.4
1325.6
1673
818.6
78.865
4030.8
14,251
967.4
634.2
876.4
2346
1337.2
908.46
1172.7
729.43
950.8
386.51
1122.6
C3
C4
C5
0.022
0.51512
−1.6831
−2.7946
−0.047736
0.04513
−0.14244
0.000083967
1.4444
0.09654
−22.709
50,373,000,000
−4
1.0317
3.7937
0.63829
5.104
0.5564
19.337
0.95485
−0.6087
−3.0418
−3.7887
−4.9793
0.377
4.2655
0.021868
0.6432
1.641
−0.5941
−2.1554
5.9704
42.486
−0.3314
−0.1708
−0.02982
0.00042478
−0.00010095
−0.14912
−0.32687
−1.7754
−0.00002443
2
−3.11E-18
7
−0.000040369
2
Tmin, K
Viscosity at
Tmin
187.65
204.81
159.95
226.1
240.91
200
220
239.66
223.16
184.99
188.44
131.65
240
160
274.18
2.258E-03
4.569E-03
4.375E-03
2.950E-03
3.796E-04
5.917E-04
1.103E-03
1.992E-03
5.311E-03
8.315E-03
6.093E-03
7.398E-04
2.041E-03
9.669E-03
6.023E-02
341.45
397.55
337.45
366.15
371
308.15
331.13
392.7
484.92
396.58
382.9
248.31
425.15
362.93
612.8
2.110E-04
2.194E-04
2.378E-04
4.695E-04
1.186E-04
1.734E-04
2.509E-04
3.045E-04
1.541E-04
2.956E-04
2.336E-04
1.490E-04
2.981E-04
2.147E-04
1.109E-04
225
291.67
413.79
284.95
293.15
260
262.15
309.58
90.35
200
220
192.15
178.2
250
258.15
250
200
253.15
104
284.29
260.15
250
160.65
245
155.15
180
140
204.15
125.26
250
200
167.55
6.696E-04
2.253E-03
1.071E-03
1.525E-03
4.124E-03
9.454E-04
3.002E-03
4.242E-03
1.247E-03
1.315E-02
1.132E-03
1.727E-03
8.012E-03
6.643E-03
6.705E-03
1.319E-03
6.406E-03
9.605E-04
6.334E-04
2.487E-03
1.305E-01
7.909E-04
1.918E-03
7.435E-04
8.035E+00
1.765E-02
7.908E-03
3.319E-03
9.520E-03
9.848E-04
1.156E-03
8.239E-03
310.48
464
559.2
374.65
613.44
382.35
526.4
616.93
300
440
473.15
289.73
413.1
486.55
466.95
394.65
404.94
378.15
250
483.15
576
329
283.85
345
510.1
417.15
326.15
386.55
308.15
372.25
337.01
371.05
2.528E-04
3.547E-04
3.214E-04
4.610E-04
1.134E-04
2.118E-04
1.220E-04
2.078E-04
3.587E-05
1.416E-04
9.061E-05
2.236E-04
2.326E-04
3.109E-04
2.822E-04
2.533E-04
2.956E-04
2.599E-04
6.142E-05
1.723E-04
1.276E-04
3.123E-04
2.863E-04
2.486E-04
2.165E-04
2.522E-04
1.949E-04
2.207E-04
2.626E-04
2.480E-04
2.086E-04
2.089E-04
Tmax, K
Viscosity at
Tmax
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
8.18
−10.064
−10.118
−10.501
−7.6591
−74.521
−48.529
−10.923
−9.6312
−19.991
−9.5468
−98.159
−40.543
−66.654
−125.81
−9.3874
−13.929
−10.819
−11.812
−2.7947
−20.182
0.1369
−56.569
−46.402
−39.324
−82.705
−11.445
−13.684
−10.903
−4.2684
−10.073
−4.7263
−3.7464
−75.781
−11.661
−11.633
−116.34
−21.927
353.99
−10.905
−11.497
−31.157
−117.73
−14.527
−6.1572
−25.317
−4.648
13.557
−2.8737
10.848
−75.6
1058.7
464.42
427.78
603.36
5081.5
3394.7
894.63
−3.841
2245.1
1147.2
3592.6
3328.3
5325.8
7996
1204.9
1321.9
841.33
1291.9
563.86
2203.5
633.77
2140.5
3448.6
3841
7404.9
1187.2
1283.4
796.19
647.6
1123.3
594.43
624.2
4175.4
24.7
316.38
3834.6
1266.5
13,928
762.11
1365.7
1926
9943.3
1497.7
178.15
1789.2
1832
−187.3
301.35
75
−3.5148
−0.17162
0.0086309
−0.53378
9.0873
5.3903
−0.00068418
−1.458
1.1982
−0.23251
14.197
4.1804
7.66
16.412
−0.32618
0.40382
0.076469
−1.1636
1.2289
−1.6659
7.5175
5.0849
3.6933
6.4721
0.0029076
0.33755
−1.0087
−0.16515
−0.86247
−1.084
9.6508
−0.261
0.56191
16.864
1.5927
−41.717
−0.11863
0.036966
2.925
14.589
0.51747
−0.95239
2.069
−1.2191
−3.6592
−1.2271
−3.297
−1.065E-08
10
−0.000029555
2
−2.2512E-28
−7.6643E-17
9.9041
6
−0.000017676
2
−2.12E-30
1.5016
10.485
0.41014
−7.27E-09
−4.10E-16
3
10
−2.5875E-10
−2962
−9.0606E-24
4
−0.5
10
53.48
232.15
129.95
131.35
155.15
273.15
281.45
200
2.2
295.13
229.8
180.15
265.83
239.15
220
234.15
250
154.12
229.92
192.22
291.31
214.93
174.65
269.25
228.55
223
217.35
217.5
133.39
170.05
192.62
141.25
183.65
274.69
13.95
185.15
158.97
259.83
189.79
187.68
250
250
409.15
288.15
90.69
175.47
301.15
250
170.45
275
7.317E-04
1.599E-03
1.438E-03
7.450E-04
1.560E-03
7.171E-03
2.319E-03
1.575E-03
3.628E-06
3.814E-03
2.971E-03
4.341E-03
9.242E-03
8.805E-02
3.856E-01
2.427E-03
1.642E-03
4.701E-03
3.097E-03
2.528E-03
3.536E-03
2.849E-03
2.379E-03
5.854E-03
8.570E-02
4.919E-01
2.561E-03
2.563E-03
7.197E-03
3.550E-03
6.035E-03
8.332E-03
2.483E-03
1.451E-03
2.546E-05
9.207E-04
1.003E-03
2.754E-04
1.545E-03
5.726E-04
2.938E-03
6.737E-04
3.386E-03
1.664E-03
2.063E-04
1.193E-02
3.995E-03
6.135E-04
6.045E-04
6.126E-04
140
453.15
235.45
194.82
253.85
493
373.71
304.5
5.1
575.3
426.15
432.16
496.15
448.6
432.9
421.15
424.18
429.92
450.09
447.2
564.15
401.15
406.08
478.85
429.9
412.4
400.7
396.65
336.63
432
425.81
412
435
522.52
33
206.45
318.15
298.85
368.92
350
450
453.15
580
434.15
188
337.85
478.15
425
373.15
400
5.954E-05
1.542E-04
2.900E-04
2.587E-04
2.645E-04
3.829E-04
5.444E-04
3.392E-04
2.532E-06
2.088E-04
2.580E-04
1.003E-04
3.754E-04
3.190E-04
2.707E-04
2.040E-04
2.318E-04
1.417E-04
2.087E-04
1.777E-04
2.054E-04
2.563E-04
1.164E-04
4.019E-04
3.343E-04
3.274E-04
2.108E-04
2.185E-04
1.959E-04
1.377E-04
2.172E-04
2.083E-04
1.368E-04
2.191E-04
3.906E-06
8.206E-04
5.777E-05
1.821E-04
1.185E-04
8.089E-05
2.649E-04
1.214E-04
4.281E-04
3.582E-04
2.262E-05
3.442E-04
2.392E-04
1.198E-04
8.846E-05
1.636E-04
(Continued)
2-277
2-278
TABLE 2-139
Eqn
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
Cmpd.
no.
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued )
Name
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Formula
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
CAS
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
Mol. wt.
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
C1
C2
C3
1074
2267.4
648.37
889.11
1048.5
4169.6
705.48
639.21
441.1
949.12
1067.3
433.58
1141.7
1009.7
1213.1
3219
3150.5
3173.2
612.62
679.07
788.86
745.32
627.18
520.68
863.65
2113.3
888.42
1168.7
0.84203
1.4173
−0.041947
0.20469
−1.5474
4.7
−0.011113
−0.38409
−1.0547
−0.00012343
−0.017484
−1.3238
0.15014
−11.216
−11.272
−11.075
−10.628
−0.099
−12.579
−12.86
−11.391
−13.912
400.35
−10.385
−4.841
−10.705
−10.569
737.75
1048.9
990.72
645
496
2224.2
946.91
1090.8
797.09
−30,387
599.59
696.7
788.94
952.38
0.019308
0.00030493
−11.632
−13.415
−10.34
−19.308
−17.945
1251.6
1050.5
519.61
1822.5
115.57
−17.044
−21.971
−10.481
−12.596
−1.035
−46.377
−10.755
−8.4453
−3.6585
−11.278
−10.97
−1.8842
−12.206
−12.002
−11.358
−6.1534
−6.6904
−6.6915
−1.8553
−4.8515
−6.7424
−10.517
−11.104
−1.0598
−10.842
−39.641
−11.27
−11.394
C4
C5
−1.4494
−1.392
−1.3046
−1.3774
−0.93238
−0.69862
0.036581
−1.4961
−0.00074603
4.308
0.024736
−0.007539
0.025885
−1.5939
0.26191
1.0752E-07
0.45308
−56.971
−0.046088
−0.9194
−0.048383
−0.063873
0.071692
0.33157
−0.013899
1.218
1.428
550,680,000
0
−2.14E-17
−3
0
10
Tmin, K
Viscosity at
Tmin
179.69
288.15
159.53
150
298.15
155.95
135.58
139.39
160.15
157.48
175.3
183.45
200
139.05
146.58
299.15
280.15
269.15
248.15
146.62
168.54
275
160
186.48
167.23
250
188
189.15
1.236E-03
2.299E-03
1.321E-03
3.542E-03
1.774E-03
5.989E+01
3.675E-03
3.164E-03
1.915E-03
5.239E-03
6.930E-03
1.628E-03
3.339E-03
8.734E-03
4.587E-02
2.584E-02
3.729E-02
1.107E-01
9.288E-04
7.669E-03
3.539E-03
4.070E-04
9.133E-04
2.266E-03
3.409E-03
6.104E-04
1.637E-03
5.222E-03
273.15
472.65
314
310
450.15
404.15
304.3
311.7
390.15
343.31
396.58
364
375.9
353.6
457.68
548.8
491.2
493.6
353.15
433.6
420.8
314.7
280.5
535.5
339.8
304.9
331.7
389.15
2.275E-04
2.149E-04
1.739E-04
1.928E-04
2.859E-04
3.891E-04
2.034E-04
1.841E-04
1.476E-04
2.006E-04
2.286E-04
2.035E-04
2.539E-04
1.066E-04
1.653E-04
8.025E-05
1.360E-04
2.356E-04
2.742E-04
1.301E-04
1.129E-04
2.891E-04
1.731E-04
7.577E-05
2.474E-04
3.134E-04
2.143E-04
2.170E-04
127.93
180.15
171.64
150.18
260
240
119.55
176
110
295.56
132.81
250
133.97
160.17
4.722E-03
4.305E-03
4.977E-03
2.022E-03
8.635E-04
3.646E-02
2.506E-02
5.554E-03
1.072E-02
5.334E-03
2.253E-03
8.002E-04
6.390E-03
7.103E-03
303.92
367.55
553.1
279.11
400
518.15
333.41
372
310.95
451.21
266.25
352.6
312.2
368.69
1.703E-04
2.212E-04
9.292E-05
2.826E-04
2.229E-04
2.519E-04
2.038E-04
2.120E-04
1.588E-04
1.006E-04
2.270E-04
2.593E-04
2.127E-04
2.333E-04
249.95
164.55
151.15
353.43
25.09
1.972E-03
4.801E-03
9.377E-04
9.077E-04
1.602E-04
438.65
328.2
278.65
633.15
44.13
2.382E-04
2.502E-04
1.929E-04
1.892E-04
2.706E-05
Tmax, K
Viscosity at
Tmax
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
C2H5NO2
N2
F3N
CH3NO2
N2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
−4.438
16.004
−9.5556
19.329
−246.65
−16.403
−4.3492
−68.54
−48.851
−39.863
−98.854
−11.069
−11.319
−2.3409
−22.688
−2.5373
−98.805
−60.795
−0.22128
−145.99
−11.736
−20.804
−11.19
−11.498
−3.8552
−27.978
−4.1476
−10.94
−19.299
−8.2185
−53.509
−37.067
−36.561
−16.456
−11.055
−2.8695
−10.667
−6.9168
−11.677
−1.7273
−3.7241
−22.472
−15.822
−11.31
195.25
−6.3528
−17.156
23.467
−8.8918
−11.208
−5.9402
746.5
−181.61
981.64
−381.68
3150.3
2119.5
1052.7
3165.3
4095
4089
7183.8
1081.7
1428
715.52
2466
900.91
3905.5
4617.8
3018.4
9296.7
1415.2
1834.6
1057.4
1362.1
684.22
2915.1
94.04
415.96
2088.6
919.43
1836.6
2856.7
3542.2
3209.9
1005.3
596.32
659.56
818.76
1091.2
424.34
516.54
2566.9
3301.8
1280
−11,072
240.85
646.25
116.07
2357.6
1079.8
617.95
−0.9385
−5.1551
200
63.15
3.420E-03
2.633E-04
387.22
124
3.027E-04
3.331E-05
−0.19453
−4.8618
49.98
0.6881
−1.0035
9.0919
5.294
3.7631
12.283
244.6
210
109.5
305.04
267.3
218.15
285.55
280
238.15
191.91
253.05
223.15
301.31
251.65
211.15
289.65
280
241.55
252.85
255.55
171.45
223.95
193.55
462.65
54.36
77.55
283.07
191.59
143.42
270
253.15
200
250
234.18
108.02
220
197.45
167.45
163.83
372.38
291.45
243.15
404.15
136.87
85.47
146.95
185.26
199
165
1.344E-03
2.065E-04
3.858E-04
4.012E-03
2.432E-03
3.306E-03
1.030E-02
1.733E-02
2.310E-01
4.372E-03
3.026E-03
3.206E-03
3.926E-03
2.555E-03
2.629E-03
6.652E-03
1.472E-02
1.856E-01
2.161E-03
2.039E-03
6.587E-03
4.837E-03
3.614E-03
6.539E-04
7.170E-04
3.787E-03
3.486E-03
3.532E-03
3.529E-03
3.773E-03
1.649E-02
6.660E-01
9.009E-04
1.024E-03
1.045E-02
1.643E-03
3.745E-03
2.322E-03
1.902E-03
1.920E-03
1.119E-02
2.368E-03
1.229E-03
5.772E-04
9.458E-03
2.069E+01
3.917E-01
3.083E-03
2.522E-03
374.35
283.09
180.05
603.15
465.52
593.15
528.75
486.25
471.7
420.02
492.95
487.2
589.86
445.15
454.96
512.85
468.35
452.9
446.15
440.65
453.52
472.19
468
516
150
208.8
543.84
375.15
465.15
458.95
410.95
392.2
375.46
375.14
303.22
385.15
399.79
378
415.2
610.03
555.4
522.4
557.65
298.15
360
370.35
355.3
508.8
322.15
3.078E-04
7.730E-05
3.791E-05
2.068E-04
2.606E-04
4.997E-05
3.670E-04
2.823E-04
3.334E-04
2.048E-04
1.912E-04
2.172E-04
2.057E-04
2.614E-04
1.111E-04
3.576E-04
2.902E-04
5.409E-04
1.913E-04
2.075E-04
1.422E-04
1.999E-04
1.868E-04
4.399E-04
6.990E-05
1.300E-04
2.091E-04
2.539E-04
4.796E-05
3.510E-04
3.842E-04
2.557E-04
2.354E-04
2.232E-04
2.051E-04
2.385E-04
2.463E-04
1.898E-04
9.980E-05
2.849E-04
5.134E-05
1.420E-04
1.986E-04
1.416E-04
4.275E-05
4.735E-04
4.892E-04
1.133E-04
2.470E-04
−0.022545
−1.222
1.5703
−1.2685
14.103
7.028
−2.8054
19.285
0.0003618
1.3403
−0.22541
1
−0.000013519
2
−0.000025112
2
0.000013141
2
−0.000019627
2
0.015575
−1.0071
2.3374
−1.207
1.1091
−0.42363
7.1409
3.7344
3.3364
−8.0487E-37
12.84
0.0039301
−1.2025
−0.59628
0.10658
−1.342
−1.1167
1.5749
−29.084
−0.58229
1.1101
−5.3372
−0.91376
−0.74183
−7.3439E-11
2,880,100,000
4
−4.0267
2-279
(Continued)
2-280
TABLE 2-139
Eqn
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
101
Cmpd.
no.
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued )
Name
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
Formula
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
CAS
Mol. wt.
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
C1
C2
C3
−23.931
−6.698
17.797
−9.8074
−18.282
−92.082
−73.735
−5.7244
−10.153
−804.54
−14.846
1834.6
753.58
−252.43
1010.4
1549.7
1907.3
2668.2
638.2
840.71
30,487
1829.4
1.9124
−0.63783
−4.291
−0.25697
1.0454
15.639
10.993
−0.76415
−0.093763
130.79
0.3729
−22.675
−104.32
46.223
3.8305
−88.793
−11.566
−215.09
−136.73
−10.321
−118.86
−10.843
5.5351
−16.671
−226.08
0.388
−111.98
−3.7067
10.142
−11.756
−9.6461
−12.928
−4.0309
−10.707
−11.504
52.176
−69.778
−22.407
−2.2333
0.26297
−10.37
−52.843
−11.91
−15.489
−7.381
1758
9615.1
−1378
41.21
6400.7
2843.2
11,612
6421.3
900.92
5829.5
1165.2
632.38
1342.5
6805.7
736.5
5468.6
585.78
−130.41
1483.1
1281.2
1137.5
990.76
1818.5
3301
−4951.9
5905.2
1462.8
320.37
276.55
823.31
3703.6
1094.9
1393.5
911.7
1.6701
12.587
−8.7475
−2.1342
10.709
31.849
19.493
−0.069128
16.605
−2.6576
0.8388
37.542
−1.7063
15.579
−1.0926
−3.2199
−0.040387
−0.29478
0.25725
−1.1771
−0.39102
−8.5676
8.0214
1.7006
−1.2915
−1.7282
5.866
0.13825
0.63711
−0.54152
C4
C5
−0.043098
−0.018364
1
1
−0.15449
1
−0.026882
−0.00002297
1
2
−0.000016991
2
−0.060853
1
−0.000016992
2
−3.6929E-28
10
570,980
−5.879E-29
−2
10
Tmin, K
Viscosity at
Tmin
252.45
180.37
250
188.36
200
87.89
180.25
142.61
159.95
213.15
388.85
2.275E-03
2.928E-03
1.002E-03
3.060E-03
6.774E-03
1.549E-02
5.852E-03
6.477E-03
4.641E-03
9.502E+02
3.642E-04
414.32
370.25
473.15
321
432.39
333.15
353.97
325.71
340.87
500.8
454
3.430E-04
2.172E-04
1.045E-04
2.908E-04
2.357E-04
5.147E-05
2.810E-04
2.784E-04
2.656E-04
3.307E-04
1.965E-04
242.54
460.85
225
223.15
289.95
700.15
329.35
277.65
164.65
237.4
293.15
373.96
250
178.18
236.5
267.67
250
200
247.79
229.33
165.78
172.22
398.4
353.15
247.57
288.45
225
173.15
130
178.35
273.16
225.3
247.98
286.41
1.919E-03
1.913E-03
6.900E-04
5.388E-04
2.477E-03
5.502E-04
1.736E-02
3.350E-03
5.505E-03
1.183E-02
1.040E-03
1.999E-04
1.269E-03
1.569E-02
2.955E-03
3.399E-03
6.135E-04
5.156E-04
2.495E-03
3.477E-03
8.636E-03
1.305E-02
2.150E-03
1.167E-02
3.240E-03
2.089E-02
1.237E-03
8.764E-04
2.425E-03
3.171E-03
1.702E-03
1.834E-03
1.735E-03
7.021E-04
418.31
591
400
318.69
318.15
795.28
723.15
554.4
373.15
576
303.15
454
393.15
383.78
387
540
359.05
308.15
449.27
442.53
541.15
387.91
676.8
625
511.2
590.15
345.65
364
400
434.52
646.15
413.1
418.1
413.1
2.268E-04
4.426E-04
6.557E-05
2.383E-04
9.456E-04
3.385E-04
1.522E-04
1.170E-04
2.446E-04
1.458E-04
9.125E-04
8.859E-05
2.625E-04
2.428E-04
3.798E-04
1.520E-04
2.028E-04
1.612E-04
1.663E-04
1.942E-04
4.530E-05
2.049E-04
3.288E-04
1.601E-04
1.569E-04
1.856E-04
2.654E-04
1.273E-04
8.272E-05
2.086E-04
5.028E-05
2.189E-04
2.459E-04
2.169E-04
Tmax, K
Viscosity at
Tmax
Except for deuterium, the liquid viscosity is calculated by Eqn 101: µ = exp(C1 + C2/T + C3 ln T + C4T C5) where µ is the viscosity in Pa∙s and T is the temperature in K. Viscosity is either 1 atm or the vapor pressure, whichever is higher.
For deuterium, liquid viscosity is calculated by Eqn 100: µ = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where µ is the viscosity in Pa∙s and T is the temperature in K.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation
of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
TRAnSPORT PROPERTIES
TABLE 2-140 Viscosities of Liquids: Coordinates for Use with Fig. 2-19
Liquid
Acetaldehyde
Acetic acid, 100%
Acetic acid, 70%
Acetic anhydride
Acetone, 100%
Acetone, 35%
Acetonitrile
Acrylic acid
Allyl alcohol
Allyl bromide
Allyl iodide
Ammonia, 100%
Ammonia, 26%
Amyl acetate
Amyl alcohol
Aniline
Anisole
Arsenic trichloride
Benzene
Brine, CaCl2, 25%
Brine, NaCl, 25%
Bromine
Bromotoluene
Butyl acetate
Butyl acrylate
Butyl alcohol
Butyric acid
Carbon dioxide
Carbon disulfide
Carbon tetrachloride
Chlorobenzene
Chloroform
Chlorosulfonic acid
Chlorotoluene, ortho
Chlorotoluene, meta
Chlorotoluene, para
Cresol, meta
Cyclohexanol
Cyclohexane
Dibromomethane
Dichloroethane
Dichloromethane
Diethyl ketone
Diethyl oxalate
Diethylene glycol
Diphenyl
Dipropyl ether
Dipropyl oxalate
Ethyl acetate
Ethyl acrylate
Ethyl alcohol, 100%
Ethyl alcohol, 95%
Ethyl alcohol, 40%
Ethyl benzene
Ethyl bromide
2-Ethyl butyl acrylate
Ethyl chloride
Ethyl ether
Ethyl formate
2-Ethyl hexyl acrylate
Ethyl iodide
Ethyl propionate
Ethyl propyl ether
Ethyl sulfide
Ethylene bromide
Ethylene chloride
Ethylene glycol
Ethylidene chloride
Fluorobenzene
Formic acid
X
Y
15.2
12.1
9.5
12.7
14.5
7.9
14.4
12.3
10.2
14.4
14.0
12.6
10.1
11.8
7.5
8.1
12.3
13.9
12.5
6.6
10.2
14.2
20.0
12.3
11.5
8.6
12.1
11.6
16.1
12.7
12.3
14.4
11.2
13.0
13.3
13.3
2.5
2.9
9.8
12.7
13.2
14.6
13.5
11.0
5.0
12.0
13.2
10.3
13.7
12.7
10.5
9.8
6.5
13.2
14.5
11.2
14.8
14.5
14.2
9.0
14.7
13.2
14.0
13.8
11.9
12.7
6.0
14.1
13.7
10.7
4.8
14.2
17.0
12.8
7.2
15.0
7.4
13.9
14.3
9.6
11.7
2.0
13.9
12.5
18.4
18.7
13.5
14.5
10.9
15.9
16.6
13.2
15.9
11.0
12.6
17.2
15.3
0.3
7.5
13.1
12.4
10.2
18.1
13.3
12.5
12.5
20.8
24.3
12.9
15.8
12.2
8.9
9.2
16.4
24.7
18.3
8.6
17.7
9.1
10.4
13.8
14.3
16.6
11.5
8.1
14.0
6.0
5.3
8.4
15.0
10.3
9.9
7.0
8.9
15.7
12.2
23.6
8.7
10.4
15.8
Liquid
Glycerol, 100%
Glycerol, 50%
Heptane
Hexane
Hydrochloric acid, 31.5%
Iodobenzene
Isobutyl alcohol
Isobutyric acid
Isopropyl iodide
Kerosene
Linseed oil, raw
Mercury
Methanol, 100%
Methanol, 90%
Methanol, 40%
Methyl acetate
Methyl acrylate
Methyl i-butyrate
Methyl n-butyrate
Methyl chloride
Methyl ethyl ketone
Methyl formate
Methyl iodide
Methyl propionate
Methyl propyl ketone
Methyl sulfide
Naphthalene
Nitric acid, 95%
Nitric acid, 60%
Nitrobenzene
Nitrogen dioxide
Nitrotoluene
Octane
Octyl alcohol
Pentachloroethane
Pentane
Phenol
Phosphorus tribromide
Phosphorus trichloride
Propionic acid
Propyl acetate
Propyl alcohol
Propyl bromide
Propyl chloride
Propyl formate
Propyl iodide
Refrigerant R-22
Sodium
Sodium hydroxide, 50%
Stannic chloride
Succinonitrile
Sulfur dioxide
Sulfuric acid, 110%
Sulfuric acid, 100%
Sulfuric acid, 98%
Sulfuric acid, 60%
Sulfuryl chloride
Tetrachloroethane
Thiophene
Titanium tetrachloride
Toluene
Trichloroethylene
Triethylene glycol
Turpentine
Vinyl acetate
Vinyl toluene
Water
Xylene, ortho
Xylene, meta
Xylene, para
X
Y
2.0
6.9
14.1
14.7
13.0
12.8
7.1
12.2
13.7
10.2
7.5
18.4
12.4
12.3
7.8
14.2
13.0
12.3
13.2
15.0
13.9
14.2
14.3
13.5
14.3
15.3
7.9
12.8
10.8
10.6
12.9
11.0
13.7
6.6
10.9
14.9
6.9
13.8
16.2
12.8
13.1
9.1
14.5
14.4
13.1
14.1
17.2
16.4
3.2
13.5
10.1
15.2
7.2
8.0
7.0
10.2
15.2
11.9
13.2
14.4
13.7
14.8
4.7
11.5
14.0
13.4
10.2
13.5
13.9
13.9
30.0
19.6
8.4
7.0
16.6
15.9
18.0
14.4
11.2
16.9
27.2
16.4
10.5
11.8
15.5
8.2
9.5
9.7
10.3
3.8
8.6
7.5
9.3
9.0
9.5
6.4
18.1
13.8
17.0
16.2
8.6
17.0
10.0
21.1
17.3
5.2
20.8
16.7
10.9
13.8
10.3
16.5
9.6
7.5
9.7
11.6
4.7
13.9
25.8
12.8
20.8
7.1
27.4
25.1
24.8
21.3
12.4
15.7
11.0
12.3
10.4
10.5
24.8
14.9
8.8
12.0
13.0
12.1
10.6
10.9
2-281
2-282
PHYSICAL AnD CHEMICAL DATA
FIG. 2-19 Nomograph for viscosities of liquids at 1 atm. For coordinates see Table 2-141. To convert centipoise to pascalseconds, multiply by 0.001.
TRAnSPORT PROPERTIES
2-283
TABLE 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm)
Dv in cm2/s
Substance
Acetic acid
Acetone
n-Amyl alcohol
sec-Amyl alcohol
Amyl butyrate
Amyl formate
i-Amyl formate
Amyl isobutyrate
Amyl propionate
Aniline
Anthracene
Argon
Benzene
Benzidine
Benzyl chloride
n-Butyl acetate
i-Butyl acetate
n-Butyl alcohol
i-Butyl alcohol
Butyl amine
i-Butyl amine
i-Butyl butyrate
i-Butyl formate
i-Butyl isobutyrate
i-Butyl proprionate
i-Butyl valerate
Butyric acid
i-Butyric acid
Cadmium
Caproic acid
i-Caproic acid
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Chlorobenzene
Chloroform
Chloropicrin
m-Chlorotoluene
o-Chlorotoluene
p-Chlorotoluene
Cyanogen chloride
Cyclohexane
n-Decane
Diethylamine
2,3-Dimethyl butane
Diphenyl
n-Dodecane
Ethane
Ethanol
Ether (diethyl)
Ethyl acetate
Ethyl alcohol
Ethyl benzene
Ethyl n-butyrate
Ethyl i-butyrate
Ethylene
Ethyl formate
Ethyl propionate
Ethyl valerate
Eugenol
Formic acid
Helium
n-Heptane
n-Hexane
Hexyl alcohol
Hydrogen
Temp., °C
0
0
0
30
0
0
0
0
0
0
30
0
20
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
25
500‡
0
0
450‡
0
30
0
25
0
0
0
0
15
45
90
0
15
0
126
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
20
38
15
0
0
25
500
Air
A
H2
0.1064
.109
.0589
.072
.040
.0543
.058
.0419
.046
.0610
.075
.0421
0.416
.361
.235
.077
.0298
.066
.058
.0612
.0703
.088
.0727
.0821
.0853
.0468
.0705
.0457
.0529
.0424
.067
.0679
.306
O2
N2
CO2
N2O
CH4
C2H6
C2H4
n-C4H10
i-C4H10
0.0716
.0422
.171
.1914
.0347
0.194
0.0797
.0528
.2364
.2716
.0425
.0476
.2771
.0483
.185
.0327
.191
.203
.173
.264
.271
.0364
.0366
.0308
.0476
.0471
.17
.050
.0513
.138
.550
.139
0.096
.163
.0996∗
0.153
.00215†
.9
.0892
.369
.651
.293
.185
1.0
0.0636
.319
.0744
.063
.137
0.116
.075
.091
.088
.054
.059
.051
.111
0.0719
.0760
.086
.306
.0841
.0884
.0657
.301
.0753
.0751
.0610
.308
.459
.377
.298
.273
.0778
.0715
.089
.102
.0658
.0579
.0591
.0840
.068
.0512
.0377
.1308
.0813
.0686
.0546
.0487
.375
.0685
.224
.229
.486
.337
.236
.205
.0407
.0413
.0573
.0450
.0367
.510
.0874
Ref.
8
6, 16
8
5
8
8
8
8
8
8
5
8
18
8, 15
8
8
8
8
8
5
8
8
8
8
8
8
8
8
8
8
13
8
8
8
19
1, 9
18
8
8
18
16, 17
5
6
10
8
8
8
10
3
6
3
8
3
8
3
8
20
7, 8
8
5
8
8
8
8
8
8
4, 8
8
8
8
8
19
.641
.705
.066§
.0663
.0499
.611
.290
.200
.0753
.697
4.2
.0757
.674
.0351
.550
.646
.535
.625
0.459
.537
0.486
.726
0.272
0.277
3
8
8
2
18
(Continued)
2-284
PHYSICAL AnD CHEMICAL DATA
TABLE 2-141
Diffusivities of Pairs of Gases and Vapors (1 atm) (Continued )
Dv in cm2/s
Substance
Temp., °C
Air
Hydrogen cyanide
Hydrogen peroxide
Iodine
Mercury
Mesitylene
Methane
Methyl acetate
Methyl alcohol
Methyl butyrate
Methyl i-butyrate
Methyl cyclopentane
Methyl formate
Methyl propionate
Methyl valerate
Naphthalene
Nitrogen
0
60
0
0
0
500
0
0
0
0
15
0
0
0
0
0
25
0
0
30
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
30
0
0.173
.188
.07
.112
.056
Nitrous oxide
n-Octane
Oxygen
Phosgene
Propionic acid
Propyl acetate
n-Propyl alcohol
i-Propyl alcohol
n-Propyl benzene
i-Propyl benzene
n-Propyl bromide
i-Propyl bromide
Propyl butyrate
Propyl formate
n-Propyl iodide
i-Propyl iodide
n-Propyl isobutyrate
i-Propyl isobutyrate
Propyl propionate
Propyl valerate
Safrol
i-Safrol
Sulfur hexafluoride
Toluene
Trimethyl carbinol
2,2,4-Trimethyl
pentane
2,2,3-Trimethyl
heptane
n-Valeric acid
i-Valeric acid
Water
H2
O2
N2
CO2
N 2O
CH4
C2H6
C2H4
n-C4H10
0.0731
.0872
.0735
0.0569
.0513
18
0.0567
.0879
.0446
.0451
0.0742
0.0758
.295
.0528
0.181
0.165
.096
0.535
.0505
0.0642
.178
.095
.0829
.067
.085
.0818
.101
.0481
.0489
.085
.0902
.0530
.0712
.079
.0802
.0549
.059
.057
.0466
.0434
.0455
.271
.697
0.0705
0.0710
0.181
.139
.330
.0588
.315
.0577
.206
.281
.0364
.0490
.212
.0388
.212
.189
.0395
.0341
.418
.076
.088
.087
0.071
0.0618
.288
0.0688
.270
0.050
0.0544
0.220
.212
.75
Ref.
10
11
8, 12, 14
8, 12, 13
8
1.1
.333
.506
.242
.257
.318
i-C4H10
0.070
.13
0.53
.084
.132
.0633
.0639
30
90
0
0
0
450
A
0.148
0.163
0.0960
0.0908
8
8
8
8
3
8
8
8
8
8
2
8
8
3
8
10
8
8
8
8
5
8
8
8
8
8
8
8
8
8
8
8
8
8
8
2
4, 8
5
8
0.0705
3
0.0684
3
8
8
8, 20
18
.0376
.138
1.3
∗ 320 mmHg.
†
40 atm.
‡
Also at other temperatures.
§
Strong function of concentration.
References
1
Amdur, Irvine, Mason, and Ross, J. Chem. Phys., 20, 436 (1952).
2
Boyd, Stein, Steingrimsson, and Rumpel, J. Chem. Phys., 19, 548 (1951).
3
Cummings and Ubbelohde, J. Chem. Soc. (London), 1953, p. 3751.
4
Fairbanks and Wilke, Ind. Eng. Chem., 42, 471 (1950).
5
Gilliland, Ind. Eng. Chem., 26, 681 (1934).
6
Gorynnova and Kuvskinskii, Zhur. Tekh. Fiz., 18, 1421 (1948).
7
Hansen, Dissertation, Jena, 1907.
8
International Critical Tables, vol. 5, p. 62.
9
Jeffries and Drickamer, J. Chem. Phys., 22, 436 (1954).
10
Klotz and Miller, J. Am. Chem. Soc., 69, 2557 (1947).
11
McMurtrie and Keyes, J. Am. Chem. Soc., 70, 3755 (1948).
12
Mullaly and Jacques, Phil. Mag., 48, 6, 1105 (1924).
13
Spier, Physica, 6 (1939): 453; 7, 381 (1940).
14
Topley and Whytlaw-Gray, Phil. Mag., 4, 873 (1927).
15
Trautz and Ludwig, Ann. Physik, 5, 5, 887 (1930).
16
Trautz and Muller, Ann. Physik, 22, 353 (1935).
17
Trautz and Ries, Ann. Physik, 8, 163 (1931).
18
Walker and Westenberg, J. Chem. Phys., 32, 136 (1960).
19
Westenberg and Walker, J. Chem. Phys., 26, 1753 (1957).
20
Winkelmann, Wied. Ann., 22, 152 (1884); 23, 203 (1884); 26, 105 (1885); 33, 445 (1888); 36, 92 (1889).
TRAnSPORT PROPERTIES
Table 2-143 has a representative selection of diffusion coefficients. The
subsection “Prediction and Correlation of Physical Properties” should be
consulted for estimation techniques.
TABLE 2-142
Diffusivities in Liquids (25çC)
Dilute solutions and 1 atm unless otherwise noted; use DLµ/T = constant to estimate effect of temperature; ∗ indicates that
reference gives effect of concentration.
Solute
Solvent
DL × 105,
sq cm/sec
Acetal∗
Acetamide∗
Acetamide∗
Acetic acid
Acetic acid
Acetic acid
Acetic acid
Acetic acid
Acetic acid∗
Acetonitrile
Acetylene
Allyl alcohol∗
Allyl alcohol
Ammonia∗
i-Amyl alcohol∗
i-Amyl alcohol
Benzene
Benzene (50 mole %)
Benzene (50 mole %)
Benzene (50 mole %)
Benzene (50 mole %)
Benzene (50 mole %)
Benzene (50 mole %)
Benzoic acid
Benzoic acid
Benzoic acid
Benzoic acid
Benzoic acid
Bromine
Bromine
Bromine
Bromobenzene
Bromoform∗
Bromoform
Bromoform
Bromoform∗
Bromoform
Bromoform
n-Butanol
Caffeine
Carbon dioxide
Carbon dioxide
Carbon disulfide (50 mole %, 200 atm.)
Carbon disulfide (50 mole %, 200 atm.)
Carbon disulfide (50 mole %, 218 atm.)
Carbon disulfide (50 mole %, 200 atm.)
Carbon disulfide (50 mole %, 100 atm.)
Carbon disulfide (50 mole %, 50 atm.)
Carbon disulfide (50 mole %, 200 atm.)
Carbon disulfide (50 mole %)
Carbon tetrachloride
Carbon tetrachloride∗
Carbon tetrachloride
Carbon tetrachloride
Carbon tetrachloride∗
Carbon tetrachloride
Carbon tetrachloride
Carbon tetrachloride
Carbon tetrachloride
Carbon tetrachloride
Chloral∗
Chloral hydrate
Ethanol
Ethanol
Water
Acetone
Benzene
Carbon tetrachloride
Ethylene glycol
Toluene
Water
Water
Water
Ethanol
Water
Water
Ethanol
Water
Carbon tetrachloride
n-Decane
2,4-Dimethyl pentane
n-Dodecane
n-Heptane
n-Hexadecane
n-Octadecane
Acetone
Benzene
Carbon tetrachloride
Ethylene glycol
Toluene
Benzene
Carbon disulfide
Water
Benzene
Acetone
i-Amyl alcohol
Ethanol
Ethyl ether
Methanol
n-Propanol
Water
Water
Ethanol
Water
n-Butanol
i-Butanol
Chlorobenzene
2,4-Dimethyl pentane
n-Heptane
Methyl cyclohexane
n-Octane
Toluene
Benzene
Cyclohexane
Decalin
Dioxane
Ethanol
n-Heptane
Kerosene
Methanol
i-Octane
Tetralin
Ethanol
Water
1.25
0.68
1.19
3.31
2.11
1.49
0.13
2.26
1.24
1.66
1.78, 2.11
1.06
1.19
1.7, 2.0, 2.3
0.87
1.0
1.53
1.72
2.49
1.40
2.47
0.96
0.86
2.62
1.38
0.91
0.043
1.49
2.7
4.1
1.3
2.30
2.90
0.53
1.08
3.62
2.20
0.94
0.96
0.63
4.0
1.96
3.57
2.42
3.00
3.63
3.0
3.5
3.10
2.06
2.04
1.49
0.776
1.02
1.50
3.17
0.961
2.30
2.57
0.735
0.68
0.77
Estimated
possible,
error, ± %1
5
5
3
3
5
5
6
5
8
5
5
6
6
1
3
2
2
2
2
2
2
2
2
2
5
7
Ref.
11
11
11
4
1, 4
4
4
4
11
11
1, 24
11
11
1, 11
11
11, 25
7
26
26
26
26
26
26
4
4
4
4
4
11
11
11
25
11
11
11
11
23
11
1, 11, 18, 25
11
11
1, 3, 5, 20, 24, 28
14
14
14
14
14
14
14
14
7, 9
9, 10∗
9
9
9, 10∗
9
9
9
9
9
11
11
(Continued)
2-285
2-286
PHYSICAL AnD CHEMICAL DATA
TABLE 2-142 Diffusivities in Liquids (25çC) (Continued )
Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that
reference gives effect of concentration.
Solute
Chlorine
Chlorobenzene
Chloroform
Chloroform
Cinnamic acid
Cinnamic acid
Cinnamic acid
Cinnamic acid
1,1′-Dichloropropanol
Dicyanodiamide∗
Diethyl ether
Diethyl ether
2,4-Dimethyl pentane (50 mole %)
2,4-Dimethyl pentane (50 mole %)
Ethanol∗
Ethyl acetate
Ethylene dichloride
Formic acid
Formic acid
Formic acid
Formic acid
Formic acid
Formic acid
Glucose
Glycerol
Glycerol
Glycerol∗
n-Heptane (50 mole %)
n-Heptane (50 mole %)
n-Heptane (50 mole %)
n-Heptane (50 mole %)
Hexamethylene tetramine
Hydrogen chloride∗
Hydrogen
Hydrogen sulfide
Hydroquinone∗
Hydroquinone∗
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine∗
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodine
Iodobenzene
Lactose∗
Maltose∗
Mannitol∗
Methanol
Nicotine∗
Nitric acid∗
Nitrobenzene
Nitrogen
Nitrous oxide
Oxalic acid∗
Solvent
DL × 105,
sq cm/sec
Water
Benzene
Benzene
Ethanol
Acetone
Benzene
Carbon tetrachloride
Toluene
Water
Water
Benzene
Water
n-Dodecane
n-Hexadecane
Water
Ethyl benzoate
Benzene
Acetone
Benzene
Carbon tetrachloride
Ethylene glycol
Toluene
Water
Water
i-Amyl alcohol
Ethanol
Water
n-Dodecane
n-Hexadecane
n-Octadecane
n-Tetradecane
Water
Water
Water
Water
Ethanol
Water
Acetic acid
Anisole
Benzene
Bromobenzene
Carbon disulfide
Carbon tetrachloride
Chloroform
Cyclohexane
Dioxane
Ethanol
Ethyl acetate
Ethyl ether
Ethylene bromide
n-Heptane
n-Hexane
Mesitylene
Methanol
Methyl cyclohexane
n-Octane
Tetrabromoethane
n-Tetradecane
Toluene
m-Xylene
Ethanol
Water
Water
Water
Water
Water
Water
Carbon tetrachloride
Water
Water
Water
1.44
2.66
2.50
1.38
2.41
1.12
0.76
2.41
1.0
1.18
2.73
0.85
1.44
0.88
1.28
0.94
2.8
3.77
2.28
1.89
0.094
2.65
1.37
0.69
0.12
0.56
0.94
1.58
1.00
0.92
1.29
0.67
3.10
5.85 (4.4)
1.61
0.53
0.88, 1.12
1.13
1.25
1.98
1.25
3.2
1.45
2.30
1.80
1.07
1.30
2.2
3.61
0.93
3.4, 2.5
4.15
1.49
1.74
2.1
2.76
2.0
0.96
2.1
1.82
1.09
0.49
0.48
0.65
1.6
0.60
2.98
1.00
1.9
1.8
1.61
Estimated
possible,
error, ± %1
4
6
3
6
4
4
10
6
6
3
5
10
8
3
3
5
5
5
8
2
2
Ref.
1, 28
25
1, 25
11
4
4
4
4
11
11
25
2
26
26
1, 7, 9,∗ 11,∗ 22
6
1, 25
4
4
4
4
11
11
11
11
1, 11∗
26
26
26
26
11
4, 11,∗ 12∗
1, 11, 24(?)
1
11
2, 11∗
11
11
9, 19, 23
4, 11, 19
11, 19, 23
9, 11, 19
11, 23
4
9
4, 11∗
11, 19
11
11
9, 11, 19
4, 9
9
19
4
4
11
4
11
9, 11
11
11
11
11
1, 7, 11
11
11
7
1, 24
1, 11
11
TRAnSPORT PROPERTIES
TABLE 2-142
Diffusivities in Liquids (25çC) (Continued )
Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that
reference gives effect of concentration.
Solute
Oxygen
Oxygen
Oxygen
Pentaerythritol∗
Phenol
Phenol
Phenol
Phenol
Phenol
Phenol
n-Propanol
Pyridine∗
Pyridine
Pyrogallol
Raffinose∗
Resorcinol∗
Resorcinol∗
Saccharose∗
Stearic acid∗
Succinic acid∗
Sucrose
Sulfur dioxide
Sulfuric acid∗
Tartaric acid∗
1,1,2,2-Tetrabromoethane
Toluene
Toluene
Toluene
Toluene
Toluene
Urea
Urea
Urethane
Water
Solvent
Glycerol∗-water
(106 poise)
Sucrose∗-water
(125 poise)
Water
Water
i-Amyl alcohol
Benzene
Carbon disulfide
Chloroform
Ethanol
Ethyl ether
Water
Ethanol
Water
Water
Water
Ethanol
Water
Water
Ethanol
Water
Water
Water
Water
Water
1,1,2,2-Tetrachloroethane
n-Decane
n-Dodecane
n-Heptane
n-Hexane
n-Tetradecane
Ethanol
Water
Water
Glycerol
DL × 105,
sq cm/sec
Estimated
possible,
error, ± %1
Ref.
0.24
13
0.25
13
2.5
0.77
0.2
1.68
3.7
2.0
0.89
3.9
1.1
1.24
0.76
0.74
0.41
0.46
0.87
0.49
0.65
0.94
0.56
1.7
1.97
0.80
0.61
2.09
1.38
3.72
4.21
1.02
0.73
1.37
1.06
0.021
References
1
Arnold, J. Am. Chem. Soc., 52, 3937 (1930).
2
Calvet, J. Chim. Phys., 44, 47 (1947).
3
Carlson, J. Am. Chem. Soc., 33, 1027 (1911).
4
Chang and Wilke, J. Phys. Chem., 59, 592 (1955).
5
Davidson and Cullen, Trans. Inst. Chem. Eng., 35, 51 (1957).
6
Dummer, Z. Anorg. Chem., 109, 31 (1949).
7
Gerlach, Ann. Phys. (Leipzig), 10, 437 (1931).
8
Gosting and Akeley, J. Am. Chem. Soc., 74, 2058 (1952).
9
Hammond and Stokes, Trans. Faraday Soc., 49, 890 (1953); 49, 886 (1953).
10
Hammond and Stokes, Trans. Faraday Soc., 52, 781 (1956).
11
International Critical Tables, vol. 5, p. 63.
12
James, Hollingshead, and Gordon, J. Chem. Phys., 7, 89 (1939); 7, 836 (1939).
13
Jordon, Ackermann, and Berger, J. Am. Chem. Soc., 78, 2979 (1956).
14
Koeller and Drickamer, J. Chem. Phys., 21, 575 (1953).
15
Kolthoff and Miller, J. Am. Chem. Soc., 63, 1013 (1941).
20
4
3
7
7
4
5
4
4
5
6
3
10
4
2
1, 3, 15, 21, 24
11
11
1
11
11
11
11
1, 7, 11
11
11
11
11
11
11
11
11
11
2, 27
15, 17
11
11
11
4
4
4
4
4
11
8, 11
11, 25
16
2-287
2-288
PHYSICAL AnD CHEMICAL DATA
THERMAL TRAnSPORT PROPERTIES
TABLE 2-143
Transport Properties of Selected Gases at Atmospheric Pressure*
Thermal conductivity,
W/(m ⋅ K) Temperature, K
Substance
Viscosity,
10–4 Pa ⋅ s Temperature, K
250
300
400
500
Acetone
Acetylene
Benzene
0.0080
0.0162
0.0077
0.0115
0.0213
0.0104
0.0201
0.0332
0.0195
0.0310
0.0452
0.0335
600
Bromine
CCl4
Chlorine
0.0038
0.0053
0.0071
0.0048
0.0067
0.0089
0.0067
0.0099
0.0124
0.0126
0.0156
0.0190
Deuterium
Propylene
R 22
SO2
0.122
0.0114
0.0080
0.0078
0.141
0.0168
0.0109
0.0096
0.176
0.0226
0.0170
0.0143
0.0430
0.0230
0.0200
0.0580
0.0290
0.0256
250
0.0561
0.0524
0.111
0.073
0.109
Prandtl number, dimensionless
Temperature, K
300
400
500
600
0.077
0.104
0.076
0.101
0.135
0.101
0.128
0.164
0.127
0.156
0.154
0.101
0.136
0.203
0.131
0.178
0.260
0.162
0.218
0.291
0.191
0.259
0.126
0.087
0.129
0.129
0.153
0.115
0.168
0.175
0.178
0.141
0.201
0.217
0.256
250
300
400
0.860
0.820
0.797
0.771
0.762
0.760
500
∗An approximate interpolation scheme is to plot the logarithm of the viscosity or the thermal conductivity versus the logarithm of the absolute temperature. At 250 K the viscosity of gaseous argon is to be read as 1.95 × 10–5 Pa ⋅ s = 0.0000195 N ⋅ s/m2.
TABLE 2-144
Prandtl number of Air*
Pressure, bar
Temperature, K
1
5
10
20
30
40
50
60
70
80
90
100
80
90
100
120
140
mix
0.796
0.786
0.773
0.763
2.31
1.76
0.872
0.813
0.782
2.32
1.77
1.54
0.89
0.82
2.35
1.78
1.53
1.44
0.94
2.37
1.79
1.53
1.65
1.20
2.40
1.81
1.53
1.54
1.59
2.42
1.82
1.53
1.48
2.14
2.45
1.83
1.53
1.43
2.43
2.48
1.85
1.53
1.40
2.07
2.51
1.87
1.54
1.38
1.78
2.54
1.89
1.54
1.36
1.62
2.57
1.91
1.55
1.34
1.52
160
180
200
240
280
0.754
0.745
0.738
0.724
0.710
0.765
0.754
0.743
0.727
0.711
0.78
0.763
0.749
0.729
0.713
0.84
0.792
0.766
0.737
0.717
0.92
0.830
0.788
0.746
0.721
1.03
0.876
0.812
0.756
0.726
1.13
0.932
0.841
0.767
0.731
1.25
1.00
0.87
0.78
0.737
1.37
1.07
0.90
0.80
0.742
1.65
1.14
0.95
0.81
0.75
1.83
1.20
0.97
0.81
0.75
1.72
1.25
1.00
0.82
0.76
300
350
400
450
500
0.705
0.699
0.694
0.691
0.689
0.707
0.699
0.694
0.691
0.689
0.708
0.699
0.694
0.691
0.689
0.712
0.701
0.695
0.691
0.689
0.715
0.703
0.696
0.692
0.689
0.717
0.705
0.697
0.692
0.690
0.721
0.707
0.698
0.693
0.690
0.725
0.709
0.699
0.693
0.690
0.728
0.711
0.700
0.694
0.690
0.732
0.712
0.701
0.695
0.691
0.737
0.714
0.703
0.695
0.691
0.742
0.716
0.704
0.696
0.691
600
700
800
900
1000
0.690
0.696
0.705
0.709
0.711
0.690
0.696
0.704
0.709
0.711
0.690
0.695
0.704
0.708
0.711
0.689
0.695
0.704
0.708
0.711
0.689
0.695
0.704
0.708
0.711
0.689
0.695
0.703
0.708
0.710
0.689
0.695
0.703
0.708
0.710
0.689
0.695
0.703
0.708
0.710
0.689
0.695
0.703
0.708
0.710
0.690
0.695
0.702
0.708
0.709
0.690
0.695
0.702
0.708
0.709
0.690
0.695
0.702
0.708
0.709
∗Compiled by P. E. Liley from tables of specific heat at constant pressure, thermal conductivity, and viscosity given in SI units for integral kelvin temperatures and
pressures in bars by Vasserman. Thermophysical Properties of Air and Its Components and Thermophysical Properties of Liquid Air and Its Components. Nauka, Moscow,
and in translated form by the National Bureau of Standards, Washington. The number of significant figures given above reflects the similar numbers appearing for the
constituent properties in the source references. While reasonable agreement occurs for atmospheric pressure with some other works, the fragmentary data available
for the saturated, etc., states show large deviations.
TABLE 2-145
Eqn
Cmpd.
no.
102
102
100
100
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
100
102
102
102
1
2
3
3
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
45
46
47
Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)]
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic acid
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyric acid
Butyronitrile
Carbon dioxide
Formula
C2H4O
C2H5NO
C2H4O2
C2H4O2
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H8O2
C4H7N
CO2
CAS
75-07-0
60-35-5
64-19-7
64-19-7
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
107-92-6
109-74-0
124-38-9
Mol. wt.
44.05256
59.0672
60.052
60.052
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
88.1051
69.1051
44.0095
C1
1.0943E-07
0.00013195
2.4148
1.0879
3.3901E-06
3.1289E-06
−26.8
8.3653E-07
0.000075782
0.024098
0.0009265
−0.000861
0.00031417
9.6608E-06
0.00059858
0.000633
0.025389
0.00001652
0.00047951
0.0001163
1.3917E-06
0.0001235
0.00023476
0.00096451
0.00015525
2.8646E-06
1.0404E-06
0.00027085
0.00099879
5.7816E-07
0.000088221
−20890
0.051094
0.00014035
−918.39
0.0011484
4.5894E-06
0.000096809
0.000067737
0.000078576
5.86E-09
0.1807
0.00097826
0.9719
0.000037269
9.9652E-07
0.7873
9.2069E-08
1.3751E-06
3.69
C2
2.0279
0.97
−0.020867
−0.0038977
1.9588
1.4618
0.9098
1.6481
1.0327
0.3285
0.7035
0.77281
0.7786
1.3799
0.7527
0.6221
0.28547
1.3117
0.7818
0.9705
1.5389
0.9495
0.8639
0.69225
0.9446
1.4098
1.4685
0.7932
0.71894
1.6666
1.0273
0.9593
0.45253
1.0032
−0.21199
0.87647
1.4484
1.1153
1.0709
1.0565
2.376
0.0082225
0.78643
−0.111
1.1427
1.6558
−0.0036161
2.0312
1.5786
−0.3838
C3
728.3
0.000059409
3.6227E-06
36053
C4
−5.4718E-08
14,086,000
126,500,000
−36.227
1325.3
627.58
−2555.2
−0.7116
31,432
577,830
112,460
354.04
70
1018.3
491
463.4
740
241,830
778.7
187.8
519.99
715.78
−391.35
2121.7
1,228,600
189,410
193,840
278,930
156,820
278.33
2358.4
165,880
75.316
−93,820,000,000
5455.5
711.66
334420
3253.7
99,063
1,979,800
−2,884,200,000
781.82
−65.881
14.63
−401.32
−129.42
1531.5
1167.2
−43.844
129,390
105,920
69,280
1,691,500
67,115
3,163,200
79,421
5.6641E-06
−2.8451E-09
964
1,860,000
Tmin, K
294.15
494.3
391.05
458.15
541.5
412.7
329.44
339.09
189.35
325.84
414.15
298.15
70
200
426.73
90
563.15
339.15
442.29
522.4
464.15
579.24
478.6
458.15
472.03
373.15
300
429.24
311.49
273
284
268.74
272.65
469.57
481.38
370.7
372.9
266.91
273.15
274.03
273
456.46
371.61
358.13
281.22
347.94
436.42
706.95
390.74
194.67
Thermal
cond. at Tmin
0.01110
0.02189
0.06749
0.06258
0.03925
0.02084
0.01363
0.01238
0.01011
0.01534
0.02027
0.00929
0.00603
0.01446
0.01809
0.00585
0.02317
0.01407
0.01861
0.02090
0.01767
0.02213
0.02167
0.01936
0.02071
0.01123
0.00452
0.01302
0.00723
0.00664
0.01172
0.01281
0.01357
0.02672
0.02110
0.02097
0.02435
0.01252
0.01105
0.01200
0.00783
0.02151
0.01832
0.01749
0.01268
0.01610
0.05147
0.05647
0.01698
0.00887
Tmax, K
1000
1000
458.15
541.5
1000
1000
1000
1000
1000
1000
1000
1000
2000
900
1000
3273.1
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
500
1000
1000
1000
1000
1000
1000
1000
1000
712.94
1000
1000
1273.15
1257
800
1000
1000
1000
1000
1000
706.95
1000
1000
1500
Thermal
cond. at Tmax
0.13269
0.06206
0.06259
0.03955
0.11105
0.07600
0.11362
0.07358
0.09545
0.08028
0.06867
0.11525
0.11675
0.11523
0.06796
0.09525
0.05618
0.09542
0.06427
0.05452
0.05758
0.04899
0.06636
0.06398
0.06171
0.06347
0.00956
0.04495
0.04267
0.05779
0.09071
0.16809
0.13799
0.08383
0.08332
0.06536
0.10161
0.12049
0.13926
0.13704
0.07634
0.07465
0.08610
0.08470
0.09644
0.09245
0.05647
0.11421
0.07484
0.09025
2-289
(Continued)
2-290
TABLE 2-145
Eqn
Cmpd.
no.
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued )
Name
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
Formula
CS2
CO
CCl4
CF4
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
CAS
75-15-0
630-08-0
56-23-5
75-73-0
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
Mol. wt.
76.1407
28.0101
153.8227
88.0043
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
C1
0.0003467
0.00059882
0.00016599
0.000092004
0.0009993
0.0004783
4.91778E-07
0.00043073
−3263.77
0.01652
0.00009154
0.00019307
0.00018648
0.00019063
1.6743E-07
0.000014433
−449910
0.000000859
0.0032207
−1095.5
0.0000901
9.5461E-06
0.0010949
−91.383
0.0000813
1.9749E-06
−668.4
3.3251E-09
−0.3072
0.000027232
0.00012058
0.000016707
0.00028527
0.00021231
0.00015878
0.00021302
0.0032694
−1067.8
−1420
−1520.8
0.0001315
0.00021054
0.0014796
0.000057603
0.000062435
−11,633
0.00001706
−0.0044894
0.0018097
0.000059249
C2
0.7345
0.6863
0.94375
1.0164
0.5472
0.8994
1.70639
0.83878
0.0675
0.44154
1.0681
0.9248
0.9302
0.9282
1.8369
1.2104
0.27364
1.7709
0.5991
−0.023408
1.0897
1.4641
0.71644
0.89718
1.0674
1.5349
0.9323
2.4876
0.489
1.257
1.0111
1.2128
0.9874
0.8052
0.8636
0.8719
0.58633
0.754
0.7614
0.754
1.0113
0.9574
0.69531
1.1148
1.103
0.4621
1.248
0.6155
0.67406
1.0713
C3
479
57.13
1449.6
270.83
458.6
1845.5
−232.008
1874.5
−46,803,200
2444.42
746.6
710
709.37
716.91
−449.46
−10,001,000,000
243
608.69
498, 780
655
632.62
175.55
−283,310,000
697.6
−4,071,000,000
−124.9
−67,500
751.7
740
−206.08
−200.51
649.51
659.5
1620
1259.9
−3,036,100,000
−4,504,000,000
−433,2800,000
1023.8
1414
2657.4
849.98
913.43
−3,793,900,000
−112.8
−3266.3
1179.7
101.84
C4
501.92
163,000
46603.4
−25,000,700,000
793,392
112,760
−9.8654E+12
509,290
−7,835,500,000
346,040
−29,400,000
153,850
21,807
300,890
77,960
174,850
45,974
Tmin, K
273.15
70
349.79
145.1
200
400
285.45
334.33
248.95
319.67
308.85
475.43
464.15
475.13
380
251.9
285.66
325
434
428.58
356.12
273
317.38
240.37
431.95
481.65
447.3
543.15
504
443.75
512.35
447.15
233.15
381.15
404.51
370.1
323.15
446.23
453.57
447.21
330.45
356.59
312.9
361.25
369.52
541.54
273.15
200
365.25
248.95
Thermal
cond. at Tmin
0.00776
0.00576
0.00812
0.00505
0.00551
0.01579
0.01004
0.00854
0.00801
0.01285
0.01222
0.02316
0.02230
0.02319
0.01534
0.01164
0.01356
0.01380
0.02399
0.02291
0.01914
0.01061
0.01360
0.01061
0.02022
0.02590
0.02173
0.02746
0.02590
0.02149
0.02709
0.02092
0.11474
0.00940
0.01077
0.00687
0.01244
0.01561
0.01507
0.01564
0.01132
0.01177
0.00847
0.01220
0.01222
0.03044
0.01148
0.00764
0.01743
0.01016
Tmax, K
1000
1500
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1500
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
600
1000
1000
Thermal
cond. at Tmax
0.03745
0.08724
0.04595
0.08108
0.03002
0.07935
0.07943
0.04920
0.07246
0.08232
0.08389
0.06716
0.06736
0.06762
0.08181
0.06174
0.14994
0.14198
0.09535
0.12704
0.10116
0.14429
0.10148
0.15854
0.07629
0.07948
0.10286
0.11029
0.09389
0.09175
0.07482
0.07667
0.44547
0.03351
0.03729
0.03356
0.07330
0.06430
0.06066
0.06417
0.07025
0.06498
0.04931
0.06881
0.06647
0.07463
0.09804
0.05181
0.08089
0.08447
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
1,2-Difluoroethane
Difluoromethane
Diisopropyl amine
Diisopropyl ether
Diisopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
66.04997
52.02339
101.19
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
2.4194E-06
0.000013015
0.00051305
0.00019879
−8.5357
0.00046265
3.7962E-06
0.00021761
1.6085
0.000034741
0.008856
0.013298
0.012144
0.00022578
0.059975
0.014449
0.000022421
0.00012822
0.0011808
0.00023614
0.00064761
0.00402358
6.4032E-07
0.00014629
0.0001123
0.000005719
−375.32
0.000073869
−0.010109
1.3575E-07
0.3935
0.000017537
0.00002012
0.00017727
829.29
0.0000748
0.0043244
8.6806E-06
0.1655
−8145800
0.00077079
−0.0003788
508
2.5804E-06
0.0052833
0.00021652
−152400
0.0015251
1.0507E-07
5.8174E-08
2.7142E-06
0.00012144
0.000053432
1.4456
1.1897
0.8076
0.9423
−0.0056423
0.81968
1.4462
0.9187
−0.1103
1.1646
0.4215
0.3692
0.3854
0.892
0.2667
0.3612
1.2137
0.9324
0.742
0.9204
0.7716
0.57548
1.7194
0.9377
0.9958
1.4699
1.0708
1.1689
0.6475
1.9681
0.0131
1.3144
1.1513
0.9428
1.0156
1.1103
0.5429
1.4559
0.1798
−0.30502
0.7713
1.115
0.9023
1.4669
0.52982
0.94192
−0.049106
0.70243
1.9854
2.0116
1.4281
0.93831
1.1576
360.19
306.8
1882.1
539.34
154,510
106,230
−65,622,000
104,530
217
2160.3
−99.956
−50.645
0.1027
52.191
697
1018.6
595.22
−146.91
752.5
1131
638
1013.3
3598.32
132,070
2,989,300
130,820
764,580
852,540
803,590
745.89
183.2
579.4
−8,783,600,000
500.73
−7332
1380
560.65
−89.583
712.4
8,955,300,000
686
333.67
299.72
3827.9
1,832,500,000
446.16
−5641
2,170,000,000
1,098,800
728,130
131,830
6400
82,563
98,000
−268,000
1,710,000
125,410
570,470
−29,403
1,600,000
−1.1842E+13
197,930
1415.7
632.16
80,955,000
1347.5
−9.3122E+11
35,085
−372.68
57,690
760.75
378,180
303.65
221.5
357.05
328.05
397.55
337.45
366.15
300.13
280.03
331.13
392.7
402.94
396.58
382.9
248.31
425.15
362.93
556.85
253.55
310.48
462.15
559.2
337.85
531.46
279.65
489.47
616.93
184.55
293.15
273.15
289.73
409.35
486.55
466.95
394.65
404.95
376.62
170
390.41
470.45
329
273.15
327.46
500.66
417.15
326.15
386.55
308.15
400
273.15
371.05
70
357.88
0.00938
0.00803
0.01836
0.01598
0.02015
0.01554
0.01936
0.01288
0.01845
0.01581
0.01884
0.01948
0.01952
0.01613
0.01139
0.02001
0.01797
0.01981
0.01291
0.01520
0.02059
0.02063
0.01427
0.02188
0.01055
0.02354
0.02563
0.00886
0.01475
0.00847
0.01622
0.02007
0.01855
0.02306
0.01583
0.02180
0.01832
0.00879
0.02272
0.02513
0.01610
0.01004
0.01426
0.02353
0.01967
0.01717
0.01889
0.01487
0.01540
0.01133
0.01268
0.00654
0.01546
993.65
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1500
1000
1000
1000
1000
1000
1000
1000
768.01
1000
1000
1000
1000
1000
1000
990.21
1000
1000
1000
1000
1000
1000
1000
590.92
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
550
1000
700
600
0.05206
0.04826
0.08967
0.09444
0.13085
0.08099
0.08279
0.09199
0.12209
0.10506
0.09500
0.09196
0.09376
0.06310
0.19458
0.07539
0.09962
0.04587
0.09296
0.08319
0.06379
0.04661
0.05855
0.05449
0.08515
0.09301
0.06968
0.15807
0.13417
0.10681
0.10532
0.09859
0.05524
0.06973
0.10314
0.09505
0.09659
0.06613
0.08915
0.09896
0.09659
0.18063
0.11921
0.06492
0.07348
0.08882
0.12768
0.08195
0.09499
0.03690
0.05223
0.05675
0.03874
2-291
(Continued)
2-292
TABLE 2-145
Eqn
Cmpd.
no.
102
102
102
102
100
100
102
102
102
102
102
102
100
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
151
152
153
154
155
155
155
156
157
158
159
160
161
161
162
163
164
165
166
167
168
169
170
171
172
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued )
Name
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Formic acid
Formic acid
Furan
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Formula
C2H5F
CH3F
CH2O
CH3NO
CH2O2
CH2O2
CH2O2
C4H4O
He
C17H36
C7H14O
C7H16
C7H14O2
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
CAS
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
64-18-6
64-18-6
110-00-9
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
Mol. wt.
48.0595
34.03292
30.02598
45.04062
46.0257
46.0257
46.0257
68.07396
4.0026
240.46774
114.18546
100.20194
130.185
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
C1
6.3522E-06
0.000048998
5.2201E-06
0.00025893
−0.8303
1.8897
0.00072291
−644950
0.00226
−114.41
1.4326E-06
−0.070028
−0.088162
4.449E-08
−0.061993
0.00018818
1348.6
2049.3
0.00002133
0.0083145
0.000060732
0.000004438
1.5427E-06
−650.5
12,049,00,000
6.1268E-08
−4935500
0.00018361
−1.2158
−0.33262
0.000064256
6.9682E-06
0.074318
0.000058116
0.000011631
0.00043196
0.002653
0.00049725
0.001865
4.6496E-06
0.000034629
1.381E-07
0.000214
0.00028183
4.8284E-06
0.00019847
8.3983E-06
5.7992E-07
0.034177
−25343
C2
1.346
1.0175
1.417
0.9083
0.0046141
−0.006901
1.8898
0.2862
0.7305
1.0566
1.5896
0.38068
0.00065022
2.133
0.2792
0.96338
1.0313
1.0323
1.2885
0.51862
1.0586
1.4949
1.5824
0.8053
−4.0059
2.0874
−0.1653
0.97199
0.026637
0.12054
1.1355
1.347
0.30035
1.0724
1.2753
0.86603
0.7452
0.63088
0.49755
1.3669
1.1224
1.8379
0.9248
0.92094
1.3599
0.9284
1.4268
1.7862
0.3312
−0.1934
C3
723.6
−5.7466E-06
6.4407E-06
4,877,600
−16,794,000,000
−18.63
−2,211,400,000
C4
−1,889,300,000
−1.7372E+13
440
−7049.9
−1.2803E-06
−2,400,500
9.1349E-10
−3336
696.02
14,832,000,000
22,983,000,000
487.8
2253
−102.79
682
−1,642,000
−1,412,100,000
−1668.8
1,563,100,000
677.05
−1711.6
−2472.6
445.15
−214.35
4470.1
−77.165
−202.84
641.48
12
331.62
358
−210.76
18.744
−352.09
698
619.17
532,590
143,140
722,550
−1.5752E+13
−13,176,000
−5,493,400
64,810
110,480
1,775,800
123,900
122,990
58,295
46,041
678.69
−49.654
2070
11,164,000
1,195,600
−67,259,000,000
Tmin, K
235.45
194.82
253.85
493
420
470
537.9
304.5
30
575.3
426.15
339.15
496.15
643.11
449.45
432.9
420.55
424.18
366.79
450.09
372.93
560.01
401.15
339.09
478.85
641.42
429.9
412.4
273
273
336.63
354.35
425.81
344.48
357.67
386.65
22
206.45
190
273.15
350
212.8
427.85
304.92
580
434.15
111.63
273
478.15
330.09
Thermal
cond. at Tmin
0.00990
0.01047
0.01333
0.02930
0.09392
0.06898
0.04120
0.01367
0.03124
0.02454
0.02168
0.01583
0.03085
0.04349
0.02345
0.02501
0.01943
0.01951
0.01845
0.02289
0.01827
0.02568
0.02031
0.01704
0.03317
0.04435
0.02220
0.02421
0.00775
0.00800
0.01644
0.01485
0.02151
0.01679
0.01506
0.02828
0.01718
0.00551
0.00880
0.00985
0.02356
0.00724
0.02206
0.01804
0.02766
0.02176
0.01263
0.01303
0.02498
0.01415
Tmax, K
1000
1000
1000
1000
470
537.9
1000
1000
2000
1000
1000
1000
643.11
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
641.42
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1600
600
700
673.15
450
600
1000
1000
1000
1000
600
684.37
1000
1000
Thermal
cond. at Tmax
0.06933
0.05529
0.09304
0.07973
0.06890
0.04118
0.11296
0.13631
0.58820
0.07649
0.08413
0.11493
0.04346
0.11150
0.10722
0.08616
0.11287
0.11145
0.10518
0.07899
0.08751
0.08055
0.08620
0.12003
0.04435
0.11206
0.11104
0.09022
0.10523
0.10980
0.10850
0.08546
0.08167
0.09155
0.08466
0.10430
0.64299
0.01812
0.03213
0.04185
0.03160
0.03258
0.07497
0.10081
0.05801
0.07210
0.08425
0.06726
0.07895
0.11878
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
0.00026544
0.4734
−55.13
0.000023963
0.0002509
0.0008968
0.0001799
2054.5
0.00019098
0.00021736
0.00015498
0.000023993
0.079414
0.000065855
1333.1
0.00037057
0.0000719
0.00011359
0.069565
0.075448
0.0024385
0.0040082
0.0019845
0.00041077
0.00024036
−4202700
0.0034805
−800040
0.00020053
−2483300
0.0026136
2.1191
−5935000
0.0071536
0.00002653
0.00072502
0.0001813
0.000061119
0.93312
0.089772
1.1776E-06
−488.1
−200.9
0.011136
0.0023574
12.248
0.21276
0.0002084
0.00032359
0.000091828
0.0011385
0.0011282
0.00033143
0.8921
−0.1111
1.065
1.1308
0.899
0.7742
0.9457
0.90109
0.9341
0.9171
0.9364
1.1976
0.23442
1.072
0.9962
0.81367
1.1274
1.0311
0.1633
0.155
0.61774
0.54462
0.6393
0.75688
0.93177
−0.1524
0.61906
−0.2285
0.95381
−0.046517
0.62
−0.19015
−0.089497
0.53907
1.1631
0.7395
0.92912
1.0861
−0.1172
0.18501
1.6618
0.8877
−0.1321
0.4831
0.67434
−0.5611
−0.022299
0.93034
0.8892
1.0345
0.6646
0.6895
0.7722
222.19
533.57
−448,200,000
−67.272
253.4
456
704.6
8,760,500,000
84.07
112.3
15.366
58.59
2671.9
−36.369
12,317,000,000
609.17
667
709.27
208.7
218.44
223.01
242.12
227.11
591.5
588.14
2,084,600,000
1810.8
248,100,000
644.42
1,313,100,000
1631.7
1453.4
3,098,800,000
2700.7
29.996
365.68
793.45
−59.592
1154.3
639.23
−1,448,500,000
104,000
21,70.3
1804.1
−1067
−194.68
364.832
623.22
731.78
8.7
679.11
16.323
79,869
1,649,600
125,720
149,500
230,640
155,720
177,690
137,400
35,667
1,366,100
106,430
1,209,500
1,252,500
477,570
559,040
434,120
−1.4577E+13
166,290
−1.5034E+12
−1.5798E+13
126,720
3,575,500
−2.7994E+13
241,730
32,519
204,360
141,260
2,961,700
1,114,700
−846,000,000
281,220
155,660
2,715,200
1,708,700
73,041
238,800
373.72
249.94
353.35
266.82
472.65
314
273.15
450.15
404.15
304.3
311.71
305.4
273.15
396.58
302.15
375.9
281.85
374.08
441.15
438.15
440.15
344.96
348.64
338.05
314.7
273
352.79
339.8
300
331.7
389.65
312
303.92
367.55
171.64
273.15
373.45
518.15
333.41
372
261.43
333.82
266.25
350
312.2
368.69
216.25
438.65
328.2
278.65
491.14
30
387.22
63.15
0.01154
0.01569
0.01259
0.01784
0.01326
0.01198
0.02266
0.02116
0.01348
0.01320
0.01304
0.01173
0.01966
0.01468
0.01495
0.01155
0.02056
0.02322
0.02415
0.02435
0.01592
0.01544
0.01501
0.01109
0.01419
0.01546
0.01653
0.01369
0.01729
0.01869
0.01221
0.01606
0.01760
0.00459
0.01171
0.01680
0.02383
0.01606
0.01828
0.01273
0.01839
0.01276
0.01402
0.01648
0.01802
0.01108
0.01969
0.01638
0.01493
0.02243
0.00846
0.01580
0.00602
1000
1000
650
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
766.87
1000
1000
1000
1000
1000
1000
1000
1000
1000
3273.1
1000
2000
0.09675
0.06904
0.07917
0.05588
0.08902
0.11176
0.07253
0.11843
0.09771
0.09504
0.08664
0.08586
0.07960
0.10120
0.10543
0.06357
0.10399
0.08238
0.08888
0.08908
0.10227
0.09578
0.09888
0.04813
0.09447
0.11740
0.08415
0.13148
0.08863
0.12433
0.06864
0.09451
0.12847
0.07516
0.07704
0.07637
0.06195
0.10242
0.08117
0.11701
0.07325
0.15513
0.10886
0.09079
0.08398
0.09590
0.07255
0.08958
0.09273
0.06730
0.24616
0.06887
0.11638
2-293
(Continued)
2-294
TABLE 2-145
Eqn
Cmpd.
no.
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
100
102
102
102
102
102
102
102
102
102
102
102
102
102
102
100
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued )
Name
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Octadecane
Octanal
Octane
Octanoic acid
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Formula
F3N
CH3NO2
N2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
C18H38
C8H16O
C8H18
C8H16O2
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
CAS
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
593-45-3
124-13-0
111-65-9
124-07-2
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
Mol. wt.
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
254.49432
128.212
114.22852
144.211
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
C1
2.1443
0.00003135
0.001096
0.0004096
0.000049571
0.00000175
−0.065771
46.08
−30.715
0.00016806
0.000021269
0.047041
0.000016681
−291.08
0.00000166
−8758
−0.20973
3.2003E-08
−0.0030238
0.00016915
−0.0020184
8.1833E-08
0.0000133
−3965.5
0.000060734
2.7969E-06
0.00044994
0.0043147
4.7796E-06
0.00000113
−684.4
0.44736
7.5284E-08
2896
0.00019575
−0.01719
22.775
2.7081E-06
0.00022307
0.00011261
0.000052415
0.00025623
0.00010167
0.038846
0.00016675
0.0000593
0.000061629
−1.12
−613.84
7.3907E-07
C4
Tmin, K
1860.3
−91.6
540
45.6
3332.3
1,216,700
128,000
−3482.3
−2460.2
8107
713.67
662.21
2460.6
−199.41
−6,019,900,000
−1,580,300
1,867,000
−156,830,000
144.09
374.35
182.3
121.38
603.05
465.52
423.97
528.75
485.2
471.7
420.02
492.95
423.85
589.86
445.15
339
512.85
637.35
468.35
452.9
446.15
440.65
394.41
472.19
399.35
516
80
161.85
543.84
375.15
273.15
458.95
706.95
410.9
392.2
273
273
303.22
385.15
399.79
313.33
329.27
610.03
454.99
439.43
557.65
238.65
231.11
370.35
355.3
C2
−0.30545
1.1119
0.667
0.7509
1.2652
1.5534
0.27198
−1.0037
−0.1075
0.96876
1.2943
0.29733
1.218
1.0615
1.5669
0.8448
0.0012201
2.18
0.8745
0.97238
1.0027
2.0418
1.3554
0.5213
1.0516
1.3164
0.7456
0.47999
1.4851
1.6323
0.764
−0.0019667
2.0589
0.8985
0.9692
0.4832
1.0019
1.5493
0.93358
1.034
1.0948
1.0073
0.988
0.2392
0.91777
1.046
1.0731
0.10972
0.7927
1.7419
C3
−27,121,000,000
−2.1843E-06
1,367,200
144,580
1.3942E-09
−13352
698.55
−20406
504.59
−1,851,900,000
−124.91
158,300
56.699
700.09
643.13
−1,055,000,000
2.9973E-06
12,735,000,000
664.04
−3798
191,000,000
41.075
794.16
693.05
−51.09
1423.7
797
985.81
730.1
765.5
1.8579
−9834.6
−1,157,400,000
−1.4141E-09
−1,235,000
8301.3
101,160
937,170
70,128
−7,535,800
Thermal
cond. at Tmin
0.00648
0.01365
0.00891
0.01094
0.02502
0.02440
0.02130
0.02815
0.02436
0.02603
0.02051
0.02559
0.01981
0.02491
0.02345
0.01503
0.02955
0.04157
0.02380
0.02545
0.02046
0.02050
0.01926
0.02505
0.01967
0.01041
0.00691
0.00931
0.02529
0.01799
0.01288
0.03938
0.05537
0.02084
0.02372
0.00877
0.00898
0.01546
0.01890
0.02019
0.01517
0.01653
0.02490
0.02183
0.01669
0.01864
0.00980
0.01114
0.02135
0.02049
Tmax, K
1000
1000
1000
750
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
637.35
1000
1000
1000
1000
1000
1000
1000
1000
1000
2000
1000
1000
1000
1000
706.95
1000
990.95
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
720.25
1000
Thermal
cond. at Tmax
0.06377
0.06553
0.07133
0.05567
0.07147
0.08003
0.10597
0.11042
0.09895
0.07904
0.09772
0.07598
0.07956
0.07395
0.08333
0.11053
0.04157
0.11097
0.10288
0.08229
0.10597
0.10923
0.10295
0.07845
0.08394
0.02488
0.12655
0.06990
0.08299
0.08912
0.12707
0.05536
0.11308
0.11087
0.09509
0.12002
0.12082
0.11472
0.07858
0.08412
0.09608
0.11119
0.05208
0.06936
0.05461
0.04615
0.09526
0.14599
0.07034
0.12428
102
102
100
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
102
298
299
300
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
C9H14
C3H6O
C3H6O2
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O2S
F6S
O3S
C8H6O4
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
13511-13-2
123-38-6
79-09-4
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
122.20746
58.07914
74.0785
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
0.00010242
9.0711E-07
1.0014
1.8905E-07
1.1671E-06
1325.3
0.2833
0.16992
0.0000449
740.1
0.00018367
0.0087425
0.0001666
−5678600
0.0000955
0.010048
5.5263E-06
10.527
0.00048883
1.0702
3.4082E-06
0.000078652
−163.62
9.5521E-06
0.00007754
0.00085604
0.000015235
0.00013384
0.00002392
0.0000952
5.3701E-06
0.000106
0.00027648
0.000098408
0.00008498
0.00001758
0.000020248
0.00020544
0.00018189
0.038012
2498.8
−3279500
0.000054197
−229.41
3510.8
6.2041E-06
3.0593E-09
4.9707E-06
9.9305E-08
1.0486
1.6709
−0.0045954
1.93
1.6033
1
0.055046
0.021288
1.2018
0.9732
0.9627
0.51733
0.9765
−0.045252
0.928
0.4033
1.344
−0.7732
0.6518
−0.2348
1.3647
0.95174
0.9193
1.4561
1.0778
0.7297
1.2816
0.98115
1.2694
1.0423
1.4751
1.0161
0.901
1.0452
1.061
1.3114
1.2284
0.87137
0.88744
0.68615
0.95209
−0.12941
1.0632
0.59582
0.225
1.3973
2.4182
1.3787
1.9229
701.56
7.1517E-06
12,235,000,000
1325.9
−54.484
421
5,646,000,000
646.01
2358.1
706
2,615,700,000
63.6
553.74
−3.5878E-09
1,817,600
1,624,800
334,590
−3.5415E+13
685,570
−1333
−117.08
2010.4
1,506,400
78,863
1,277,000
−282.82
−1,087,600,000
662.22
729
531.99
−111.88
645.95
537
1243.3
599.09
91
167.68
720.49
708
392.9
−174.72
807.3
803.39
34,663
20,167,000,000
1,710,400,000
−70.589
−169,430,000
401,720,000
289,490
−569.28
−225.64
−469.93
213,840
124,120
132,900
132,200
147,800
8,721,900
−1.2727E+13
90,617
121,060
66,786
113,460
431.65
322.15
414.32
616.15
370.25
374.65
321
432.39
225.45
353.97
325.71
340.87
460.75
454
333.55
418.31
591
250
273.15
317.9
795.28
373.15
526.73
339.12
480.77
394.27
379.44
357.31
383.78
387
508.62
273.15
273.15
449.27
442.53
355.15
387.91
629.6
625
469.08
520.3
345.65
278.25
259.25
363.85
273.16
320
320
320
0.02262
0.01407
0.06993
0.04578
0.01532
0.01520
0.01709
0.02022
0.01054
0.01403
0.01616
0.01654
0.02624
0.02593
0.01761
0.01837
0.02934
0.00745
0.01163
0.01386
0.03097
0.00950
0.02517
0.01564
0.02395
0.01801
0.01964
0.01525
0.01901
0.01125
0.02422
0.01018
0.01280
0.02238
0.02098
0.01846
0.02001
0.02474
0.02410
0.02259
0.02486
0.01515
0.01123
0.00963
0.01198
0.01574
0.00867
0.01492
0.01019
1000
1000
616.15
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
702.45
1000
1000
900
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1073.15
1000
1000
1000
0.08421
0.09340
0.04578
0.11657
0.07534
0.10832
0.10000
0.07658
0.12737
0.10893
0.08624
0.08439
0.08302
0.12665
0.03837
0.07276
0.05949
0.03969
0.04587
0.04930
0.04233
0.05598
0.08615
0.13419
0.07676
0.07579
0.10528
0.07139
0.10007
0.05684
0.08942
0.09680
0.10734
0.07816
0.07583
0.10847
0.10079
0.04675
0.04635
0.09798
0.08899
0.12177
0.08222
0.08300
0.04135
0.10652
0.09965
0.08084
0.09060
2-295
Except for acetic acid, butyric acid, formic acid, heptanoic acid, octanoic acid, pentanoic acid, propionic acid, the vapor thermal conductivity is calculated by Eqn 102: k = C1T C2/(1 + C3/T + C4/T 2) where k is the thermal conductivity
in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure, whichever is lower.
Eqn 100, used for the limited temperature ranges as noted for the associating compounds above, k = C1 + C2T + C3T 2 + C4T 3
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation
of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
2-296
PHYSICAL AnD CHEMICAL DATA
TABLE 2-146
Thermophysical Properties of Miscellaneous Saturated Liquids
Temperature, °C
Substance
Property
Acetaldehyde ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
Acetic acid
−50
−40
−30
−20
−10
863
2.05
460
0.211
4.47
852
2.08
404
0.206
4.08
840
2.11
358
0.200
3.78
828
2.14
321
0.195
3.52
816
2.17
290
0.189
3.33
0
804
2.20
263
0.184
3.14
10
794
2.24
241
0.182
2.97
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
20
30
40
50
60
70
80
90
100
972
960
783
2.28
222
0.180
2.81
1049
2.031
1210
0.173
14.2
1039
1028
1018
1006
995
984
1102
0.170
1010
0.168
795
0.167
600
0.165
0.163
0.161
Aniline
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
1039
2.024
10200
0.186
111
1030
2.047
6500
0.184
72
1022
2.071
4400
0.182
50
1013
2.093
3160
0.180
36.7
1005
2.113
2370
0.177
28.3
996
2.132
1850
0.174
22.7
987
2.17
1510
0.171
19.2
978
2.20
1270
0.169
16.5
969
2.23
1090
0.168
14.5
960
2.27
935
0.167
12.7
951
2.32
825
0.167
11.5
Butanol
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
845
1.947
34700
0.175
3860
841
1.996
22400
0.174
2570
837
2.046
14700
0.173
1740
833
2.100
10300
0.172
1260
829
2.153
7400
0.171
930
825
2.202
5190
0.170
670
817
2.262
3870
0.168
120
810
2.345
2950
0.167
41
803
2.437
2300
0.166
33.8
797
2.524
1780
0.165
27.2
791
2.621
1410
0.164
22.5
784
776
768
760
753
1140
0.163
930
0.162
760
630
535
0.161 0.160 0.159
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
1362
0.988
630
0.194
3.21
1348
0.989
580
0.190
3.02
1334
0.990
535
0.186
2.85
1320
0.991
496
0.182
2.70
1306
0.993
463
0.178
2.58
1292
0.996
435
0.174
2.49
1278
1.004
405
0.170
2.39
1263
1.017
375
0.166
2.30
350
0.161
330
0.158
0.156
0.154
0.152
0.150
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
789
2.068
1175
0.122
19.9
779
2.081
980
0.120
17.0
769
2.094
820
0.119
14.4
759
2.106
710
0.118
12.7
750
2.119
605
0.117
11.0
740
731
721
540
0.116
0.114
0.112
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
2.01
6400
0.188
68.4
2.04
4790
0.186
52.5
2.08
3650
0.184
41.3
2.13
2825
0.181
33.2
2.19
2220
0.179
27.2
806
2.27
1770
0.177
22.7
798
2.35
1470
0.175
19.7
789
2.43
1200
0.173
16.9
781
2.52
1000
0.171
14.7
776
2.62
835
0.168
13.0
763
2.73
700
0.165
11.6
754
2.83
590
0.162
10.3
745
2.93
500
0.159
9.2
735
3.03
435
0.156
8.4
725
3.19
370
0.153
7.7
716
3.30
314
0.151
6.9
947
935
924
912
888
876
863
851
838
825
811
797
580
510
901
2.01
455
0.145
6.3
400
0.142
370
0.139
345
0.136
310
0.133
280
0.130
250
230
220
0.127 0.123 0.119
Carbon
disulfide
Cyclohexane
Ethanol
Ethyl
acetate
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s) 1090
k (W/m⋅K)
Pr
Ethylamine
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
761
2.95
580
0.204
8.39
750
2.97
500
0.201
7.39
739
2.98
435
0.199
6.51
729
3.00
390
0.196
5.97
718
3.01
350
0.194
5.43
707
3.03
320
0.191
5.08
695
683
671
658
646
633
620
607
Ethyl
ether
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
790
2.135
550
0.159
7.39
780
2.156
470
0.155
6.54
769
2.179
410
0.151
5.92
758
2.205
365
0.147
5.48
747
2.233
330
0.144
5.12
736
2.265
290
0.140
4.69
725
2.299
265
0.139
4.38
714
2.332
233
0.134
4.05
702
2.36
214
0.129
3.92
689
2.39
197
0.125
3.77
676
2.43
181
0.120
3.67
666
2.47
166
0.116
3.54
653
2.51
153
0.112
3.43
640
625
611
140
129
118
Ethyl
iodide
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
0.656 0.663 0.670 0.677
730
0.092
5.37
0.684
655
0.090
4.98
0.691
590
0.088
4.63
0.698
539
0.086
4.30
0.705
495
0.085
4.11
0.712
455
0.083
3.90
0.718
420
0.081
3.72
0.724
390
0.080
3.53
Ethylene
glycol
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
1127
2.272
57000
0.254
510
1120
2.327
33300
0.255
305
1113
2.381
20200
0.256
190
1106
2.431
13400
0.258
126
1099
2.484
9100
0.259
87.3
1092
2.536
7070
0.260
69.0
1085
2.586
4000
1077
2.636
3450
1070 1063 1056
2.685 2.734 2.779
3000 2440 2000
Formic acid
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
1241
1231
1220
1209
1196
1184
1170
1156
1140
0.265
2260
0.261
1800
0.257
1470
0.257
1220
0.253
1030
0.250
890
0.246
780
0.243
680
615
550
0.240 0.236 0.232
1124
1108
TRAnSPORT PROPERTIES
2-297
TABLE 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids (Continued )
Temperature, °C
Substance
Gasoline
Glycerol
Kerosene
Property
−50
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s) 1710
k (W/m⋅K) 0.131
Pr
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
—
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s) 1150
k (W/m⋅K)
Pr
−40
1400
0.128
—
−30
−20
−10
784
1.88
1170 990
0.125 0.123
15.1
775
1.92
850
0.121
13.5
—
—
—
0
20
30
40
50
60
70
759
2.02
645
0.118
11.0
751
2.06
530
0.116
9.41
743
2.11
464
0.114
8.59
735
2.15
410
0.112
7.87
721
2.20
367
0.110
7.34
717
2.25
330
0.108
6.88
708
2.30
298
0.106
6.47
1276
1270
1248
2.457
1242
2.504
2.548
2.588
2.625 2.657 2.686
4.0.+6
1260
2.393
1.5.+6
0.284
12650
1254
2.406
1.2.+7
0.285
0.287
0.288
0.289
0.291
0.293 0.294 0.295
2.28
73
2.32
66
2.35
60
2.38
55
767
1.97
735
0.120
12.1
725
500
360
275
781
1.91
215
0.140
2.93
10
774
1.96
173
0.139
2.44
767
2.02
149
0.139
2.17
760
2.07
126
0.138
1.89
754
2.13
108
0.138
1.67
748
2.18
95
0.137
1.51
742
2.23
83
0.137
1.35
80
90
100
699
2.35
270
0.104
6.10
690
2.41
246
0.102
5.81
681
2.46
225
0.100
5.54
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k(W/m⋅K)
Pr
2.30
2305
0.225
23.6
2.32
1800
0.222
18.8
2.35
1410
0.219
15.1
2.37
1170
0.216
12.9
2.40
975
0.212
11.0
2.42
820
0.209
9.53
2.45
692
0.206
8.23
2.47
590
0.203
7.18
783
2.49
510
0.199
6.38
774
2.52
455
0.195
5.88
766
2.55
400
0.192
5.31
756
2.65
355
0.189
4.98
746
2.78
315
0.187
4.68
736
2.94
271
0.184
4.34
725
3.13
240
0.182
4.13
711
3.30
218
0.180
3.99
Methyl
formate
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
1069
1.84
830
0.217
7.04
1056
1.86
711
0.213
6.21
1043
1.88
618
0.209
5.56
1030
1.90
544
0.205
5.04
1017
1.92
481
0.200
4.62
1003
1.95
430
0.195
4.30
989
1.99
380
0.191
3.96
975
2.03
345
0.186
3.77
960
2.08
315
0.180
3.64
944
929
913
897
880
863
845
Oil,
castor
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
2,420,000
0.182
986,000 451,000 231,000 125,000 74,000 43,000
0.181
0.180
0.179
0.178
0.177 0.176 0.175 0.174 0.17
Methanol
Oil,
olive
Pentane
Propanol
Sulfuric
acid
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
138,000
0.170
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
693
2.060
489
0.142
7.14
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
849
1.955
20,200 13,500 9500 6900
0.167 0.166 0.165
236
684
2.084
428
0.139
6.42
674
2.110
379
0.136
5.88
665
2.137
339
0.132
5.49
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
Turpentine
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
923
1.535
1670
0.149
17.8
913
1.556
1345
0.147
14.2
904
1.579
1100
0.144
12.1
36,300
0.167
24,500
0.166
17,000 12,400
0.166 0.165 0.165 0.164 0.164
616
606
596
585
574
562
209
0.115
190
0.112
175
0.108
161
0.105
148
0.101
137
124
113
0.098 0.095 0.091
646
2.206
279
0.125
4.92
636
2.239
254
0.122
4.66
626
2.273
234
0.119
4.47
811
814
796
788
779
770
761
752
5110
819
2.219
3900
2900
2245
1720
0.171
1400
0.169
1130
0.168
921
0.167
760
0.165
630
508
447
0.164 0.163 0.162
1834
1.382
25,400
15,700
11,500
8820
7220
6090
5190
829
1.80
380
0.124
5.5
820
1.83
355
0.122
5.3
810
1.87
325
0.119
5.1
820
730
675
48,400 35,200
0.314
932
1.514
2120
0.152
21.1
52,000
0.168
656
2.167
307
0.128
5.20
ρ (kg/m3)
cp (kJ/ kg⋅K)
µ (10−6Pa⋅s)
k (W/m⋅K)
Pr
Toluene
914
1.633
84,000
0.169
810
895
1.602
915
0.142
10.3
886
1.633
770
0.139
9.0
876
1.652
670
0.137
8.1
867
1.675
590
0.134
7.4
858
1.701
520
0.132
6.7
848
1.73
470
0.129
6.3
839
1.76
420
0.126
5.9
1.72
2250
0.130
29.8
1.76
1780
0.129
24.3
1.80
1490
0.128
20.9
1270
0.127
18.4
1070
0.126
16.1
1.93
925
0.125
14.3
550
747
800
1.92
295
0.117
4.8
538
743
790
1.97
270
0.114
4.7
2-298
TABLE 2-147
Cmpd.
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)]
Name
Acetaldehyde
Acetamide
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetylene
Acrolein
Acrylic acid
Acrylonitrile
Air
Ammonia
Anisole
Argon
Benzamide
Benzene
Benzenethiol
Benzoic acid
Benzonitrile
Benzophenone
Benzyl alcohol
Benzyl ethyl ether
Benzyl mercaptan
Biphenyl
Bromine
Bromobenzene
Bromoethane
Bromomethane
1,2-Butadiene
1,3-Butadiene
Butane
1,2-Butanediol
1,3-Butanediol
1-Butanol
2-Butanol
1-Butene
cis-2-Butene
trans-2-Butene
Butyl acetate
Butylbenzene
Butyl mercaptan
sec-Butyl mercaptan
1-Butyne
Butyraldehyde
Butyric acid
Butyronitrile
Carbon dioxide
Carbon disulfide
Carbon monoxide
Carbon tetrachloride
Carbon tetrafluoride
Formula
C2H4O
C2H5NO
C2H4O2
C4H6O3
C3H6O
C2H3N
C2H2
C3H4O
C3H4O2
C3H3N
Mixture
H3N
C7H8O
Ar
C7H7NO
C6H6
C6H6S
C7H6O2
C7H5N
C13H10O
C7H8O
C9H12O
C7H8S
C12H10
Br2
C6H5Br
C2H5Br
CH3Br
C4H6
C4H6
C4H10
C4H10O2
C4H10O2
C4H10O
C4H10O
C4H8
C4H8
C4H8
C6H12O2
C10H14
C4H10S
C4H10S
C4H6
C4H8O
C4H8O2
C4H7N
CO2
CS2
CO
CCl4
CF4
CAS
75-07-0
60-35-5
64-19-7
108-24-7
67-64-1
75-05-8
74-86-2
107-02-8
79-10-7
107-13-1
132259-10-0
7664-41-7
100-66-3
7440-37-1
55-21-0
71-43-2
108-98-5
65-85-0
100-47-0
119-61-9
100-51-6
539-30-0
100-53-8
92-52-4
7726-95-6
108-86-1
74-96-4
74-83-9
590-19-2
106-99-0
106-97-8
584-03-2
107-88-0
71-36-3
78-92-2
106-98-9
590-18-1
624-64-6
123-86-4
104-51-8
109-79-5
513-53-1
107-00-6
123-72-8
107-92-6
109-74-0
124-38-9
75-15-0
630-08-0
56-23-5
75-73-0
Mol. wt.
44.05256
59.0672
60.052
102.08864
58.07914
41.0519
26.03728
56.06326
72.06266
53.0626
28.96
17.03052
108.13782
39.948
121.13658
78.11184
110.17684
122.12134
103.1213
182.2179
108.13782
136.19098
124.20342
154.2078
159.808
157.0079
108.965
94.93852
54.09044
54.09044
58.1222
90.121
90.121
74.1216
74.1216
56.10632
56.10632
56.10632
116.15828
134.21816
90.1872
90.1872
54.09044
72.10572
88.1051
69.1051
44.0095
76.1407
28.0101
153.8227
88.0043
C1
0.33515
0.39363
0.214
0.23638
0.2878
0.30755
0.33363
0.2703
0.2441
0.30751
0.28472
1.169
0.23494
0.1819
0.28485
0.23444
0.20996
0.2391
0.20603
0.25867
0.17847
0.2029
0.20316
0.19053
–0.2185
0.16983
0.1629
0.16143
0.21966
0.22231
0.27349
0.064621
–0.0032865
0.22888
0.18599
0.22153
0.21378
0.21153
0.21721
0.18707
0.21143
0.2069
0.22334
0.24962
0.1967
0.24077
0.4406
0.2333
0.2855
0.1589
0.20771
C2
–0.00055227
–0.00037053
–0.0001834
–0.00024263
–0.000427
–0.000402
–0.00083655
–0.0003764
–0.0002904
–0.000487
–0.0017393
–0.002314
–0.00026477
–0.0003176
–0.00025225
–0.00030572
–0.0002146
–0.0002325
–0.00021023
–0.00022516
–0.000065843
–0.0002226
–0.00019912
–0.00015145
0.0042143
–0.0001981
–0.00021198
–0.00021287
–0.0003436
–0.0003664
–0.00071267
0.00067625
0.0011463
–0.00025
–0.00017227
–0.00035023
–0.00035445
–0.00035056
–0.00026563
–0.00020037
–0.000258
–0.0002568
–0.0003515
–0.000325
–0.000168
–0.00028665
–0.0012175
–0.000275
–0.001784
–0.0001987
–0.00078883
C3
C4
C5
–0.00000411
–0.000017753 3.1041E-08
5.1555E-07
–1.0491E-06
–1.5525E-06
–2.0108E-11
Tmin, K
149.78
353.33
289.81
200.15
178.45
229.32
192.4
185.45
286.15
189.63
75
195.41
235.65
83.78
403
278.68
258.27
395.45
260.28
321.35
257.85
275.65
243.95
342.2
266
242.43
154.25
179.44
136.95
164.25
134.86
220
196.15
183.85
158.45
87.8
134.26
167.62
199.65
185.3
157.46
133.02
147.43
176.8
267.95
161.3
216.58
161.11
68.15
250.33
89.56
Thermal cond.
at Tmin
0.2524
0.2627
0.1608
0.1878
0.2116
0.2154
0.1727
0.2005
0.1610
0.2152
0.1543
0.7168
0.1725
0.1264
0.1832
0.1492
0.1545
0.1472
0.1513
0.1863
0.1615
0.1415
0.1546
0.1387
0.1299
0.1218
0.1302
0.1232
0.1726
0.1621
0.1868
0.1626
0.1618
0.1829
0.1587
0.1908
0.1662
0.1528
0.1642
0.1499
0.1708
0.1727
0.1715
0.1922
0.1517
0.1945
0.1769
0.1890
0.1639
0.1092
0.1371
Tmax, K
Thermal
cond. at Tmax
294.15
494.3
391.05
412.7
343.15
354.81
250
325.84
484.5
350.45
125
400.05
512.5
150
563.15
413.1
442.29
596
464.15
664
478.6
528.6
472.03
723.15
584
429.24
327
413.15
284
268.74
400
469.57
481.38
391
372.9
266.91
276.87
274.03
453.75
473.15
371.61
358.13
281.22
347.94
573.15
390.74
300
319.37
125
349.79
145.1
0.1727
0.2105
0.1423
0.1362
0.1413
0.1649
0.1245
0.1477
0.1034
0.1368
0.0673
0.2433
0.0993
0.0418
0.1428
0.1081
0.1150
0.1005
0.1085
0.1092
0.1470
0.0852
0.1092
0.0810
0.0316
0.0848
0.0936
0.0735
0.1221
0.1238
0.0709
0.1508
0.1888
0.1311
0.1218
0.1281
0.1156
0.1155
0.0967
0.0923
0.1156
0.1149
0.1245
0.1365
0.1004
0.1288
0.0754
0.1455
0.0625
0.0894
0.0933
2-299
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
Chlorine
Chlorobenzene
Chloroethane
Chloroform
Chloromethane
1-Chloropropane
2-Chloropropane
m-Cresol
o-Cresol
p-Cresol
Cumene
Cyanogen
Cyclobutane
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexene
Cyclopentane
Cyclopentene
Cyclopropane
Cyclohexyl mercaptan
Decanal
Decane
Decanoic acid
1-Decanol
1-Decene
Decyl mercaptan
1-Decyne
Deuterium
1,1-Dibromoethane
1,2-Dibromoethane
Dibromomethane
Dibutyl ether
m-Dichlorobenzene
o-Dichlorobenzene
p-Dichlorobenzene
1,1-Dichloroethane
1,2-Dichloroethane
Dichloromethane
1,1-Dichloropropane
1,2-Dichloropropane
Diethanol amine
Diethyl amine
Diethyl ether
Diethyl sulfide
1,1-Difluoroethane
1,2-Difluoroethane
Difluoromethane
Di–isopropyl amine
Di–isopropyl ether
Di–isopropyl ketone
1,1-Dimethoxyethane
1,2-Dimethoxypropane
Dimethyl acetylene
Dimethyl amine
Cl2
C6H5Cl
C2H5Cl
CHCl3
CH3Cl
C3H7Cl
C3H7Cl
C7H8O
C7H8O
C7H8O
C9H12
C2N2
C4H8
C6H12
C6H12O
C6H10O
C6H10
C5H10
C5H8
C3H6
C6H12S
C10H20O
C10H22
C10H20O2
C10H22O
C10H20
C10H22S
C10H18
D2
C2H4Br2
C2H4Br2
CH2Br2
C8H18O
C6H4Cl2
C6H4Cl2
C6H4Cl2
C2H4Cl2
C2H4Cl2
CH2Cl2
C3H6Cl2
C3H6Cl2
C4H11NO2
C4H11N
C4H10O
C4H10S
C2H4F2
C2H4F2
CH2F2
C6H15N
C6H14O
C7H14O
C4H10O2
C5H12O2
C4H6
C2H7N
7782-50-5
108-90-7
75-00-3
67-66-3
74-87-3
540-54-5
75-29-6
108-39-4
95-48-7
106-44-5
98-82-8
460-19-5
287-23-0
110-82-7
108-93-0
108-94-1
110-83-8
287-92-3
142-29-0
75-19-4
1569-69-3
112-31-2
124-18-5
334-48-5
112-30-1
872-05-9
143-10-2
764-93-2
7782-39-0
557-91-5
106-93-4
74-95-3
142-96-1
541-73-1
95-50-1
106-46-7
75-34-3
107-06-2
75-09-2
78-99-9
78-87-5
111-42-2
109-89-7
60-29-7
352-93-2
75-37-6
624-72-6
75-10-5
108-18-9
108-20-3
565-80-0
534-15-6
7778-85-0
503-17-3
124-40-3
70.906
112.5569
64.5141
119.37764
50.4875
78.54068
78.54068
108.13782
108.13782
108.13782
120.19158
52.0348
56.10632
84.15948
100.15888
98.143
82.1436
70.1329
68.11702
42.07974
116.22448
156.2652
142.28168
172.265
158.28108
140.2658
174.34668
138.24992
4.0316
187.86116
187.86116
173.83458
130.22792
147.00196
147.00196
147.00196
98.95916
98.95916
84.93258
112.98574
112.98574
105.13564
73.13684
74.1216
90.1872
66.04997
66.04997
52.02339
101.19
102.17476
114.18546
90.121
104.14758
54.09044
45.08368
0.2246
0.1841
0.23779
0.1778
0.25381
0.21851
0.21232
0.18241
0.19186
0.17971
0.1855
0.37845
0.22262
0.19813
0.1715
0.17557
0.20926
0.2066
0.21776
0.24348
0.18374
0.21363
0.2063
0.206
0.236171
0.20237
0.20134
0.20839
1.264
0.1426
0.13622
0.17558
0.19418
0.16694
0.16994
0.16977
0.18881
0.214
0.23847
0.18
0.19653
0.0218
0.2587
0.2495
0.21065
0.27019
0.23171
0.37296
0.1844
0.19162
0.22076
0.22078
0.22998
0.22773
0.2454
–0.000064
–0.0001917
–0.000395209
–0.0002023
–0.000431803
–0.00033762
–0.0003149
–0.00011109
–0.0001303
–0.00012037
–0.00020895
–0.00069945
–0.00034082
–0.0002505
–0.0001255
–0.00012392
–0.00026037
–0.0002696
–0.00027783
–0.00042568
–0.0001925
–0.00023004
–0.00025
–0.0002
–0.00025
–0.00024187
–0.00020826
–0.00023622
–0.00016402
–0.0001179
–0.00022499
–0.00022246
–0.0001667
–0.0001637
–0.0001799
–0.00026083
–0.000266
–0.00033366
–0.00023144
–0.00025012
0.0010315
–0.00054343
–0.000407
–0.0002623
–0.000661
–0.00038503
–0.00088707
–0.000239
–0.0002762
–0.00027624
–0.00031271
–0.00030372
–0.00034804
–0.000338
–0.000000788
–0.000001355
4.2097E-07
3.443E-07
2.5762E-07
172.12
227.95
136.75
209.63
175.43
150.35
155.97
285.39
304.19
307.93
177.14
245.25
182.48
279.69
296.6
242
169.67
179.28
138.13
145.59
189.64
285
243.51
304.75
280.05
206.89
247.56
229.15
20.4
210.15
282.85
220.6
175.3
248.39
262.87
326.14
176.19
253.15
178.01
192.5
172.71
301.15
223.35
156.85
169.2
154.56
179.6
136.95
176.85
187.65
204.81
159.95
226.1
240.91
180.96
0.1902
0.1404
0.1837
0.1354
0.1781
0.1677
0.1632
0.1507
0.1522
0.1426
0.1485
0.2069
0.1604
0.1281
0.1343
0.1456
0.1651
0.1583
0.1794
0.1815
0.1472
0.1481
0.1454
0.1451
0.1662
0.1523
0.1498
0.1543
1.2640
0.1081
0.1029
0.1259
0.1552
0.1255
0.1269
0.1111
0.1429
0.1467
0.1791
0.1354
0.1533
0.2095
0.1583
0.1857
0.1663
0.1763
0.1626
0.2563
0.1421
0.1398
0.1642
0.1708
0.1613
0.1439
0.1842
410
404.87
348.15
400
333
393.15
386.7
475.43
464.15
475.13
413.15
251.9
285.66
353.87
563.15
428.58
356.12
322.4
333.15
240.37
431.95
481.65
447.3
543.15
503
443.75
512.35
447.15
20.4
498.4
404.51
370.1
523.15
446.23
351.71
548
416.9
356.59
325
438
457.6
673.15
453.15
433.15
365.25
363.15
372.8
302.56
357.05
400.1
460
337.45
366.15
300.13
403.15
0.0659
0.1065
0.1002
0.0969
0.1100
0.0858
0.0906
0.1296
0.1314
0.1225
0.0992
0.2023
0.1253
0.1095
0.1008
0.1225
0.1165
0.1197
0.1252
0.1412
0.1006
0.1028
0.0945
0.0974
0.1104
0.0950
0.0946
0.1028
1.2640
0.0609
0.0885
0.0923
0.0778
0.0926
0.1124
0.0712
0.0801
0.1191
0.1300
0.0786
0.0821
0.1022
0.0989
0.0732
0.1148
0.0756
0.0882
0.1282
0.0991
0.0811
0.0937
0.1153
0.1188
0.1233
0.1091
(Continued)
2-300
TABLE 2-147
Cmpd.
no.
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued )
Name
2,3-Dimethylbutane
1,1-Dimethylcyclohexane
cis-1,2-Dimethylcyclohexane
trans-1,2-Dimethylcyclohexane
Dimethyl disulfide
Dimethyl ether
N,N-Dimethyl formamide
2,3-Dimethylpentane
Dimethyl phthalate
Dimethylsilane
Dimethyl sulfide
Dimethyl sulfoxide
Dimethyl terephthalate
1,4-Dioxane
Diphenyl ether
Dipropyl amine
Dodecane
Eicosane
Ethane
Ethanol
Ethyl acetate
Ethyl amine
Ethylbenzene
Ethyl benzoate
2-Ethyl butanoic acid
Ethyl butyrate
Ethylcyclohexane
Ethylcyclopentane
Ethylene
Ethylenediamine
Ethylene glycol
Ethyleneimine
Ethylene oxide
Ethyl formate
2-Ethyl hexanoic acid
Ethylhexyl ether
Ethylisopropyl ether
Ethylisopropyl ketone
Ethyl mercaptan
Ethyl propionate
Ethylpropyl ether
Ethyltrichlorosilane
Fluorine
Fluorobenzene
Fluoroethane
Fluoromethane
Formaldehyde
Formamide
Formic acid
Furan
Formula
C6H14
C8H16
C8H16
C8H16
C2H6S2
C2H6O
C3H7NO
C7H16
C10H10O4
C2H8Si
C2H6S
C2H6OS
C10H10O4
C4H8O2
C12H10O
C6H15N
C12H26
C20H42
C2H6
C2H6O
C4H8O2
C2H7N
C8H10
C9H10O2
C6H12O2
C6H12O2
C8H16
C7H14
C2H4
C2H8N2
C2H6O2
C2H5N
C2H4O
C3H6O2
C8H16O2
C8H18O
C5H12O
C6H12O
C2H6S
C5H10O2
C5H12O
C2H5Cl3Si
F2
C6H5F
C2H5F
CH3F
CH2O
CH3NO
CH2O2
C4H4O
CAS
Mol. wt.
C1
C2
79-29-8
590-66-9
2207-01-4
6876-23-9
624-92-0
115-10-6
68-12-2
565-59-3
131-11-3
1111-74-6
75-18-3
67-68-5
120-61-6
123-91-1
101-84-8
142-84-7
112-40-3
112-95-8
74-84-0
64-17-5
141-78-6
75-04-7
100-41-4
93-89-0
88-09-5
105-54-4
1678-91-7
1640-89-7
74-85-1
107-15-3
107-21-1
151-56-4
75-21-8
109-94-4
149-57-5
5756-43-4
625-54-7
565-69-5
75-08-1
105-37-3
628-32-0
115-21-9
7782-41-4
462-06-6
353-36-6
593-53-3
50-00-0
75-12-7
64-18-6
110-00-9
86.17536
112.21264
112.21264
112.21264
94.19904
46.06844
73.09378
100.20194
194.184
60.17042
62.134
78.13344
194.184
88.10512
170.2072
101.19
170.33484
282.54748
30.069
46.06844
88.10512
45.08368
106.165
150.1745
116.15828
116.15828
112.21264
98.18606
28.05316
60.09832
62.06784
43.0678
44.05256
74.07854
144.211
130.22792
88.14818
100.15888
62.13404
102.1317
88.14818
163.506
37.9968064
96.1023032
48.0595
34.03292
30.02598
45.04062
46.0257
68.07396
0.1774
0.1807
0.18092
0.17675
0.21373
0.31174
0.26
0.17964
0.13905
0.25547
0.23942
0.3142
0.21956
0.3027
0.18686
0.2224
0.2047
0.2178
0.35758
0.2468
0.2501
0.30059
0.1999
0.20771
0.2175
0.21043
0.17662
0.18334
0.4194
0.36434
0.088067
0.3097
0.26957
0.2587
0.20954
0.19356
0.21928
0.22873
0.23392
0.2137
0.22717
0.19653
0.2758
0.20962
0.25866
0.48162
0.336003243
0.3847
0.302
0.2198
–0.0002436
–0.0002177
–0.0002108
–0.0002077
–0.0002447
–0.0005638
–0.000255
–0.000246
0.0001509
–0.0004411
–0.0003311
–0.00030809
–0.000209955
–0.0004827
–0.00014953
–0.000314
–0.0002326
–0.0002233
–0.0011458
–0.000264
–0.0003563
–0.000581
–0.00023823
–0.00021265
–0.0002407
–0.00024903
–0.0002014
–0.0002228
–0.001591
–0.0004433
0.00094712
–0.0004023
–0.0003984
–0.00033
–0.00022251
–0.00024102
–0.00032568
–0.0002913
–0.0003206
–0.0002515
–0.0003298
–0.00016907
–0.0016297
–0.00028034
–0.000498
–0.0010709
–0.00054
–0.0001065
–0.000108
–0.00031405
C3
C4
–3.978E-07
6.1866E-07
6.602E-07
0.000001306
–1.3114E-06
–1.6698E-07
0
0
C5
Tmin, K
145.19
239.66
223.16
184.99
188.44
131.65
250
160
273.15
122.93
174.88
291.67
413.79
284.95
300.03
210.15
263.57
309.58
90.35
159.05
189.6
192.15
178.2
238.45
258.15
175.15
161.84
134.71
104
284.29
260.15
195.2
160.65
193.55
155.15
180
140
204.15
125.26
199.25
145.65
167.55
53.48
238.15
129.95
131.35
155.15
275.7
281.45
187.55
Thermal cond.
at Tmin
0.1420
0.1285
0.1339
0.1383
0.1676
0.2375
0.1963
0.1403
0.1506
0.2012
0.1815
0.2243
0.1327
0.1652
0.1420
0.1564
0.1434
0.1487
0.2591
0.2048
0.1825
0.2133
0.1574
0.1570
0.1554
0.1668
0.1440
0.1533
0.2681
0.2383
0.2457
0.2312
0.2056
0.1948
0.1750
0.1502
0.1737
0.1693
0.1938
0.1636
0.1791
0.1635
0.1886
0.1429
0.1939
0.3410
0.2522
0.3553
0.2716
0.1609
Tmax, K
Thermal
cond. at Tmax
331.15
392.7
402.94
596.15
382.9
320.03
425.15
362.93
556.85
253.55
310.48
464
559.2
374.47
531.46
382
489.47
616.93
300
353.15
350.21
293.15
413.1
549.4
516.5
453.15
404.94
376.62
280
390.41
470.45
329
283.85
433.15
500.66
466.4
391.2
450.1
308.15
495
400.07
371.05
130
353.15
235.45
194.82
253.85
493
373.71
304.5
0.0967
0.0952
0.0960
0.0529
0.1200
0.1313
0.1516
0.0904
0.0997
0.1436
0.1366
0.1712
0.1022
0.1219
0.1074
0.1025
0.0909
0.0800
0.0695
0.1536
0.1253
0.1870
0.1015
0.0909
0.0932
0.0976
0.0951
0.0994
0.0763
0.1913
0.2434
0.1773
0.1565
0.1158
0.0981
0.0812
0.0919
0.0976
0.1351
0.0892
0.0952
0.1108
0.0639
0.1106
0.1414
0.2730
0.1989
0.3322
0.2616
0.1242
2-301
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
Helium-4
Heptadecane
Heptanal
Heptane
Heptanoic acid
1-Heptanol
2-Heptanol
3-Heptanone
2-Heptanone
1-Heptene
Heptyl mercaptan
1-Heptyne
Hexadecane
Hexanal
Hexane
Hexanoic acid
1-Hexanol
2-Hexanol
2-Hexanone
3-Hexanone
1-Hexene
3-Hexyne
Hexyl mercaptan
1-Hexyne
2-Hexyne
Hydrazine
Hydrogen
Hydrogen bromide
Hydrogen chloride
Hydrogen cyanide
Hydrogen fluoride
Hydrogen sulfide
Isobutyric acid
Isopropyl amine
Malonic acid
Methacrylic acid
Methane
Methanol
N-Methyl acetamide
Methyl acetate
Methyl acetylene
Methyl acrylate
Methyl amine
Methyl benzoate
3-Methyl-1,2-butadiene
2-Methylbutane
2-Methylbutanoic acid
3-Methyl-1-butanol
2-Methyl-1-butene
2-Methyl-2-butene
2-Methyl -1-butene-3-yne
Methylbutyl ether
Methylbutyl sulfide
3-Methyl-1-butyne
Methyl butyrate
He
C17H36
C7H14O
C7H16
C7H14O2
C7H16O
C7H16O
C7H14O
C7H14O
C7H14
C7H16S
C7H12
C16H34
C6H12O
C6H14
C6H12O2
C6H14O
C6H14O
C6H12O
C6H12O
C6H12
C6H10
C6H14S
C6H10
C6H10
H4N2
H2
BrH
ClH
CHN
FH
H2S
C4H8O2
C3H9N
C3H4O4
C4H6O2
CH4
CH4O
C3H7NO
C3H6O2
C3H4
C4H6O2
CH5N
C8H8O2
C5H8
C5H12
C5H10O2
C5H12O
C5H10
C5H10
C5H6
C5H12O
C5H12S
C5H8
C5H10O2
7440-59-7
629-78-7
111-71-7
142-82-5
111-14-8
111-70-6
543-49-7
106-35-4
110-43-0
592-76-7
1639-09-4
628-71-7
544-76-3
66-25-1
110-54-3
142-62-1
111-27-3
626-93-7
591-78-6
589-38-8
592-41-6
928-49-4
111-31-9
693-02-7
764-35-2
302-01-2
1333-74-0
10035-10-6
7647-01-0
74-90-8
7664-39-3
7783-06-4
79-31-2
75-31-0
141-82-2
79-41-4
74-82-8
67-56-1
79-16-3
79-20-9
74-99-7
96-33-3
74-89-5
93-58-3
598-25-4
78-78-4
116-53-0
123-51-3
563-46-2
513-35-9
78-80-8
628-28-4
628-29-5
598-23-2
623-42-7
4.0026
240.46774
114.18546
100.20194
130.185
116.20134
116.20134
114.18546
114.18546
98.18606
132.26694
96.17018
226.44116
100.15888
86.17536
116.158
102.17476
102.175
100.15888
100.15888
84.15948
82.1436
118.24036
82.1436
82.1436
32.04516
2.01588
80.91194
36.46094
27.02534
20.0063432
34.08088
88.10512
59.11026
104.06146
86.08924
16.0425
32.04186
73.09378
74.07854
40.06386
86.08924
31.0571
136.14792
68.11702
72.14878
102.1317
88.1482
70.1329
70.1329
66.10114
88.14818
104.214
68.11702
102.1317
–0.013833
0.20926
0.22841
0.215
0.202
0.234063
0.21142
0.2026
0.2108
0.19664
0.2037
0.21098
0.20749
0.22832
0.22492
0.1855
0.230656
0.21391
0.21076
0.23493
0.19112
0.20996
0.2058
0.21492
0.2119
1.3675
–0.0917
0.234
0.8045
0.43454
0.7516
0.4842
0.21668
0.237
0.28231
0.2306
0.41768
0.2837
0.23743
0.2777
0.23648
0.26082
0.33446
0.22142
0.1983
0.21246
0.22284
0.17471
0.19447
0.19636
0.20385
0.22235
0.20698
0.20348
0.21748
0.022913
–0.0002215
–0.00026273
–0.000303
–0.0002
–0.00025
–0.00024793
–0.0002234
–0.000246
–0.00016623
–0.0002252
–0.00026652
–0.00021917
–0.00026482
–0.0003533
–0.000146
–0.00025
–0.00026042
–0.00024
–0.0002912
–0.000083519
–0.0002692
–0.0002324
–0.0002899
–0.00027048
–0.0015895
0.017678
–0.0004636
–0.002102
–0.0007008
–0.0010874
–0.001184
–0.0002556
–0.000332
–0.00024019
–0.00025201
–0.0024528
–0.000281
–0.0002362
–0.000417
–0.00041639
–0.0003506
–0.00067427
–0.00022759
–0.0002822
–0.00033581
–0.0002516
–0.0001256
–0.0002901
–0.000291
–0.0002874
–0.0003044
–0.00024439
–0.0003106
–0.00025913
–0.0054872
0.0004585
–2.5241E-07
–5.1407E-07
–0.000382
3.5588E-06
8.033E-07
–3.3324E-06
1.0266E-07
2.2
295.13
229.8
182.57
265.83
239.15
220
234.15
238.15
154.12
229.92
192.22
291.31
214.93
177.83
269.25
228.55
223
217.35
217.5
133.39
170.05
192.62
141.25
183.65
274.69
13.95
185.15
273.15
259.83
189.79
193.15
227.15
177.95
409.15
288.15
90.69
175.47
301.15
175.15
170.45
196.32
179.69
260.75
159.53
113.25
357.15
155.95
135.58
139.39
160.15
157.48
175.3
183.45
187.35
0.0149
0.1439
0.1680
0.1597
0.1488
0.1743
0.1569
0.1503
0.1522
0.1650
0.1519
0.1597
0.1436
0.1714
0.1621
0.1462
0.1735
0.1558
0.1586
0.1716
0.1708
0.1642
0.1610
0.1740
0.1622
0.9309
0.0754
0.1482
0.2303
0.2525
0.5452
0.2555
0.1586
0.1779
0.1840
0.1580
0.2245
0.2344
0.1663
0.2047
0.1655
0.1920
0.2392
0.1621
0.1533
0.1744
0.1330
0.1551
0.1551
0.1558
0.1578
0.1744
0.1641
0.1465
0.1689
4.8
575.3
426.15
371.58
496.15
573.15
432.9
553.15
424.05
366.79
450.09
372.93
560.01
401.15
370
603.15
575
412.4
400.85
466
336.63
354.35
425.81
344.48
357.67
623.15
31
290.62
323.15
298.85
394.45
292.42
482.75
305.55
580
530
180
337.85
478.15
386.15
249.94
421
283.15
547.9
314
368.13
480.9
404.15
304.3
311.7
305.4
463.15
396.58
302.15
493.15
0.0204
0.0818
0.1164
0.1024
0.1028
0.0908
0.1041
0.0790
0.1065
0.1017
0.1023
0.1116
0.0848
0.1221
0.0942
0.0974
0.0869
0.1065
0.1146
0.0992
0.1048
0.1146
0.1068
0.1151
0.1152
0.3770
0.0848
0.0993
0.1252
0.2251
0.3227
0.1380
0.0933
0.1356
0.1430
0.0970
0.0915
0.1888
0.1245
0.1167
0.1324
0.1132
0.2079
0.0967
0.1097
0.0888
0.1018
0.1239
0.1062
0.1057
0.1161
0.0814
0.1101
0.1096
0.0897
(Continued)
2-302
TABLE 2-147
Cmpd.
no.
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued )
Name
Methylchlorosilane
Methylcyclohexane
1-Methylcyclohexanol
cis-2-Methylcyclohexanol
trans-2-Methylcyclohexanol
Methylcyclopentane
1-Methylcyclopentene
3-Methylcyclopentene
Methyldichlorosilane
Methylethyl ether
Methylethyl ketone
Methylethyl sulfide
Methyl formate
Methylisobutyl ether
Methylisobutyl ketone
Methyl Isocyanate
Methylisopropyl ether
Methylisopropyl ketone
Methylisopropyl sulfide
Methyl mercaptan
Methyl methacrylate
2-Methyloctanoic acid
2-Methylpentane
Methyl pentyl ether
2-Methylpropane
2-Methyl-2-propanol
2-Methyl propene
Methyl propionate
Methylpropyl ether
Methylpropyl sulfide
Methylsilane
alpha-Methyl styrene
Methyl tert-butyl ether
Methyl vinyl ether
Naphthalene
Neon
Nitroethane
Nitrogen
Nitrogen trifluoride
Nitromethane
Nitrous oxide
Nitric oxide
Nonadecane
Nonanal
Nonane
Nonanoic acid
1-Nonanol
2-Nonanol
1-Nonene
Nonyl mercaptan
1-Nonyne
Formula
CH5ClSi
C7H14
C7H14O
C7H14O
C7H14O
C6H12
C6H10
C6H10
CH4Cl2Si
C3H8O
C4H8O
C3H8S
C2H4O2
C5H12O
C6H12O
C2H3NO
C4H10O
C5H10O
C4H10S
CH4S
C5H8O2
C9H18O2
C6H14
C6H14O
C4H10
C4H10O
C4H8
C4H8O2
C4H10O
C4H10S
CH6Si
C9H10
C5H12O
C3H6O
C10H8
Ne
C2H5NO2
N2
F3N
CH3NO2
N 2O
NO
C19H40
C9H18O
C9H20
C9H18O2
C9H20O
C9H20O
C9H18
C9H20S
C9H16
CAS
993-00-0
108-87-2
590-67-0
7443-70-1
7443-52-9
96-37-7
693-89-0
1120-62-3
75-54-7
540-67-0
78-93-3
624-89-5
107-31-3
625-44-5
108-10-1
624-83-9
598-53-8
563-80-4
1551-21-9
74-93-1
80-62-6
3004-93-1
107-83-5
628-80-8
75-28-5
75-65-0
115-11-7
554-12-1
557-17-5
3877-15-4
992-94-9
98-83-9
1634-04-4
107-25-5
91-20-3
7440-01-9
79-24-3
7727-37-9
7783-54-2
75-52-5
10024-97-2
10102-43-9
629-92-5
124-19-6
111-84-2
112-05-0
143-08-8
628-99-9
124-11-8
1455-21-6
3452-09-3
Mol. wt.
80.5889
98.18606
114.18546
114.18546
114.18546
84.15948
82.1436
82.1436
115.03396
60.09502
72.10572
76.1606
60.05196
88.14818
100.15888
57.05132
74.1216
86.1323
90.1872
48.10746
100.11582
158.23802
86.17536
102.17476
58.1222
74.1216
56.10632
88.10512
74.1216
90.1872
46.14384
118.1757
88.1482
58.07914
128.17052
20.1797
75.0666
28.0134
71.00191
61.04002
44.0128
30.0061
268.5209
142.23862
128.2551
158.238
144.2545
144.255
126.23922
160.3201
124.22334
C1
C2
0.24683
0.1791
0.21558
0.21839
0.21828
0.1929
0.20023
0.1994
0.21956
0.27304
0.2197
0.22136
0.3246
0.222
0.2301
0.2822
0.24154
0.2332
0.20978
0.26119
0.2583
0.20911
0.19334
0.21698
0.20455
0.21258
0.2802
0.22534
0.24817
0.21103
0.2774
0.19657
0.22526
0.28035
0.17096
0.2971
0.247
0.2654
–0.00038854
–0.0002291
–0.00022728
–0.00025776
–0.0002557
–0.0002492
–0.00025581
–0.00026149
–0.00032153
–0.0004518
–0.0002505
–0.00028938
–0.000468
–0.00032217
–0.00028899
–0.00042037
–0.0003774
–0.0003044
–0.00026468
–0.00038345
–0.000379
–0.00021852
–0.00028038
–0.00028998
–0.00036589
–0.00029864
–0.000786
–0.0002683
–0.0003774
–0.00025985
–0.00054608
–0.0002118
–0.00037235
–0.0004646
–0.00010059
–0.017356
–0.0002814
–0.001677
0.3276
0.10112
0.1878
0.21229
0.21905
0.209
0.204
0.240538
0.2081
0.20468
0.20244
0.20954
–0.000405
0.0010293
–0.00022
–0.00024013
–0.000264
–0.0002
–0.00025
–0.00022869
–0.00025738
–0.00021343
–0.00024588
C3
C4
C5
6.516E-07
1.1689E-07
0
0.0005911
–0.000007421
–0.00000943
0
Tmin, K
Thermal cond.
at Tmin
Tmax, K
Thermal
cond. at Tmax
139.05
273.15
299.15
280.15
269.15
130.73
146.62
168.54
182.55
160
186.48
167.23
174.15
188
189.15
256.15
127.93
180.15
171.64
150.18
290.15
208.2
119.55
176
113.54
298.97
132.81
185.65
133.97
160.17
116.34
249.95
164.55
151.15
353.43
25
183.63
63.15
0.1928
0.1165
0.1476
0.1462
0.1495
0.1603
0.1627
0.1553
0.1609
0.2008
0.1730
0.1730
0.2431
0.1614
0.1754
0.1745
0.1933
0.1784
0.1644
0.2036
0.1483
0.1636
0.1598
0.1659
0.1630
0.1233
0.1873
0.1755
0.1976
0.1694
0.2139
0.1436
0.1672
0.2101
0.1354
0.1167
0.1953
0.1595
281.85
374.08
548.8
484.2
484.8
344.95
348.64
338.05
314.7
341.34
352.79
339.8
373.15
390
451.42
312
370
435.9
357.91
279.11
363.45
555.2
389.25
432.3
400
404.96
395.2
475
373
368.69
216.25
438.65
328.2
341.1
646.97
44
387.22
124
0.1373
0.0934
0.0909
0.0936
0.0943
0.1069
0.1110
0.1110
0.1184
0.1188
0.1313
0.1230
0.1500
0.0964
0.0996
0.1510
0.1019
0.1005
0.1150
0.1542
0.1206
0.0878
0.0842
0.0916
0.0582
0.0916
0.0713
0.0979
0.1074
0.1152
0.1593
0.1037
0.1156
0.1219
0.1059
0.0457
0.1380
0.0575
244.6
277.59
110
305.04
267.3
219.66
285.55
268.15
238.15
191.91
253.05
223.15
0.2285
0.1011
0.1869
0.1452
0.1549
0.1510
0.1469
0.1735
0.1536
0.1553
0.1484
0.1547
374.35
277.59
176.4
603.05
465.52
423.97
528.75
578.65
471.7
420.02
492.95
423.85
0.1760
0.1011
0.0759
0.0796
0.1073
0.0971
0.0983
0.0959
0.1002
0.0966
0.0972
0.1053
2-303
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
Octadecane
Octanal
Octane
Octanoic acid
1-Octanol
2-Octanol
2-Octanone
3-Octanone
1-Octene
Octyl mercaptan
1-Octyne
Oxalic acid
Oxygen
Ozone
Pentadecane
Pentanal
Pentane
Pentanoic acid
1-Pentanol
2-Pentanol
2-Pentanone
3-Pentanone
1-Pentene
2-Pentyl mercaptan
Pentyl mercaptan
1-Pentyne
2-Pentyne
Phenanthrene
Phenol
Phenyl isocyanate
Phthalic anhydride
Propadiene
Propane
1-Propanol
2-Propanol
Propenylcyclohexene
Propionaldehyde
Propionic acid
Propionitrile
Propyl acetate
Propyl amine
Propylbenzene
Propylene
Propyl formate
2-Propyl mercaptan
Propyl mercaptan
1,2-Propylene glycol
Quinone
Silicon tetrafluoride
Styrene
Succinic acid
Sulfur dioxide
Sulfur hexafluoride
Sulfur trioxide
Terephthalic acid
C18H38
C8H16O
C8H18
C8H16O2
C8H18O
C8H18O
C8H16O
C8H16O
C8H16
C8H18S
C8H14
C2H2O4
O2
O3
C15H32
C5H10O
C5H12
C5H10O2
C5H12O
C5H12O
C5H10O
C5H10O
C5H10
C5H12S
C5H12S
C5H8
C5H8
C14H10
C6H6O
C7H5NO
C8H4O3
C3H4
C3H8
C3H8O
C3H8O
C9H14
C3H6O
C3H6O2
C3H5N
C5H10O2
C3H9N
C9H12
C3H6
C4H8O2
C3H8S
C3H8S
C3H8O2
C6H4O2
F4Si
C8H8
C4H6O4
O 2S
F6S
O 3S
C8H6O4
593-45-3
124-13-0
111-65-9
124-07-2
111-87-5
123-96-6
111-13-7
106-68-3
111-66-0
111-88-6
629-05-0
144-62-7
7782-44-7
10028-15-6
629-62-9
110-62-3
109-66-0
109-52-4
71-41-0
6032-29-7
107-87-9
96-22-0
109-67-1
2084-19-7
110-66-7
627-19-0
627-21-4
85-01-8
108-95-2
103-71-9
85-44-9
463-49-0
74-98-6
71-23-8
67-63-0
13511-13-2
123-38-6
79-09-4
107-12-0
109-60-4
107-10-8
103-65-1
115-07-1
110-74-7
75-33-2
107-03-9
57-55-6
106-51-4
7783-61-1
100-42-5
110-15-6
7446-09-5
2551-62-4
7446-11-9
100-21-0
254.49432
128.212
114.22852
144.211
130.22792
130.228
128.21204
128.21204
112.21264
146.29352
110.19676
90.03488
31.9988
47.9982
212.41458
86.1323
72.14878
102.132
88.1482
88.1482
86.1323
86.1323
70.1329
104.21378
104.21378
68.11702
68.11702
178.2292
94.11124
119.1207
148.11556
40.06386
44.09562
60.09502
60.095
122.20746
58.07914
74.0785
55.0785
102.1317
59.11026
120.19158
42.07974
88.10512
76.16062
76.16062
76.09442
108.09476
104.07911
104.14912
118.08804
64.0638
146.0554192
80.0632
166.13084
0.2137
0.22273
0.2156
0.203
0.235281
0.20955
0.2132
0.21732
0.20467
0.2012
0.2095
0.26335
0.2741
0.17483
0.20649
0.23894
0.2537
0.1848
0.223042
0.21875
0.2161
0.21569
0.21361
0.20597
0.2086
0.22102
0.21282
0.13753
0.18831
0.16326
0.22946
0.23081
0.26755
0.23144
0.20161
0.1831
0.31721
0.1954
0.26743
0.2332
0.2632
0.18707
0.24719
0.2247
0.21706
0.2202
0.2152
0.26524
–0.0002252
–0.00025037
–0.00029483
–0.0002
–0.00025
–0.00023733
–0.0002494
–0.00024969
–0.0002675
–0.0002142
–0.00025334
–0.00022461
–0.00138
0.00075288
–0.00021911
–0.00029724
–0.000576
–0.0001434
–0.00025
–0.00027849
–0.00024866
–0.00024081
–0.00030777
–0.00024518
–0.00024536
–0.000322
–0.0002856
–0.000025247
–0.0001
–0.00017777
–0.00021345
–0.0004078
–0.00066457
–0.00025
–0.00021529
–0.00020275
–0.000528
–0.000164
–0.00033418
–0.0003096
–0.0004278
–0.00019846
–0.00048824
–0.000264
–0.00028952
–0.00028535
–0.0000497
–0.00028676
0.20215
0.27216
0.38218
0.2544
0.92882
0.3063
–0.0002201
–0.00023183
–0.0006254
–0.0006595
–0.0030803
–0.00028541
–2.5228E-06
0.000000344
2.774E-07
0.000000412
0.00000266
301.31
251.65
216.38
289.65
257.65
241.55
252.85
255.55
171.45
223.95
193.55
462.65
60
77.35
283.07
191.59
143.42
239.15
273.15
200
196.29
234.18
108.02
160.75
197.45
167.45
163.83
372.38
314.06
243.15
404.15
136.87
85.47
200
185.26
199
165
252.45
180.37
178.15
188.36
173.55
87.89
180.25
142.61
159.95
213.15
388.85
0.1458
0.1597
0.1518
0.1451
0.1709
0.1522
0.1501
0.1535
0.1588
0.1532
0.1605
0.1594
0.1913
0.2180
0.1445
0.1820
0.1782
0.1505
0.1548
0.1631
0.1673
0.1593
0.1804
0.1666
0.1602
0.1671
0.1660
0.1281
0.1569
0.1200
0.1432
0.1750
0.2128
0.1814
0.1617
0.1428
0.2301
0.1540
0.2072
0.1780
0.1972
0.1526
0.2043
0.1771
0.1758
0.1746
0.2046
0.1537
589.86
445.15
398.83
512.85
570.15
452.9
499
440.65
394.41
472.19
399.35
516
150
161.85
543.84
375.15
445
458.65
353.15
392.2
375.46
375.14
303.22
385.15
399.79
313.33
329.27
610.03
454.99
439.43
557.65
238.65
350
370.35
425
431.65
322.15
543.15
370.25
434.82
333.15
583.15
340.49
483.15
325.71
340.87
460.75
545
0.0809
0.1113
0.0980
0.1004
0.0927
0.1021
0.0888
0.1073
0.0992
0.1001
0.1083
0.1475
0.0671
0.2306
0.0873
0.1274
0.0655
0.1190
0.1348
0.1095
0.1227
0.1254
0.1203
0.1115
0.1105
0.1201
0.1188
0.1221
0.1428
0.0851
0.1104
0.1335
0.0689
0.1389
0.1101
0.0956
0.1471
0.1063
0.1437
0.0986
0.1664
0.0713
0.0810
0.0972
0.1228
0.1229
0.1923
0.1090
242.54
460.85
197.67
223.15
289.95
700.15
0.1488
0.1653
0.2586
0.1072
0.2593
0.1065
418.31
591
400
318.69
481.47
795.28
0.1101
0.1351
0.1320
0.0442
0.0624
0.0793
(Continued)
2-304
TABLE 2-147
Cmpd.
no.
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued )
Name
o-Terphenyl
Tetradecane
Tetrahydrofuran
1,2,3,4-Tetrahydronaphthalene
Tetrahydrothiophene
2,2,3,3-Tetramethylbutane
Thiophene
Toluene
1,1,2-Trichloroethane
Tridecane
Triethyl amine
Trimethyl amine
1,2,3-Trimethylbenzene
1,2,4-Trimethylbenzene
2,2,4-Trimethylpentane
2,3,3-Trimethylpentane
1,3,5-Trinitrobenzene
2,4,6-Trinitrotoluene
Undecane
1-Undecanol
Vinyl acetate
Vinyl acetylene
Vinyl chloride
Vinyl trichlorosilane
Water
m-Xylene
o-Xylene
p-Xylene
Formula
C18H14
C14H30
C4H8O
C10H12
C4H8S
C8H18
C4H4S
C7H8
C2H3Cl3
C13H28
C6H15N
C3H9N
C9H12
C9H12
C8H18
C8H18
C6H3N3O6
C7H5N3O6
C11H24
C11H24O
C4H6O2
C4H4
C2H3Cl
C2H3Cl3Si
H2O
C8H10
C8H10
C8H10
CAS
84-15-1
629-59-4
109-99-9
119-64-2
110-01-0
594-82-1
110-02-1
108-88-3
79-00-5
629-50-5
121-44-8
75-50-3
526-73-8
95-63-6
540-84-1
560-21-4
99-35-4
118-96-7
1120-21-4
112-42-5
108-05-4
689-97-4
75-01-4
75-94-5
7732-18-5
108-38-3
95-47-6
106-42-3
Mol. wt.
230.30376
198.388
72.10572
132.20228
88.17132
114.22852
84.13956
92.13842
133.40422
184.36142
101.19
59.11026
120.19158
120.19158
114.22852
114.22852
213.10452
227.1311
156.30826
172.30766
86.08924
52.07456
62.49822
161.48972
18.01528
106.165
106.165
106.165
C1
0.16853
0.20293
0.19428
0.14563
0.20414
0.17835
0.20571
0.20463
0.20731
0.20447
0.1918
0.23813
0.18854
0.19216
0.1659
0.16815
0.18421
0.19898
0.20515
0.218744
0.256
0.22838
0.2333
0.21831
–0.432
0.20044
0.19989
0.20003
C2
–0.00010817
–0.00021798
–0.000249
–0.0000536
–0.00021217
–0.00023704
–0.00020028
–0.00024252
–0.00024997
–0.00022612
–0.0002453
–0.00038397
–0.0001963
–0.0002105
–0.00022686
–0.00020535
–0.00016097
–0.00017659
–0.00023933
–0.00025
–0.0003542
–0.00035173
–0.00039223
–0.00029122
0.0057255
–0.00023544
–0.0002299
–0.00023573
C3
C4
–0.000008078 1.861E-09
C5
Tmin, K
329.35
279.01
164.65
237.38
176.98
373.96
234.94
178.18
236.5
267.76
158.45
156.08
247.79
229.33
165.78
172.22
398.4
354
247.57
281
180.35
173.15
119.36
178.35
273.16
225.3
247.98
286.41
Thermal cond.
at Tmin
0.1329
0.1421
0.1533
0.1329
0.1666
0.0897
0.1587
0.1614
0.1482
0.1439
0.1529
0.1782
0.1399
0.1439
0.1283
0.1328
0.1201
0.1365
0.1459
0.1485
0.1921
0.1675
0.1865
0.1664
0.5672
0.1474
0.1429
0.1325
Tmax, K
Thermal
cond. at Tmax
723.15
526.73
339.12
480.77
394.27
426
357.31
474.85
482
508.62
483.15
276.02
449.27
442.53
372.39
387.91
629.6
625
469.08
561.2
410
278.25
345.6
434.52
633.15
413.1
417.58
413.1
0.0903
0.0881
0.1098
0.1199
0.1205
0.0774
0.1341
0.0895
0.0868
0.0895
0.0733
0.1321
0.1003
0.0990
0.0814
0.0885
0.0829
0.0886
0.0929
0.0784
0.1108
0.1305
0.0978
0.0918
0.4272
0.1032
0.1039
0.1026
The liquid thermal conductivity is calculated by k = C1 + C2T + C3T2 + C4T3 + C5T4 where k is the thermal conductivity in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure,
whichever is higher.
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and
reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data
Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
TRAnSPORT PROPERTIES
TABLE 2-148
FIG. 2-20 and TABLE 2-148
Nomograph (right) for thermal conductivity of organic liquids. (From B.V. Mallu and Y.J. Rao, Hydroc. Proc. 78, 1988.)
2-305
2-306
PHYSICAL AnD CHEMICAL DATA
TABLE 2-149
Thermal-Conductivity-Temperature Table for Metals and nonmetals*
Thermal conductivities tabulated in watts per meter-kelvin
Temperature, K
Substance
20
40
60
80
7
38,000
470
47
240
32
13,500
230
196
100
300
400
500
121
2,300
110
810
45
174
850
80
1,400
31
160
380
60
1,650
24
125
300
48
1,490
22
55
237
32
480
18
36
273
26
272
16
26
240
22
196
14
20
237
20
146
12
165
900
400
250
4
305
250
570
450
9
400
150
450
380
16
327
120
250
250
18
230
110
180
190
19
170
110
158
160
20
45
105
111
120
23
25
104
90
100
25
15
101
87
85
27
Copper
Gallium
Gold
Graphite†
Graphite‡
19,000
2,200
2,800
27
81
10,700
640
1,500
108
420
2,100
250
520
135
1,630
850
200
380
81
2,980
570
170
350
54
4,290
483
140
345
39
4,980
413
100
327
15
3,250
398
85
315
10
2,000
Hastelloy
Inconel
Iridium
Iron
Lead
1
2
1,300
710
175
3
4
1,900
1,000
57
4
8
750
560
43
5
10
360
270
42
6
11
230
170
41
7
11
172
132
40
9
14
147
94
37
10
15
145
80
35
Magnesium
Magnesium oxide
Manganese
Manganin
Mercury
1,200
1,100
2
2
54
1,300
3,100
2
4
40
620
2,200
4
9
35
290
950
5
11
33
190
460
5
13
33
169
260
6
13
32
159
75
7
17
32
Molybdenum
Nickel
Nylon
Palladium
Platinum
150
2,600
0.04
1,200
1,200
280
1,700
0.10
610
490
350
570
0.17
160
130
250
290
0.20
100
92
210
200
0.23
88
82
179
158
0.25
80
79
PTFE§
Pyrex
Quartz
Rhodium
Rubber
0.94
0.12
1,200
2,900
1.43
0.20
480
3,900
1.94
0.33
82
1,000
0.13
2.1
0.42
40
370
0.15
2.15
0.51
30
250
0.16
140
57
25
15
16,500
108
300
5,200
146
93
1,100
88
29
14
320
28
130
39
880
100
110
59
Alumina
Aluminum
Antimony
Beryllium oxide
Bismuth
Boron
Cadmium
Chromium
Cobalt
Constantan
Selenium (axis)
Silica
Silver
Tantalum
Tellurium
Tin
Titanium
Tungsten
Uranium
Zinc
Zirconium
10
100
200
1000
1200
16
232
10
220
8
93
7
99
6
105
111
70
47
33
25
12
99
85
70
30
81
71
65
62
61
392
388
383
371
357
342
312
7
1,460
309
5
1,140
304
4
930
292
3
680
278
3
530
262
2
440
2
370
11
13
143
69
34
140
61
33
55
31
43
19
33
22
28
24
31
26
156
48
8
22
8
153
36
9
28
10
151
27
9
34
11
149
21
146
13
84
10
98
8
112
7
40
12
13
14
143
106
0.28
78
75
138
91
0.30
78
73
134
80
130
72
126
66
118
67
112
72
105
76
100
80
78
72
80
72
72
73
78
78
81
2.16
0.57
2.20
0.88
2.25
1.1
190
0.17
160
0.20
10
8
6
630
68
17
500
62
13
430
59
11
358
61
62
101
37
330
20
150
42
90
33
310
22
135
38
84
31
280
23
130
34
2.3
1.6
2.5
2.1
150
0.22
145
0.24
140
0.25
425
58
6
4
1.34
424
57
4
3
1.52
420
58
3
2
1.70
413
58
3
72
26
190
26
123
25
67
21
180
28
120
23
62
20
170
30
116
22
60
20
150
32
110
21
600
1.87
405
59
800
2.22
389
59
2.60
374
60
1400
19
140
110
21
∗ Especially at low temperatures, the thermal conductivity can often be markedly reduced by even small traces of impurities. This table, for the highest-purity specimens available,
should thus be used with caution in applications with commercial materials. From Perry, Engineering Manual, 3d ed., McGraw-Hill, New York, 1976. A more detailed table appears
as Section 5.5.6 in the Heat Exchanger Design Handbook, Hemisphere Pub. Corp., Washington, DC, 1983.
†
Parallel to basal plane.
‡
Perpendicular to basal plane.
§
Also known as Teflon, etc.
TRAnSPORT PROPERTIES
TABLE 2-150
Thermal Conductivity of Chromium Alloys*
TABLE 2-151 Thermal Conductivity of Some Alloys
at High Temperature*
k = Btu/(h⋅ft2)(°F/ft)
American iron and steel
institute type no.
301, 302, 302B, 303, 304, 316†
308
309, 310
321, 347
403, 406, 410, 414, 416†
430, 430F†
442
501, 502†
k at
212°F
k at
932°F
9.4
8.8
8.0
9.3
14.4
15.1
12.5
21.2
12.4
12.5
10.8
12.8
16.6
15.2
14.2
19.5
2-307
Thermal conductivity, Btu/( ft)(hr)(°R)
°R
∗ Table 2-150 is based on information from manufacturers.
†
Shelton and Swanger (National Bureau of Standards), Trans. Am. Soc. Steel Treat., 21,
1061–1078 (1933).
Kovar
Advance
Monel
Hastelloy A
Inconel
Nichrome V
5.6
6.2
6.8
7.3
7.8
6.0
6.5
7.0
7.6
8.1
5.5
6.1
6.7
7.3
7.8
500
600
700
800
900
7.8
8.3
8.6
8.7
8.7
11.4
12.6
13.9
15.1
9.0
10.2
11.2
12.3
13.4
1000
1100
1200
1300
1400
8.9
9.2
9.5
9.8
10.2
16.4
17.6
18.8
20.0
21.2
14.4
15.4
16.5
17.6
18.7
8.4
9.0
9.5
10.1
10.7
8.6
9.1
9.7
10.2
10.8
8.4
9.0
9.5
10.1
10.7
1500
1600
1700
1800
1900
10.5
10.8
11.1
11.3
11.5
22.5
23.8
25.0
26.2
27.4
19.8
20.8
21.9
23.0
24.0
11.3
11.8
12.3
12.9
13.4
11.3
11.8
12.4
13.0
13.6
11.3
11.9
12.4
13.0
13.5
2000
2100
2200
11.8
12.1
12.3
28.7
30.0
25.1
26.1
27.2
14.0
14.6
15.1
14.0
14.5
15.0
14.1
14.7
15.3
∗Silverman, J. Metals, 5, 631 (1953). Copyright American Institute of Mining,
Metallurgical and Petroleum Engineers, Inc.
TABLE 2-152
Thermophysical Properties of Selected nonmetallic Solid Substances
Material
Density,
kg/m3
Alumina
Asphalt
Bakelite
Beryllia
Brick
3975
2110
1300
3000
1925
Brick, fireclay
Carbon, amorphous
Clay
Coal
Cotton
2640
1950
1460
1350
80
Diamond
Granite
Hardboard
Magnesite
Magnesia
3500
2630
1000
3025
3635
Emissivity
Specific heat,
kJ/(kg⋅K)
Thermal conductivity,
W/(m⋅K)
0.82
0.93
0.765
0.920
1.465
1.030
0.835
36
0.06
1.4
270
0.72
11.9
0.03
0.74
88
0.45
0.960
0.724
0.880
1.26
1.30
1.0
1.6
1.3
0.26
0.06
0.39
1.13
1.01
0.15
0.58
0.509
0.775
1.38
1.13
0.943
2300
2.79
0.15
4.0
48
1290
1.37
0.11
1.2
14
0.93
0.86
0.91
0.80
0.38
0.72
Oak
Paper
Pine
Plaster board
Plywood
770
930
525
800
540
0.90
0.83
0.84
0.91
Pyrex
Rubber
Rubber, foam
Salt
Sandstone
2250
1150
70
2150
0.92
0.92
0.90
0.34
0.59
Silica
Sapphire
Silicon carbide
Soil
3975
3160
2050
Teflon
Thoria
Urethane foam
Vermiculite
2200
4160
70
120
2.38
1.34
2.75
Thermal diffusivity,
m2/s × 106
0.18
0.011
0.12
0.17
0.12
0.10
0.01
0.54
0.74
0.09
0.854
0.745
1.4
0.2
0.03
7.1
2.9
0.79
0.48
0.86
0.38
0.743
0.765
0.675
1.84
1.3
46
110
0.52
15
230
0.14
0.92
0.28
0.35
0.71
1.05
0.84
0.26
14
0.03
0.06
0.34
4.7
0.36
0.60
1.22
0.835
2.00
0.18
1.8
note: Difficulties of accurately characterizing many of the specimens mean that many of the values presented here must be regarded as being
of order of magnitude only. For some materials, actual measurement may be the only way to obtain data of the required accuracy. To convert kilograms per cubic meter to pounds per cubic foot, multiply by 0.062428; to convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Fahrenheit, multiply by 0.23885.
2-308
TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons
LFL
UFL
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Paraffin hydrocarbons
Olefins
Olefins
Olefins
Olefins
Olefins
Olefins
Acetylenes
Group
Methane
Ethane
Propane
n-Butane
Isobutane
n-Pentane
Isopentane
Neopentane
n-Hexane
n-Heptane
2,3-Dimethylpentane
n-Octane
2,2,4-Trimethylpentane
n-Nonane
n-Decane
Ethylene
Propylene
1-Butene
cis-2-Butene
trans-2-Butene
1-Pentene
Acetylene
Compound
74-82-8
74-84-0
74-98-6
106-97-8
75-28-5
109-66-0
78-78-4
463-82-1
110-54-3
142-82-5
565-59-3
111-65-9
540-84-1
111-84-2
124-18-5
74-85-1
115-07-1
106-98-9
590-18-1
624-64-6
109-67-1
74-86-2
CAS
CH4
C2H6
C3H8
C4H10
C4H10
C5H12
C5H12
C5H12
C6H14
C7H16
C7H16
C8H18
C8H18
C9H20
C10H22
C2H4
C3H6
C4H8
C4H8
C4H8
C5H10
C2H2
Formula
5.00
3.00
2.10
1.60
1.80
1.40
1.40
1.40
1.20
1.05
1.10
0.96
0.95
0.85
0.75
2.70
2.15
1.60
1.70
1.70
1.40
2.50
15.00
12.40
9.50
8.40
8.40
7.80
7.60
7.50
7.20
6.70
6.70
6.50
6.00
5.60
5.40
36.00
11.20
10.00
9.70
9.70
8.70
80.00
Flash point (K)
87.12
139.00
171.00
199.15
191.00
224.15
218.00
205.00
250.15
269.00
261.00
287.15
265.00
304.15
322.85
129.00
169.00
198.00
205.00
203.00
222.00
151.00
Acetylenes
Acetylenes
Aromatics
Aromatics
Aromatics
Aromatics
Aromatics
Aromatics
Cyclic hydrocarbons
Cyclic hydrocarbons
Cyclic hydrocarbons
Cyclic hydrocarbons
Cyclic hydrocarbons
Cyclic hydrocarbons
Cyclic hydrocarbons
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Alcohols
Aldehydes
Aldehydes
Aldehydes
Vinylacetylene
Methylacetylene
Benzene
Toluene
o-Xylene
Ethylbenzene
Cumene
Anthracene
Cyclopropane
Furan
Cyclopentadiene
Cyclohexane
Methylcyclohexane
Phenol
Dicyclopentadiene
Methanol
Ethanol
Allyl Alcohol
1-Propanol
Isopropanol
1-Butanol
2-Butanol
2-Methyl-1-propanol
2-Methyl-2-propanol
Cyclohexanol
Formaldehyde
Acetaldehyde
Acrolein
689-97-4
74-99-7
71-43-2
108-88-3
95-47-6
100-41-4
98-82-8
120-12-7
75-19-4
110-00-9
542-92-7
110-82-7
108-87-2
108-95-2
77-73-6
67-56-1
64-17-5
107-18-6
71-23-8
67-63-0
71-36-3
78-92-2
78-83-1
75-65-0
108-93-0
50-00-0
75-07-0
107-02-8
C4H4
C3H4
C6H6
C7H8
C8H10
C8H10
C9H12
C14H10
C3H6
C4H4O
C5H6
C6H12
C7H14
C6H6O
C10H12
CH4O
C2H6O
C3H6O
C3H8O
C3H8O
C4H10O
C4H10O
C4H10O
C4H10O
C6H12O
CH2O
C2H4O
C3H4O
2.20
1.70
1.20
1.10
1.10
1.00
0.88
0.60
2.40
2.00
1.70
1.30
1.15
1.70
0.80
7.18
3.30
2.50
2.10
2.00
1.70
1.70
1.70
1.84
1.20
7.00
4.00
2.80
31.70
57.30
8.00
7.10
6.40
6.70
6.50
5.20
10.40
23.00
14.60
7.80
6.70
8.60
6.30
36.50
19.00
18.00
14.00
12.70
11.30
9.80
11.00
9.00
11.10
73.00
30.00
31.00
211.00
192.00
262.00
279.15
305.15
296.15
309.15
458.15
180.00
237.00
227.00
255.93
269.15
352.15
318.15
284.15
286.15
294.00
297.59
285.15
310.50
296.15
302.32
284.26
334.15
219.80
232.00
247.15
Autoignition T (K)
810.00
745.00
723.00
561.00
733.15
516.00
693.15
723.15
498.00
477.00
608.15
479.00
684.15
478.00
474.00
723.15
728.15
657.00
598.00
597.00
546.00
578.15
Decomposes violently on heating.
Forms explosive peroxides with air or oxygen.
613.15
833.15
753.15
736.15
703.15
697.00
813.15
771.00
663.15
913.15
518.15
523.15
988.00
783.15
737.00
696.00
651.00
644.00
728.75
616.00
663.15
681.15
751.00
573.15
697.15
449.15
507.00
Aldehydes
Aldehydes
Aldehydes
Aldehydes
Aldehydes
Aldehydes
Ethers
Ethers
Ethers
Ethers
Ketones
Ketones
Ketones
Acids
Acids
Acids
Esters
Esters
Esters
Esters
Esters
Esters
Esters
Esters
Esters
Esters
Inorganic
Inorganic
Inorganic
Oxides
Oxides
Oxides
Oxides
Oxides
Peroxides
Sulfur containing
Sulfur containing
Sulfur containing
Sulfur containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Chlorine containing
Bromides
Glycols
Glycols
Propanal
trans-Crotonaldehyde
cis-Crotonaldehyde
2-Methylpropanal
Butanal
Furfural
Dimethyl ether
Methyl vinyl ether
Diethyl ether
Diphenyl ether
Acetone
Methyl ethyl ketone
Acetophenone
Acetic acid
Hydrogen cyanide
Formic acid
Methyl formate
Ethyl formate
Methyl acetate
Vinyl acetate
Ethyl acetate
n-Propyl acetate
Isopropyl acetate
n-Butyl acetate
Isobutyl acetate
n-Pentyl acetate
Hydrogen
Ammonia
Cyanogen
Carbon monoxide
Ethylene oxide
1,2-Propylene oxide
1,4-Dioxane
Mesityl oxide
Di-t-Butyl peroxide
Carbon disulfide
Hydrogen sulfide
Carbonyl sulfide
Dimethyl sulfide
Methyl chloride
Ethyl chloride
Isopropyl chloride
1,2-Dichloroethane
1,2-Dichloropropane
Dichloromethane
2-Chloroethanol
Trichloroethylene
Hexachloro-1,3-Butadiene
Vinyl chloride
Monochlorobenzene
Benzyl chloride
Bromomethane
Ethylene glycol
Diethylene glycol
123-38-6
123-73-9
15798-64-8
78-84-2
123-72-8
98-01-1
115-10-6
107-25-5
60-29-7
101-84-8
67-64-1
78-93-3
98-86-2
64-19-7
74-90-8
64-18-6
107-31-3
109-94-4
79-20-9
108-05-4
141-78-6
109-60-4
108-21-4
123-86-4
110-19-0
628-63-7
1333-74-0
7664-41-7
460-19-5
630-08-0
75-21-8
75-56-9
123-91-1
141-79-7
110-05-4
75-15-0
7783-06-4
463-58-1
75-18-3
74-87-3
75-00-3
75-29-6
107-06-2
78-87-5
75-09-2
107-07-3
79-01-6
87-68-3
75-01-4
108-90-7
100-44-7
74-83-9
107-21-1
111-46-6
C3H6O
C4H6O
C4H6O
C4H8O
C4H8O
C5H4O2
C2H6O
C3H6O
C4H10O
C12H10O
C3H6O
C4H8O
C8H8O
C2H4O2
CHN
CH2O2
C2H4O2
C3H6O2
C3H6O2
C4H6O2
C4H8O2
C5H10O2
C5H10O2
C6H12O2
C6H12O2
C7H14O2
H2
H3N
C2N2
CO
C2H4O
C3H6O
C4H8O2
C6H10O
C8H18O2
CS2
H2S
COS
C2H6S
CH3Cl
C2H5Cl
C3H7Cl
C2H4Cl2
C3H6Cl2
CH2Cl2
C2H5ClO
C2HCl3
C4Cl6
C2H3Cl
C6H5Cl
C7H7Cl
CH3Br
C2H6O2
C4H10O3
2.60
2.10
2.10
1.60
1.90
2.10
3.30
2.60
1.70
0.80
2.60
1.80
1.10
4.00
5.60
12.00
5.20
2.76
3.13
2.60
2.18
1.80
1.76
1.40
1.42
1.10
4.00
15.00
6.60
12.50
3.00
2.20
2.00
1.30
0.74
1.30
4.00
12.00
2.20
8.10
3.80
2.80
4.50
3.30
14.00
4.90
12.00
2.90
3.60
1.30
1.10
10.10
3.10
1.70
17.00
15.50
15.50
11.00
12.50
19.30
26.20
39.00
46.00
6.00
13.00
11.00
6.70
19.90
40.00
38.00
23.00
15.70
14.00
13.40
11.50
8.00
7.20
7.60
8.00
7.10
75.00
28.00
32.00
74.20
100.00
35.50
22.00
8.80
8.20
50.00
44.00
29.00
19.70
17.20
15.40
10.70
16.00
14.50
22.00
15.90
29.00
15.70
33.00
9.60
7.10
16.00
42.00
37.00
243.15
286.15
285.93
254.15
262.15
333.15
193.00
217.15
228.15
388.15
253.15
264.15
350.15
312.04
255.00
323.15
247.00
254.15
260.15
265.37
269.00
283.71
274.82
298.15
291.00
310.15
14.00
209.00
214.00
71.00
225.00
236.00
284.15
301.00
277.15
243.15
167.00
186.00
237.15
203.00
223.15
238.15
286.00
286.15
265.00
328.15
305.15
389.00
205.00
301.15
333.15
230.00
384.15
413.15
500.15
505.00
505.00
478.00
503.15
589.00
499.15
560.15
433.15
891.15
738.15
789.00
843.15
700.00
811.00
753.00
729.00
728.15
775.00
700.00
700.00
723.00
733.15
694.00
696.00
633.15
793.15
924.00
984.00
882.00
702.00
703.15
453.15
618.00
Organic peroxides can ignite easily
363.15
533.15
477.00
478.15
905.00
802.00
866.00
686.00
830.00
888.15
698.15
683.15
883.15
745.00
911.00
858.15
800.00
669.00
636.15
2-309
(Continued)
2-310
TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons (Continued )
Group
Glycols
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Amines
Miscellaneous
Miscellaneous
Miscellaneous
Miscellaneous
Miscellaneous
Miscellaneous
Miscellaneous
Miscellaneous
Compound
Triethylene glycol
Methylamine
Ethylamine
Dimethylamine
Isopropylamine
Trimethylamine
Allylamine
Diethylamine
Tert-Butylamine
Triethylamine
Cyclohexylamine
Monoethanolamine
Diethanolamine
Dimethylethanolamine
Acrylonitrile
Aniline
Diborane
Methyl methacrylate
Styrene
Biphenyl
Methyl acrylate
Phthalic anhydride
CAS
112-27-6
74-89-5
75-04-7
124-40-3
75-31-0
75-50-3
107-11-9
109-89-7
75-64-9
121-44-8
108-91-8
141-43-5
111-42-2
108-01-0
107-13-1
62-53-3
19287-45-7
80-62-6
100-42-5
92-52-4
96-33-3
85-44-9
Formula
C6H14O4
CH5N
C2H7N
C2H7N
C3H9N
C3H9N
C3H7N
C4H11N
C4H11N
C6H15N
C6H13N
C2H7NO
C4H11NO2
C4H11NO
C3H3N
C6H7N
B2H6
C5H8O2
C8H8
C12H10
C4H6O2
C8H4O3
LFL
UFL
0.90
4.90
2.70
2.80
2.00
2.00
2.03
1.70
1.70
1.20
0.66
3.00
1.70
1.40
3.05
1.30
0.80
1.70
1.10
0.70
2.18
1.20
9.20
20.70
14.00
14.40
10.40
11.60
24.30
10.10
8.90
8.00
9.40
13.10
9.80
12.20
17.00
11.00
88.00
12.50
6.10
5.80
14.40
9.20
Flash point (K)
429.15
217.00
227.00
223.15
236.15
207.00
252.00
245.15
236.00
262.15
299.65
366.55
445.15
312.15
268.15
344.15
142.00
284.15
305.00
383.15
270.00
425.00
Autoignition T (K)
644.00
703.15
657.00
595.00
673.15
463.15
647.039
583.15
648.15
522.15
566.15
683.15
935.00
568.15
754.00
890.00
325.00
708.15
763.15
813.15
741.15
857.00
Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE,
and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles,
DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”.
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
2-311
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES*
InTRODUCTIOn
Physical property values, sufficiently accurate for many engineering
applications, can be estimated in the absence of reliable experimental data.
The purpose of this section is to provide a set of recommended prediction
methods for general engineering use. It is not intended to be a comprehensive review, and many additional methods are available in the literature. Methods recommended in this section were selected on the basis of
accuracy, generality, and, in most cases, simplicity or ease of use. They generally correspond to the methods tested and given priority in the DIPPR 801
database project.*
Properties included in this subsection are divided into 10 categories: (1)
physical constants including critical properties, normal melting and boiling
points, acentric factor, radius of gyration, dipole moment, refractive index,
and dielectric constant; (2) liquid and solid vapor pressure; (3) thermal
properties including enthalpy and Gibbs energy of formation and ideal gas
entropy; (4) latent enthalpies of vaporization, fusion, and sublimation; (5)
heat capacities for ideal and real gases, liquids, and solids; (6) densities of
gas, liquid, and solid phases; (7) gas and liquid viscosity; (8) gas and liquid
thermal conductivity; (9) surface tension; and (10) flammability properties
including flash point, flammability limits, and autoignition temperature.
Each of the 10 subsections gives a definition of the properties and a description of one or more recommended prediction methods. Each description
lists the type of method, its uncertainty, its limitations, and the expected
*The Design Institute for Physical Properties (DIPPR) is an industrial consortium
under the auspices of AIChE; Project 801, Evaluated Process Design Data, is a purecomponent database of industrially important compounds. Values and procedures
used with permission of the DIPPR 801 Technical Committee.
uncertainty of the predicted value. A numerical example is also given to
illustrate use of the method. For brevity, symbols used for physical properties and for variables and constants in the equations are defined under
Nomenclature and are not necessarily defined after their first use except
where doing so clarifies usage. A list of equation and table numbers in which
variables appear is included in the Nomenclature section for quick crossreferencing. Although emphasis is on pure-component properties, some
mixture estimation techniques have been included for physical constants,
density, viscosity, thermal conductivity, surface tension, and flammability.
Correlation and estimation of properties that are inherently multicomponent (e.g., diffusion coefficients, mixture excess properties, activity coefficients) are treated elsewhere in this handbook.
UnITS
The International System (SI) of metric units has been used throughout
this section. Where possible, the estimation equations are set up in dimensionless groups to eliminate the need to specify units of variables and to
facilitate unit conversions. For example, rather than use Pc as an equation variable, the dimensionless group (Pc/Pa) is used. When a value for Pc
expressed in any units (say, Pc = 6.53 MPa) is inserted into this group, the
result is dimensionless with an explicit indication of conversion factors that
must be included, such as
Pc 6.53 MPa 6.53 MPa 10 6 Pa
=
=
= 6.53 × 10 6
Pa
Pa
Pa MPa
Appropriate unit conversion factors are found in Sec. 1 of this handbook.
nomenclature
Physical constants
h
k
NA
R
Properties
Definition
Planck’s constant
Boltzmann’s constant
Avogadro’s number
Gas constant
Value
6.626 × 10−34 J ⋅ s
1.3806 × 10−23 J/(molecule ⋅ K)
6.022 × 1026 molecule/kmol
8314.3 Pa ⋅ m3/(kmol ⋅ K)
Definition
Typical units
A, B, C
AIT
Avdw
B, B(T)
CP
C op
Molecular principal moments of inertia
Autoignition temperature
Van der Waals area
Second virial coefficient
Isobaric molar heat capacity
Ideal gas isobaric molar heat capacity
kg ⋅ m2
K
m2/kmol
m3/kmol
J/(kmol ⋅ K)
J/(kmol ⋅ K)
Cv
Hi
k
LFL
M
n
P
P
Pc
Pr
P*
P*meas
Pr*
Pt*
RD
Rg
So
Ss
Sr
Svib
Constant-volume molar heat capacity
Enthalpy of compound i
Thermal conductivity
Lower flammability limit
Molecular weight
Refractive index
Pressure
Parachor
Critical pressure
Reduced pressure; Pr = P/Pc
Vapor pressure
Measured vapor pressure value
Reduced vapor pressure; Pr* = P*/Pc
Vapor pressure at triple point
Molar refraction
Radius of gyration
Ideal gas entropy
Standard state entropy
Rotational contribution to entropy
Vibrational contribution to entropy
J/(kmol ⋅ K)
J/kmol
W/(m ⋅ K)
%
kg/kmol
unitless
Pa
unitless
Pa
unitless
Pa
Pa
unitless
Pa
cm3/mol
m
J/(kmol ⋅ K)
J/(kmol ⋅ K)
J/(kmol ⋅ K)
J/(kmol ⋅ K)
2-312
PHYSICAL AnD CHEMICAL DATA
nomenclature (Continued )
Properties
Definition
Typical units
T
Tad
Tb
Tbr
Tc
TFP
Tm
Tmeas
Tr
UFL
V
Vc
Vr
wi
xi
yi
Z
Zc
Zi
∆G of
Temperature
Adiabatic flame temperature
Normal boiling point temperature
Reduced temperature at Tb; Tbr = Tb/Tc
Critical temperature
Flash point temperature
Melting temperature
T at which a dependent property was measured
Reduced temperature; Tr = T/Tc
Upper flammability limit
Molar volume
Critical volume
Reduced volume; Vr = ZTr/Pr
Mass fraction of component i
Mole fraction of component i
Mole fraction of component i in vapor phase
Compressibility factor; Z = PV/RT
Critical compressibility factor; Zc = PcVc/RTc
Compressibility factor of reference fluid i
Ideal gas standard Gibbs energy of formation
K
K
K
unitless
K
K
K
K
unitless
%
m3/kmol
m3/kmol
unitless
unitless
unitless
unitless
unitless
unitless
unitless
J/kmol
∆G sf
Standard state Gibbs energy of formation
J/kmol
∆H of
Ideal gas standard enthalpy of formation
J/kmol
∆H sf
Standard state enthalpy of formation
J/kmol
DHfus
DHrxn
DHsub
DHu
∆S sf
Enthalpy of fusion
Enthalpy change per mole of reaction as written
Enthalpy of sublimation
Enthalpy of vaporization
Standard state entropy of formation
J/kmol
J/kmol
J/kmol
J/kmol
J/(kmol ⋅ K)
∆S of
Ideal gas entropy of formation
J/(kmol ⋅ K)
DSfus
DZv
d
e
h
ho
m
mr
r
ρc
ρr
ρS, ρL, ρV
σ
σm
t
tb
fi
w
Latent entropy of fusion
Change in compressibility factor upon vaporization
Solubility parameter
Dielectric constant
Viscosity
Viscosity at low pressure
Dipole moment
Reduced dipole moment [defined in Eq. (2-66)]
Molar density; r = V −1
Critical molar density; ρc = Vc−1
Reduced molar density; ρr = ρ/ρc
Density of solid, liquid, vapor, respectively
Surface tension
Surface tension of mixture
Complementary reduced temperature (1 − Tr)
t at the normal boiling point (1 − Tbr)
Volume fraction of component i
Acentric factor
J/(kmol ⋅ K)
unitless
J1/2 ⋅ m−3/2
unitless
Pa ⋅ s
Pa ⋅ s
D
unitless
kmol/m3
kmol/m3
unitless
kmol/m3
mN/m
mN/m
unitless
unitless
unitless
unitless
Equation variables
Definition
a
a, b, c, . . .
a, b, c
ai
a, b
a, b
ai, bi, di
aα
A, B, C, . . .
EoS constant
GC values for Cp and h
Correlation coefficients
GC values
Terms in second virial correlation
Chickos correlation parameters
GC values for liquid Cp
EoS constant for mixture
Correlation constants/parameters
A
Ai
b
bi, ci, . . .
bi
Factor in liquid k correlation
o
Constants in C p correlation
EoS constant
Reference EoS constants
GC value for AIT
Appears in (Eq. 2-?) or
[Table 2-?]
(70), [172]
(54), (57), (96), [174]
(25), (27), (42), (43), (44), (69)
(46), (96), [164], [174]
(65)
(42), (43), (44)
(54), [166]
(78)
(2), (23), (24), (26), (28), (28a),
(38), (40), (53), (54), (56), (69),
(71), (82), (84), (86), (87), (94),
(95), (100), (101), (102)
(110), [176]
(48), (49), (70)
(70), [172]
(69), [171]
(129), [180]
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
nomenclature (Continued )
Equation variables
Definition
Appears in (Eq. 2-?) or
[Table 2-?]
b
B(i)
C
EoS constant for mixture
Second virial expansion term
Number of components in mixture
C
Ci
Parameter in modified Pachaiyappan method
GC values for some methods
Cij
(Cop)i
Csj
Cst
Ctj
fi
F(i)
F
GI
Gij
gEc
gEr
h
K
m
nhvy
nA
nE
NG
ni
Group-group intramolecular interaction pair
GC values for ideal gas heat capacity
Chickos GC value for C—H group
Fuel concentration for stoichiometric combustion
Chickos GC value for functional group
Halogen correction for DHsub correlation
Vapor pressure deviation function
Factor in surface tension equation
Group-group interaction correction term
Adjustable mixture viscosity parameter
UNIFAC combinatorial excess Gibbs energy
UNIFAC residual excess Gibbs energy
Parameter in Riedel vapor pressure equation
Parameter in Riedel vapor pressure equation
Parameter in modified Pachaiyappan method
Number of non-hydrogen atoms
Number of atoms in the molecule
Number of occurrences of element E in compound
Number of interacting groups
Number of occurrences of group i
nf
ns
nx
N
Number of different functional groups
Number of C—H groups bonded to functional groups
Number of halogen and H atoms
Total number of groups in molecule
NC
Nfi
Ngi
NH
NCR
NO
NR
NS
Nsi
NSi
NX
Pc
q
qi
Qk
ri
r*
Rk
(So)i
t
tm1,i
tm2,i
Tc
Tc,ij
xP
U*
UFLi
Z(0)
Z(1)
Zc,ij
ZRA
ZRA
α, b, g, . . .
Number of C atoms
Number of functional groups of type i
Number of C—H groups of type i bonded to C
Number of H atoms
Number of CH2 groups forming cyclic paraffin
Number of O atoms
Number of nonaromatic rings
Number of S atoms
Number of C—H groups bonded to functional group
Number of Si atoms
Number of halogen atoms
Pseudocritical pressure for mixture
(77)
(62), (63), (64), (65)
(74), (75), (76), (77), (78), (79),
(80), (81), (98)
(109)
(9), (10), (11), (18), (86), [175],
[173]
(12), [156]
(52), [165]
(44), [162]
(127), (128)
(44), [163]
(46), [164]
(29)
(118), (119)
(9), (10), (11), (12)
(97)
(98)
(98)
(28a)
(28a)
(109)
(11), (12), (18)
(1), (34), (35), (51)
(58)
(12)
(9), (10), (11), (13), (15), (16),
(31), (46), (52), (54), (55), (86),
(117), (124), (127), (129)
(44)
(44)
(46)
(18), (31) (46), (54), (57), (58),
(86), (96), (117), (124), (127),
(129)
(123)
(44)
(44)
(123)
(43)
(123)
(43)
(123)
(44)
(123)
(123)
(75)
Rackett equation power for Zc
UNIFAC molecular surface area
UNIFAC group surface area
UNIFAC molecular volume
Dimensionless separation distance
UNIFAC group volume
GC value for entropy
Total number of functional groups
First-order GC contribution for Tm
Second-order GC contribution for Tm
Pseudocritical temperature for mixture
(72), (80)
following (99)
following (99)
following (99)
(4)
following (99)
(31), [161]
(44)
(16), [158]
(16), [159]
(74), (75), (79)
Cross term in mixing rule
Term in the Pailhes method [= log(1 atm/P)]
Dimensionless intermolecular potential
GC contribution
Compressibility factor of simple fluid
Acentric deviation term for Z
Cross term in mixing rule
Modified Rackett correlation parameter
Modified Rackett parameter for mixture
Correlation parameters for k
(79)
(17)
(4)
(127), [178]
(68), [169]
(68), [170]
(79)
following (72)
(80), (81)
(107), (108), (110), [176]
2-313
2-314
PHYSICAL AnD CHEMICAL DATA
nomenclature (Continued )
Equation variables
Appears in (Eq. 2-?) or
[Table 2-?]
Definition
EoS temperature-dependent function
Parameter in Riedel vapor pressure equation
Viscosity group-group interactions
Reference EoS constant
Stoichiometric coefficient for combustion
Nonlinear correction term in correlation
Reference EoS constant
α(Tr)
αc
αmn
b
b
bi
g
d
d
DE
DP
DT
DV
(DHfo)i
DPi
Dpci
Dsi
DTad,i
Dtci
e
e
f
n
ni
= 0 for nonlinear molecules; = 1 for linear
EoS parameter
Contribution of element E to heat capacity
GC contribution to Pc
GC contribution to Tc
GC contribution to Vc
GC value for enthalpy of formation
GC for Parachor
Group i contribution to critical pressure
GC value for group i
Group i contribution to adiabatic flame temperature
Group i contribution to critical temperature
Lennard-Jones well depth parameter
EoS parameter
UNIFAC molecular volume fraction
LFL enthalpic term
Stoichiometric coefficient (+ for product and − for reactant)
for compound i in reaction
Frequency of vibrational mode j
UNIFAC molecular surface fraction
UNIFAC group surface fraction
Characteristic rotational T of molecule
Characteristic vibrational T of mode j
Lennard-Jones size parameter
Rotational external symmetry number
Modified reduced dipole moment
Parameter in Riedel vapor pressure equation
Parameter in correlation of k for gases
UNIFAC interaction factor
Viscosity de-dimensionalizing factor
Pseudo-acentric factor for mixture
nj
q
Q
QA, QB, QC
Qj
σ
σ
µ*r
y
y
ymn
x
ω
(70), [172]
(28a)
(99), [175]
(69), [171]
(122), (123), (128)
(46), (57), [164], [167]
(69), [171]
(1), (35), before (50), (51)
(70), [172]
(58), [168]
(7), [154]
(6), [154]
(8), [154]
(31), [161]
(117), [177]
(15)
(44), [162, 163]
(124)
(13)
following (4)
(70), [172]
following (99)
(126)
(32), (33), (34)
(50)
following (99)
following (99)
before and following (35)
(1), (35)
following (4)
following (35)
(84), (85)
(28a)
(106), (107)
(99)
(88), (89), (90), (91), (92), (93)
(76)
Acronyms and abbreviations
Definition
CC
CS
DIPPR
EoS
GC
LJ
MC
MD
QSPR
Computational chemistry
Corresponding states
Design Institute for Physical Properties
Equation of state
Group contributions
Lennard-Jones
Monte Carlo
Molecular dynamics
Quantitative structure-property relationships
GEnERAL REFEREnCES
Prediction Methods
[PGL4] Reid, R. C., J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids,
4th ed., McGraw-Hill, New York, 1987.
[PGL5] Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and
Liquids, 5th ed., McGraw-Hill, New York, 2001.
Property Databases
[DIPPR] Rowley, R. L., et al., DIPPR Data Compilation of Pure Chemicals Properties, Design
Institute for Physical Properties, AIChE, New York, 2007.
[TRC] TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research
Center, The Texas A&M University System, College Station, Tex., extant 2004; TRC
Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, The Texas
A&M University System, College Station, Tex., extant 2004.
[JANAF] Chase, M. W., Jr., et al., “JANAF Thermochemical Tables,” J. Phys. Chem. Ref. Data,
14, suppl. 1, 1985.
[SWS] Stull, D. R., F. F. Westrum, Jr., and G. C. Sinke, The Chemical Thermodynamics
of Organic Compounds, John Wiley & Sons, New York, 1969.
[TDS] Daubert, T. E., and R. P. Danner, Technical Data Book—Petroleum Refining, 5th ed.,
American Petroleum Institute, Washington, extant 1994.
CLASSIFICATIOn OF ESTIMATIOn METHODS
Physical property estimation methods may be classified into six general
areas: (1) theory and empirical extension of theory, (2) corresponding
states, (3) group contributions, (4) computational chemistry, (5) empirical
and quantitative structure-property relations (QSPR) correlations, and
(6) molecular simulation. A quick overview of each class is given below to
provide context for the methods and to define the general assumptions,
accuracies, and limitations inherent in each.
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
Theory and Empirical Extension of Theory Methods based on theory
generally provide better extrapolation capability than empirical fits of experimental data. Assumptions required to simplify the theory to a manageable
equation suggest accuracy limitations and possible improvements, if necessary. For example, the ideal gas isobaric heat capacity, rigorously obtained
from statistical mechanics under the assumption of independent harmonic
vibrational modes, is (Rowley, R. L., Statistical Mechanics for Thermophysical
Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994)
C op
R
=
8 − δ 3 n A −6+δ
+ ∑
2
j =1
2
Θ /T
e j
Θj
T Θ j /T
− 1)2
(e
(2-1)
0 nonlinear molecules
δ =
1 linear molecules
where Qj is the characteristic temperature for the jth vibrational frequency
in a molecule of nA atoms. The temperature dependence of this equation is
exact to the extent that the frequencies are harmonic.
Extension of theory often requires introduction of empirical models and
parameters in lieu of terms that cannot be rigorously calculated. Good accuracy is expected in the region where the model parameters were fitted to
experimental data, but only limited accuracy when an empirical model is
extrapolated to other conditions. For example, a simplified theory suggests
that vapor pressure should have the form
ln P * = A −
B
T
(2-2)
where the empirical parameter B is given by
B=
∆ Hυ
R ∆ Zυ
(2-3)
and ∆Hυ and ∆Zυ are differences between the vapor and liquid enthalpies
and compressibility factors, respectively. Equation (2-2) can be used to correlate vapor pressures over a moderate temperature range, but it is inadequate to represent vapor pressures over the whole liquid temperature range
because ∆Hυ also varies with temperature.
Corresponding States (CS) The principle of CS applies to conformal
fluids [Leland, T. L., Jr., and P. S. Chappelear, Ind. Eng. Chem., 60 (1968): 15].
Two fluids are conformal if their intermolecular interactions are equivalent
when scaled in dimensionless form. For example, the Lennard-Jones (LJ)
intermolecular pair potential energy U can be written in dimensionless form as
U* = 4(r∗−12 − r∗−6)
(2-4)
where r∗ = r/σ, U ∗ = U/ε, σ is the LJ size parameter, and ε is the LJ attractive well depth parameter. At equivalent scaled temperatures kT/ε (k is
Boltzmann’s constant) and pressures Pσ3/ε, all LJ fluids will have identical
dimensionless properties because the molecules interact through the identical scaled intermolecular potential given by Eq. (2-4). Generalization of
this scaling principle is commonly done using critical temperature Tc and
critical pressure Pc as scaling factors. At the same reduced coordinates
(Tr = T/Tc and Pr = P/Pc) conformal fluids will have the same dimensionless properties. For example, Z = Z(Tr, Pr) where the compressibility factor
is defined as Z = PV/RT. A correlation of experimental data for one fluid
can then be used as the reference for the properties of all conformal fluids.
Nonconformality is the main accuracy limitation. For instance, interactions
between nonspherical or polar molecules are not adequately represented
by Eq. (2-4), and so the scaled properties of these fluids will not conform
to those of a fluid with interactions well represented by Eq. (2-4). A correction for nonconformality is usually made by the addition of one or more
reference fluids whose deviations from the first reference fluid are used to
characterize the effect of nonconformality. For example, in the Lee-Kesler
method [Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510] n-octane is used
as a second, nonspherical reference fluid, and deviations of n-octane scaled
properties from those of the spherical reference fluid at equivalent reduced
conditions are assumed to be a linear function of the acentric factor.
Group Contributions (GCs) Physical properties generally correlate
well with molecular structure. GC methods assume a summative behavior
of the structural groups of the constituent molecules. For example, ethanol
(CH3—CH2—OH) properties would be obtained as the sum of contributions from the —CH3, —CH2, and —OH groups. The contribution of each
group is obtained by regression of experimental data that include as many
different compounds containing that group as possible. Structural groups
must be used exactly as defined in the original correlation of the groups.
A general principle when parsing a structure into constituent groups is that
2-315
the more specific the group, the higher its priority. For example, the structural piece —COOCH3 in a methyl ester could be divided in more than one
way, but if the —COO— and —CH3 groups are available in the method, then
they should be used rather than the combination of the two less specific
groups —(C == O)— and —O—. These latter group values were most likely
regressed only from ketone and ether data, respectively. Excellent accuracy can usually be expected from GC methods in which the group values
were regressed from large quantities of experimental data. However, if the
ratio of the number of groups to regressed experimental data is large, significant errors can result when the method is applied to new compounds
(extrapolation). Such excessive specificity in the group definitions leads to
poor extrapolation capabilities even though the fit of the regressed data may
have been excellent.
First-order GC methods assume simple summations of the group values
are adequate to represent the molecular value. Second-order effects, caused
by steric and electron induction effects from neighboring groups, can
alter group values. Second-order GC methods require considerably more
experimental data to tune the method, and large tables of group values are
required because differences in bonded neighbors require separate groups.
Computational Chemistry (CC) Commercial software is available
that solves the Schrödinger equation by using approximate forms of the
wave function. Various levels of sophistication (termed model chemistry)
for the wave function can be chosen at the expense of computational time.
Results include structural information (bond lengths, bond angles, dihedral
angles, etc.), electron/charge distribution information, internal vibrational
modes ( for ideal gas properties), and energy of the molecule, valid for the
chosen model chemistry. Because calculations are usually performed on
individual molecules, the results are best suited for ideal gas properties. Relative energies for the same model chemistry are more accurately obtained
than absolute energies, so enthalpies and entropies of reaction are also common industrial uses of CC predictions.
Empirical QSPR Correlations Quantitative structure-property
relationship (QSPR) methods correlate physical properties with molecular descriptors that characterize the structural and electronic character
of the molecule. Large amounts of experimental data are used to statistically determine the most significant descriptors to be used in the correlation and their contributions. The resultant correlations are simple to apply
if the descriptors are available. Descriptors must be generated by the user
with computational chemistry software or obtained from some tabulation.
QSPR methods are often very accurate for specific families of compounds
for which the correlation was developed, but extrapolation to other families
generally results in considerable loss of accuracy.
Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton’s equations of motion for a small number (on the order
of 103) of molecules to obtain the time evolution of the system. MD methods
can be used for equilibrium and transport properties. Monte Carlo (MC)
simulations use a model for the potential energy between molecules to
simulate configurations of the molecules in proportion to their probability
of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc.
Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not commonly available.
PHYSICAL COnSTAnTS
Critical Properties The critical temperature Tc, pressure Pc, and
volume Vc of a compound are important, widely used constants. They
are important in determining the phase boundaries of a compound and
(particularly Tc and Pc) are required input parameters for many property
estimation methods, particularly CS methods.
The critical temperature of a compound is the temperature above which
a liquid phase cannot be formed, regardless of the system pressure. The
critical pressure is the vapor pressure of the compound at the critical temperature. The molar critical volume is the volume occupied by 1 mol of a
chemical at its critical temperature and pressure. The critical compressibility factor Zc is determined from the experimental or predicted values of the
critical properties by its definition
Zc =
PcVc
RTc
(2-5)
Recommended Methods The Ambrose method is recommended for
all three critical properties of hydrocarbons and n-alcohols. The Nannoolal
method is recommended for all three critical properties of all other organic
molecules. The Wilson-Jasperson method is a simple method also recommended for estimating Tc and Pc for organic and some inorganic chemicals.
2-316
PHYSICAL AnD CHEMICAL DATA
The first-order Wilson-Jasperson method often gives better results than the
second-order method except strongly polar, hydrogen-bonding, and associating fluids.
Method: Ambrose method.
Reference: Ambrose, D., Natl. Phys. Lab. Report Chem. 92 (1978); Natl. Phys.
Lab Report Chem. 98 (1979).
Classification: Group contributions.
Expected uncertainty: ~6 K for Tc (about 1 percent), ~2 bar for Pc (about
5 percent), ~8 cm3/mol for Vc (about 3 percent).
Applicability: Organic compounds.
Input data: Tb, M, group contributions DT, DP, and DV from Table 2-154.
Description: A GC method with first-order contributions and corrections
(delta Platt number) for branched alkanes. Variables Tc, Pc, and Vc are given
by the following relations:
(
)
−1
Pc
M
0.339 + ∑ ∆ P
=
bar kg/kmol
)
Tc = Tb 1 + 1.242 + ∑ ∆T
(
Description: A GC method with first-order contributions. Variables Tc, Pc,
and Vc are given by the following relations:
1
Tc = Tb 0.6990 +
0.8607
0.9889 + ∑ niC i + GI
i
(2-9)
−0.14041
M
kg/kmol
Pc
=
2
kPa
0.00939 + ∑ niC i + GI
(2-10)
i
(2-6)
−2
Vc
=
10 m3 /mol
(2-7)
Vc
= 40 + ∑ ∆V
cm /mol
(2-8)
3
i
i
i
n
-0.2266
hvy
+ 86.1539
(2-11)
where ni is the number of groups of type i; Ci are group contributions from
Table 2-155; M is molecular weight; and GI is the total correction for groupgroup interactions calculated using
GI =
Example Use the Ambrose method to estimate the critical constants of
2,2,4-trimethylpentane.
Required data: From the DIPPR 801 database, Tb = 372.39 K and M = 114.229 kg/kmol.
Structure:
∑n C + GI
-6
1
nhvy
NG
NG
i =1
j =1
C ij
∑ ∑ NG − 1
(2-12)
where Cji = Cij. The values for the interactions are shown in this format in
Table 2-156. The sum of all group pairs within the molecule is divided by the
number of nonhydrogen atoms, nhvy, and by 1 less than the number of interacting groups NG. In the example below, there are no group-group interactions. The calculation of GI using Eq. (2-12) is illustrated later in an example
calculation for the normal boiling point.
Group contributions from Table 2-154:
Example Estimate the critical constants of o-xylene using the Nannoolal
Group
ni
Alkyl carbons
>CH— (correction)
>C< (correction)
Delta Platt no.
8
1
1
0
DT
DP
0.138
−0.043
−0.120
−0.023
0.226
−0.006
−0.030
−0.026
DV
55.1
−8
−17
—
Calculations using Eqs. (2-6), (2-7), and (2-8):
∑∆
T
Required input data: From the DIPPR 801 database, Tb = 417.58 K. From Table 2-155:
= (8) (0.138) + (1)(−0.043) + (1)(−0.120) = 0.941
Tc = Tb(1.4581) = (372.39 K)(1.4581) = 543.0 K
∑∆
P
= (8)(0.226) + (1)(−0.006) + (1)(−0.030) = 1.772
(
Pc
M
0.339 + ∑ ∆ P
=
bar kg/kmol
∑∆
V
method.
Structure:
)
−2
=
114.229
= 25.63
(0.339 + 1.772)2
Pc = 25.63 bar
= (8)(55.1) + (1)(−8) + (1)(−17) = 415.8
Group
ni
Ci (TC)
Ci (PC)
=C(a)}
CH3−(a)
=C(a)<(ne)
ortho
GI
4
2
2
1
—
0.0161154
−0.001071
0.0682045
0.0012823
0
0.00021064
0.0004166
0.00041826
0.00007061
0
19.402
26.7237
25.0434
−3.5964
0
From Eqs. (2-9), (2-10), and (2-11):
Vc = (40 + 415.8) cm3/mol = 455.8 cm3/mol
∑C (T ) = (4)(0.0161154) + (2)(−0.001071) + (2)(0.0682045)
i
c
Results:
Property
Ci (VC)
+ (1)(0.0012823) = 0.20001
DIPPR
recommended value
Ambrose estimation
% Difference
−0.15
Tc /K
543.8
543.0
Pc /bar
25.70
25.63
Vc /(cm3/mol)
468.0
455.8
1
Tc = Tb 0.6990 +
0.8607 = 1.5060Tb
0.9889 + ( 0.20001)
Tc = (1.5060)(417.58 K) = 628.87 K
0.27
−2.6
∑C ( P ) = (4)(0.00021064) + (2)(0.0004166) + (2)(0.00041826)
i
c
+(1)(0.00007061) = 0.0025829
Method: Nannoolal method.
Reference: Nannoolal, Y., J. Rarey, and D. Ramjugernath, Fluid Phase
Equilib. 252 (2007): 1.
Classification: Group contributions.
Expected uncertainty: ~6 K or 1 percent for Tc; ~2 bar or 5 percent for Pc;
~8 cm3/mol or 3 percent for Vc.
Applicability: Organic compounds.
Input data: Tb, group contributions Ci from Table 2-155, intramolecular
group-group interactions Cij, from Table 2-156, and the number of nonhydrogen atoms in the molecule nhvy.
Pc
(106.165 ) 0.14041
=
2 = 3623.55
kPa ( 0.00939 + 0.00258289 )
−
∑C (V ) = (4)(19.402) + (2)(26.7237) + (2)(25.0434)
i
c
+ (1)(−3.5964) = 177.5458
nhvy = 8
Vc
177.5458
177.5458
= −0.2266 + 86.1539 =
+ 86.1539 = 370.57
10 −6 m 3 /mol nhvy
(8)−0.2266
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-154
Ambrose Groupa Contributions for Critical Constants
Group
Carbon atoms in alkyl groups
Corrections
>CH} (each)
>C< (each)
Double bonds (nonaromatic)
Triple bonds
Delta Platt number,b multiply by
Aliphatic functional groups:
}O}
>CO
}CHO
}COOH
}CO}O}OC}
}CO}O}
}NO2}
}NH2
}NH}
>N}
}CN
}S}
}SH
}SiH3
}O}Si(CH3)2
}F
}Cl
}Br
}I
Halogen correction in aliphatic compounds:
F is present
F is absent, but Cl, Br, I are present
Aliphatic alcoholsc
Ring compound increments (listed only when different from aliphatic values):
}CH2}, >CH}, >C<
>CH} in fused ring
Double bond
}O}
}NH}
}S}
Aromatic compounds:
Benzene
Pyridine
C4H4 ( fused as in naphthalene)
}F
}Cl
}Br
}I
}OH
Corrections for nonhalogenated substitutions:
First
Each subsequent
Ortho pairs containing }OH
Ortho pairs with no }OH
Highly fluorinated aliphatic compounds:
}CF3, }CF2}, >CF}
}CF2}, >CF} (ring)
>CF} (in fused ring)
}H (monosubstitution)
Double bond (nonring)
Double bond (ring)
(other increments as in nonfluorina ted compounds)
DT
DP
DV
0.138
0.226
55.1
−0.043
−0.120
−0.050
−0.200
−0.023
−0.006
−0.030
−0.065
−0.170
−0.026
−8
−17
−20
−40
—
0.138
0.220
0.220
0.578
1.156
0.330
0.370
0.208
0.208
0.088
0.423
0.105
0.090
0.200
0.496
0.055
0.055
0.055
0.055
0.160
0.282
0.220
0.450
0.900
0.470
0.420
0.095
0.135
0.170
0.360
0.270
0.270
0.460
—
0.223
0.318
0.500
—
20
60
55
80
160
80
78
30
30
30
80
55
55
119
—
14
45
67
90
0.125
0.055
d
e
0.090
0.030
−0.030
0.090
0.090
0.090
0.182
0.182
—
—
—
—
0.448
0.448
0.220
0.080
0.080
0.080
0.080
0.198
0.924
0.850
0.515
0.183
0.318
0.600
0.850
−0.025
0.010
0.030
−0.080
−0.040
0
0.020
−0.050
−0.050
0.200
0.140
0.030
−0.050
−0.150
−0.030
0.550
0.420
—
−0.350
−0.500
—
15
44.5
44.5
−15
10
—
30
f
a
Ambrose, D., Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds, Natl. Phys. Lab Report Chem. 92 (1978); Correlation and Estimation of Vapour-Liquid Critical Properties. II. Critical
Pressures and Volumes of Organic Compounds, Natl. Phys. Lab Report Chem. 98 (1979).
b
The delta Platt number is defined as the Platt number of the isomer minus the Platt number of the corresponding alkane. (For
n-alkanes the Platt number is n − 3.) The Platt number is the total number of groups of four carbon atoms three bonds apart [Platt,
J. R., J. Chem. Phys., 15(1947): 419; 56(1952): 328]. This correction is used only for branched alkanes.
c
Includes naphthenic alcohols and glycols but not aromatic alcohols such as xylenol.
d
First determine the hydrocarbon homomorph, i.e., substitute }CH3 for each }OH and calculate ∑DT for this compound.
Subtract 0.138 from ∑DT for each }OH substituted. Next, add 0.87 − 0.11n + 0.003n2 where n = [Tb/K (alcohol) − 314]/19.2. Exceptions include methanol (∑DT = 0), ethanol (∑DT = 0.939), and any alcohol whose value of n exceeds 10.
e
Determine the hydrocarbon homomorph as in footnote d. Calculate ∑Dp and subtract 0.226 for each }OH substituted. Add
0.100 − 0.013n, where n is computed as in footnote d.
f
When estimating the critical volumes of aromatic substances, use ring compound values, if available, and correct for double
bonds.
2-317
2-318
PHYSICAL AnD CHEMICAL DATA
TABLE 2-155
Group Contributions for the nannoolal et al. Method for Critical Constantsa and normal Boiling Pointb
Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon; (Ca) =
aromatic carbon; b = any nonhydrogen atom
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
74
Group
CH3—(ne)
CH3—(e)
CH3—(a)
—C(c)H2—
>C(c)H—
>C(c)<
>C(c)<(e)
>C(c)<(Ca)
—C(r)H2—
>C(r)H—
>C(r)<
>C(r)<(e, c)
>C(r)<(e, r)
>C(r)<(Ca)
=C(a)H—
=C(a)<(ne)
=C(a)<(e)
(a) = C(a)<2(a)
F—(C, Si)
—CF= C<
F—(C,Si)(F)(2b)
F—(C,Si)([F, Cl])(b)
F—(C,Si)([F, Cl]2)
F—(Ca)
Cl—(C,Si)
Cl—(C,Si)([F, Cl])
Cl—(C, Si)([F, Cl]2)
Cl—(Ca)
—CCl=C<
Br—(C,Si)
Br—(Ca)
I—(C, Si)
—OH tert
HO—(C,Si) sec
HO—(C,Si) long
HO—(C,Si) short
—OH (Ca)
(C,Si)—O—(C,Si)
>(OC2)<
NH2—(C, Si)
NH2—(Ca)
(C,Si)—NH—(C,Si)
(C,Si)2>N—(C,Si)
COOH—(C)
(C)—COO—(C)
HCOO—(C)
—C(r)OO—
—CON<
—CONH—
—CONH2
O=C<(Can)2
CHO—(Can)
SH—(C)
(C)—S—(C)
(C)—S—S—(C)
—S(a)—
(C)—C≡N
>C(c)=C(c)<
>C(c)=C(c)<(Ca)
—(e)C(c)=C(c)<
H2C(c)=C<
>C(r)=C(r)<
—C≡C—
HC≡C—
(Ca)—O(a)—(Ca)
=N(a)—(r5)
=N(a)—(r6)
NO2—(C)
NO2—(Ca)
>Si<
>Si<(O)
NO3—
O=N—O—(C)
Description
CH3— not connected to N, O, F, or Cl
CH3— connected to N, O, F, or Cl
CH3— connected to an aromatic atom (not necessarily C)
—CH2— in a chain
>CH— in a chain
>C< in a chain
>C< in a chain connected to at least one F, Cl, N, or O
>C< in a chain connected to at least one aromatic carbon
—CH2— in a ring
>CH— in a ring
>C< in a ring
>C< in a ring; connected to at least one N, O, Cl, or F not in the ring
>C< in a ring connected to at least one N or O which is part of the ring
>C< in a ring connected to at least one aromatic carbon
aromatic =CH—
aromatic =C< not connected to O, N, Cl, or F
aromatic =C< connected to O, N, Cl, or F
aromatic =C< with three aromatic neighbors
F— connected to C or Si
F— on a C=C (vinyl fluoride)
F— connected to C or Si substituted with at least one F and two other atoms
F— connected to a C or Si substituted with one F or Cl and one other atom
F— connected to C or Si already substituted with two F or Cl atoms
F— connected to an aromatic carbon
Cl— connected to C or Si not already substituted with F or Cl
Cl— connected to C or Si already substituted with one F or Cl
Cl— connected to C or Si already substituted with at least two F or Cl
Cl— connected to aromatic C
Cl— on a C=C (vinyl chloride)
Br— connected to a nonaromatic C or Si
Br— connected to an aromatic C
I— connected to C or Si
—OH connected to tertiary carbon
—OH connected to secondary C or Si
—OH connected to primary C or Si; chain >4 C or Si
—OH connected to primary C or Si; chain <5 C or Si
—OH connected to an aromatic C (phenols)
ether —O— connected to two C or Si
>(OC2)< (epoxide)
NH2— connected to either C or Si
NH2— connected to an aromatic C
—NH— connected to two C or Si (secondary amine)
>N— connected to three C or Si (tertiary amine)
—COOH connected to C
—COO— connected to two C (ester)
HCOO— connected to C ( formic acid ester)
—COO— in ring, C is connected to C (lactone)
—CON< disubstituted amide
—CONH— (monosubstituted amide)
—CONH2 (amide)
—CO— connected to two nonaromatic C (ketones)
CHO— connected to nonaromatic C (aldehydes)
—SH connected to C (thiols)
—S— connected to two C
—S—S— (disulfide) connected to two C
—S— in an aromatic ring
—C≡N (cyanide) connected to C
>C=C< (both C have at least one non-H neighbor)
noncyclic >C=C< connected to at least one aromatic C
noncyclic >C=C< with at least one F, Cl, N, or O
H2C=C< (1-ene)
cyclic >C=C<
—C≡C—
HC≡C— (1-yne)
—O—in an aromatic ring with aromatic C neighbors
aromatic —N— in a five-member ring, free electron pair
aromatic =N— in a six-member ring
NO2— connected to aliphatic C
NO2— connected to aromatic C
>Si<
>Si< connected to at least one O
nitrate (esters of nitric acid)
nitrites (esters of nitrous acid)
TC × 103
PC × 104
VC
NBP
41.8682
33.1371
−1.0710
40.0977
30.2069
−3.8778
52.8003
9.4422
21.2898
26.3513
−17.0459
51.7974
18.9549
−29.1568
16.1154
68.2045
68.1923
29.8039
15.6068
11.0757
18.1302
19.1772
20.8519
−24.0220
−1.3329
2.6113
15.5010
−16.1905
60.1907
5.2621
−21.5199
−8.6881
84.8567
79.3047
49.5968
130.1320
14.0159
12.5082
41.3490
18.3404
−50.6419
17.1780
−0.5820
199.9042
75.7089
58.0782
109.1930
102.1024
8.1620
5.5262
4.1660
5.2623
2.3009
−2.9925
3.4310
2.3665
3.4027
3.6162
−5.1299
4.1421
0.8765
−0.1320
2.1064
4.1826
3.5500
1.0997
0.7328
4.3757
3.4933
2.6558
1.6547
0.5236
−2.2611
−1.4992
0.4883
−0.9280
11.8687
−4.3170
−2.2409
−4.7841
−7.4244
−4.4735
−1.8153
−6.8991
−12.1664
2.0592
0.1759
−4.4164
−9.0065
−0.4086
2.3625
3.9873
4.3592
1.0266
0.4329
0.5172
28.7855
28.8811
26.7237
32.0493
32.1108
28.0534
33.7577
28.8792
24.8517
30.9323
5.9550
29.5901
20.2325
10.5669
19.4020
25.0434
5.6704
16.4118
−5.0331
1.5646
3.3646
1.0897
1.1084
19.3190
22.0457
23.9279
26.2582
36.7624
34.4110
36.0223
30.7004
48.2989
10.6790
5.6645
2.0869
3.7778
25.6584
11.6284
46.7680
13.2571
73.7444
20.5722
6.0178
40.3909
42.6733
36.1286
56.1572
44.2000
−7.1070
0.5887
0.1190
−2.3615
−9.4154
−8.2595
30.9229
25.5034
34.7699
38.0185
−7.7181
117.1330
45.1531
−4.9259
5.1666
7.1581
20.3127
43.7983
67.9821
45.4406
56.4059
−19.9737
36.0883
10.4146
18.9903
10.9495
82.6239
−6.2791
9.6413
3.4731
−2.2718
2.4489
−0.5403
8.3052
−4.7101
−5.0929
51.0710
48.1957
34.1240
40.9263
29.8612
4.7476
−25.3680
23.6094
34.8472
25.4209
72.5587
5.7270
2.7602
75.7193
69.5645
177.3066
251.8338
157.9527
239.4531
240.6785
249.5809
266.8769
201.0115
239.4957
222.1163
209.9749
250.9584
492.0707
244.3581
235.3462
315.4128
348.2779
367.9649
106.5492
49.2701
53.1871
78.7578
103.5672
−19.5575
330.9117
287.1863
267.4170
205.7363
292.5816
419.4959
377.6775
556.3944
349.9409
390.2446
443.8712
488.0819
361.4775
146.4836
820.7118
321.1759
441.4388
223.0992
126.2952
1080.3139
636.2020
642.0427
1142.6119
1052.6072
1364.5333
1487.4109
618.9782
553.8090
434.0811
461.5784
864.5074
304.3321
719.2462
475.7958
586.1413
500.2434
412.6276
475.9623
512.2893
422.2307
37.1936
453.3397
306.7139
866.5843
821.4141
282.0181
207.9312
920.3617
494.2668
64.3506
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-155
2-319
Group Contributions for the nannoolal Method for Critical Constantsa and normal Boiling Point b (Continued )
Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon;
(Ca) = aromatic carbon; b = any nonhydrogen atom
ID
76
77
78
79
80
81
82
83
87
88
89
90
91
92
93
94
97
99
100
101
102
103
104
107
109
111
113
115
Group
Description
—C=O—O—C=O—
COCl—
>Si<(F,Cl)
O=C(—O—)2
OCN—
SCN—(C)
(C)—SO2—(C)
(C)2>Sn<(C)2
>C=C=C<
>C=C—C=C<(r)
>C=C—C=C<(c)
CHO—(Ca)
(C,Si) =N—
(O= C< (C)2)a
>Si<(C,H)2
—O—O—
(C,Si)a—NH—(Ca,Si)a
—OCON<
>N—(C=O)—N<
(C,Si)2>N< (C,Si)2
F—(C,Si)(Cl)(b)2
—OCOO—
>SO4
>S=O
>N(C=O)
(N)—C≡N
>P<
—ON=(C,Si)
TC × 103
anhydride connected to two C
COCl— connected to C (acid chloride)
>Si< connected to at least one F or Cl
noncyclic carbonate
OCN— connected to C or Si (cyanate)
SCN— (thiocyanate) connected to C
noncyclic sulfone connected to two C (sulfones)
>Sn< connected to four carbons
cumulated double bond
conjugated double bond in a ring
conjugated double bond in a chain
CHO— connected to aromatic C (aldehydes)
double-bonded amine connected to at least one C or Si
—CO— connected to two C with at least one aromatic C (ketones)
>Si< attached to two carbon or hydrogen
peroxide
—NH— connected to two C or Si, at least one aromatic (secondary amines)
—CO connected to O and N (carbamate)
—CO connected to two N (urea)
Quaternary amine connected to four C or Si
F— connected to C or Si with at least one Cl and two other atoms
—CO connected to two O (carbonates)
S(= O)2 connected to two O (sulfates)
sulfoxide
—CO connected to N
—C≡N (cyanide) connected to N
phosphorus connected to at least 1 C or S (phosphine)
—ON= connected to C or Si (isoazole)
PC × 104
VC
NBP
164.3355
4.0458
157.3401
97.2830
153.7225
12.6786
0.2822
90.9726
62.3642
53.6350
24.7302
−23.9221
0.7043
12.6128
−10.2451
68.0701
38.4681
−4.0133
20.0440
63.6504
34.2058
−5.0403
3.2023
28.7127
55.3822
27.3441
−4.3834
29.3068
1.3231
764.9595
3.3971
58.9190
1.3597
36.0361
−5.1116
16.2688
32.1829
11.4437
−1.3023
−34.3037
−1.3798
−2.7180
11.3251
−4.7516
1.2823
6.7099
7.3149
4.1439
0.4387
−4.2678
4.8944
2.8103
−0.3035
0.0930
0.7061
−0.7246
−3.8033
27.5326
1.5807
−2.6235
−5.3091
−6.1909
3.2219
−6.3900
−3.5964
1.5196
−33.8201
−18.4815
−23.6024
−24.5802
−35.6113
−8.8457
−2.2542
−3.2460
−5.3113
1.0934
−4.6483
−5.0563
−6.3267
4.9392
2.8889
52.8789
27.1026
64.4616
1251.2675
778.9151
540.0895
879.7062
660.4645
1018.4865
1559.9840
510.4223
664.0903
957.6388
928.9954
560.1024
229.2288
606.1797
273.1755
201.3224
886.7613
1045.0343
–109.6269
111.0590
1573.3769
1483.1289
1379.4485
492.0707
971.0365
428.8911
612.9506
Corrections
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
(C=O)—C([F,Cl]2,3)
(C=O)—C([F,Cl]2,3)2
C—[F,Cl]3
(C)2—C—[F,Cl]2
No hydrogen
One hydrogen
(3,4) ring
5-ring
Ortho pair(s)
Meta pair(s)
Para pair(s)
((C= )(C)C—CC3)
C2C—CC2
C3C—CC2
C3C—CC3
C=C—C=O
carbonyl connected to C with two or more halogens
carbonyl connected to two C, each with at least two halogens
carbon with three halogens
secondary carbon with two halogens
component has no hydrogen
component has one hydrogen
a three- or four-member nonaromatic ring
a five-member nonaromatic ring
ortho- position counted only once and only if no meta or para pairs
meta- position counted only once and only if no para or ortho pairs
para- position counted only once and only if no meta or ortho pairs
carbon with four carbon neighbors and one double-bonded carbon neighbor
carbon with four carbon neighbors, two on each side
carbon with five carbon neighbors
carbon with six carbon neighbors
—C=O connected to sp3 carbon
–82.2328
–247.8893
–20.3996
15.4720
–172.4201
–99.8035
–62.3740
–40.0058
–27.2705
–3.5075
16.1061
25.8348
35.8330
51.9098
111.8372
40.205
Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1.
Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45.
a
b
Description: A GC method with first- and some second-order contributions. Variables Tc, Pc, and Vc are given by the following relations:
Results:
Property
Tc /K
Pc /bar
Vc /(cm3/mol)
DIPPR 801
recommendation
630.3
37.32
370
Nannoolal
estimation
% Difference
628.9
36.24
370.6
−0.2
−2.9
0.2
Method: Wilson-Jasperson method.
Reference: Wilson, G. M., and L. V. Jasperson, “Critical Constants Tc, Pc,
Estimation Based on Zero, First and Second Order Methods,” AIChE Spring
Meeting, New Orleans, La., 1996.
Classification: Group contributions.
Expected uncertainty: ~6 K or 1 percent for Tc; ~2 bar or 5 percent for Pc.
Applicability: Organic and some inorganic compounds.
Input data: M, Tb, group contributions Ci from Table 2-157, and molecular
structure.
Tc =
Tb
0.048271 − 0.019846nr + ∑ nk ∆tc k + ∑ n j ∆tc j
k
j
0.2
Pc 0.0186233(Tc /K)
=
bar exp(Y ) − 0.96601
Y = − 0.00922295 − 0.0290403nr + 0.041 ∑ nk ∆pc k + ∑ n j ∆pc j
k
j
(2-13)
(2-14)
(2-15)
where nr is the number of rings in the molecule; Dtck and Dpck are the firstorder group contributions tabulated in Table 2-157 with nk the number of
such occurrences in the molecule; and Dtcj and Dpcj are the second-order
2-320
PHYSICAL AnD CHEMICAL DATA
TABLE 2-156 Intermolecular Interaction Corrections for the nannoolal et al.
Method for Critical Constantsa and normal Boiling Pointb
—OH :: —OH
—OH :: —COOH
—OH :: —O—
—OH :: >(OC2)<
—OH :: —COOC—
—OH :: —CO—
—OH :: —O(a)—
—OH :: —S(na)—
—OH :: —SH
—OH :: —NH2
—OH :: >NH
—OH :: —CN
—OH :: =N(a)–(r6)
—OH(a) :: —OH(a)
—OH(a) :: —COOH
—OH(a) :: —O—
—OH(a) :: —COOC—
—OH(a) :: —CHO
—OH(a) :: —NH2
—OH(a) :: Nitrate
—OH(a) :: =N(a)–(r6)
—COOH :: —COOH
—COOH :: —O—
—COOH :: —COOC—
—COOH :: —CO—
—O— :: —O—
—O— :: >(OC2)<
—O— :: —COOC—
—O— :: —CO—
—O— :: —CHO
—O— :: —O(a)—
—O— :: —S(na)—
—O— :: —NH2
—O— :: >NH
—O— :: —CN
—O— :: Nitrate
>(OC2)< :: >(OC2)<
>(OC2)< :: —CO—
>(OC2)< :: —CHO
—COOC— :: —COOC—
—COOC— :: —CO—
—COOC— :: —O(a)—
—COOC— :: —NH2
—COOC— :: >NH
—COOC— :: —CN
—COOC— :: Nitrate
—CO— :: —CO—
—CO— :: —CHO
—CO— :: —O(a)—
—CO— :: —S(a)—
—CO— :: >NH
—CO— :: —CN
—CO— :: Nitrate
—CO— :: =N(a)–(r6)
—CHO— :: —CHO—
—CHO— :: —O(a)—
—CHO— :: —S(a)—
—CHO— :: Nitrate
—O(a)— :: —NH2
—O(a)— :: =N(a)–(r5)
—S(na)— :: —S(na)—
—S(na)— :: —NH2
—S(a)— :: —CN
—S(a)— :: =N(a)–(r5)
—SH :: —SH
—NH2 :: —NH2
—NH2 :: >NH
—NH2 :: Nitrate
—NH2 :: =N(a)–(r6)
>NH :: >NH
>NH :: =N(a)–(r6)
—OCN :: —OCN
—OCN :: Nitrate
—CN :: =N(a)–(r6)
Nitrate :: Nitrate
=N(a)–(r6) :: =N(a)–(r6)
PC × 104
−434.8568
−5.6023
−146.7881
7.3373
19.7707
120.9166
−30.4354
69.8200
6.1331
−8.0423
144.4697
57.8350
97.5425
162.6878
707.4116
128.2740
2.6751
88.8752
−1.0295
−23.6366
−329.5074
−55.5112
−654.1363
−738.0515
25.8246
−125.5983
−37.2468
0.5195
−74.8680
1605.564
−78.2743
−413.3976
24.0243
−861.1528
−35.1998
43.9001
217.9243
−403.1196
131.7924
−19.7033
164.2930
−60.9217
−0.6754
−49.7641
22.1871
741.8565
366.2663
−32.3208
−57.1233
44.1062
−1866.097
Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1.
b
Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45.
a
VC
TC × 103
12.5371
−26.4556
NBP
291.7985
146.7286
135.3991
226.4980
211.6814
46.3754
435.0923
–74.0193
38.6974
314.6126
286.9698
306.3979
1334.6747
288.6155
–1477.9671
130.3742
−1184.9784
43.9722
797.4327
–1048.124
–614.3624
117.2044
612.8821
−183.2986
−55.9871
91.4997
178.7845
322.5671
15.6980
17.0400
329.0050
394.5505
124.3549
101.8475
293.5974
963.6518
1006.388
22.5208
163.5475
431.0990
22.5208
707.9404
182.6291
317.0200
517.0677
–205.6165
−303.9653
−391.3690
176.5481
381.0107
−215.3532
−574.2230
–3628.903
124.1943
562.1763
674.6858
397.575
140.9644
395.4093
–888.612
–11.9406
−562.306
−101.232
–348.740
217.6360
174.0258
510.3473
663.8009
27.2735
239.8076
758.9855
−356.5017
–263.0807
–370.9729
65.1432
–271.9449
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
group contributions, also tabulated in Table 2-157, with nj occurrences of
these second-order groups in the molecule.
TABLE 2-157 Wilson-Jasperson First- and Second-Order
Contributions for Critical Temperature and Pressurea
First-order atom
Example Estimate Tc and Pc of sec-butanol by using the Wilson-Jasperson
method.
Required input data: From DIPPR 801 database, Tb = 372.9 K.
Structure:
Group contributions from Table 2-157:
Group
nk
Dtck
Dpck
nj
Dtcj
Dpcj
H
10
0.002793
0.12660
—
—
—
O
1
0.020341
0.43360
—
—
—
C
4
0.008532
0.72983
—
—
—
−OH, C4 or less
—
—
1
—
0.0350
0
From Eqs. (2-13), (2-14), and (2-15):
∑ n ∆tc
k
k
= (10)(0.002793) + (1)(0.020341) + (4)(0.008532) = 0.082399
Tc =
∑ n ∆pc
k
k
Tb
372.9 K
=
= 534.25 K
(0.048271 + 0.082399 + 0.0350)0.2 0.6980
= (10)(0.12660) + (1)(0.43360) + (4)(0.72983) = 4.61892
Y = − 0.00922295 + 0.041(4.61892) = 0.18015
Pc 0.0186233(Tc /K)
(0.0186233)(534.25)
=
=
= 43.00
bar exp(Y ) − 0.96601 exp(0.18015) − 0.96601
Results:
Property
DIPPR 801
recommendation
Wilson-Jasperson
estimation
% Difference
Tc /K
536.2
534.25
−0.4
43.00
2.3
Pc /bar
42.02
Normal Melting Point The normal melting point is defined as the
temperature at which melting occurs at atmospheric pressure. Methods to
estimate the melting point are not particularly effective because the melting
point depends strongly on solid crystal structure and that structure is not
effectively correlated with standard GC or CS methods.
Recommended Method The method of Constantinou and Gani is
recommended with caution.
Reference: Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697.
Classification: Group contributions.
Expected uncertainty: 25 percent.
Applicability: Organic compounds.
Input data: First- and second-order group contributions from molecular
structure.
Description: A group contribution method given by
Tm = (102.425 K) ⋅ ln ∑ ni t m1, i +
i
∑n t
j m 2, j
j
ni
2
1
1
tm1,i
Second-order group
}OH, C4 or less
}OH, C5 or more
}O}
}NH2, >NH, >N}
}CHO
>CO
}COOH
}COO}
}CN
}NO2
Organic halides (once per
molecule)
}SH, }S}, }SS}
Siloxane bond
Dpck
0.12660
0.43400
0.91000
0.72983
0.44805
0.43360
0.32868
0.12600
6.05000
1.34000
1.22000
1.04713
0.97711
0.79600
1.19000
—
—
1.42000
2.68000
1.20000
0.97151
1.11000
—
1.11000
2.71000
1.69000
1.95000
—
0.43000
1.31593
1.66000
6.33000
1.07000
—
1.08000
—
—
−0.08000
0.69000
2.05000
2.04000
Dtcj
Dpcj
0.0350
0.0100
−0.0075
−0.0040
0.0000
−0.0550
0.0170
−0.0150
0.0170
−0.0200
0.0020
0.00
0.00
0.00
0.00
0.50
0.00
0.50
0.00
1.50
1.00
0.00
0.0000
−0.0250
0.00
−0.50
As cited in PGL5.
Calculation using Eq. (2-16):
Tm = (102.425 K) ln [(2)(0.4640) + 12.6275 + 1.5656] = 278 K
Example Estimate the melting point of 2,6-dimethylpyridine.
Structure and group contributions:
Group
Dtck
0.002793
0.320000
0.019000
0.008532
0.019181
0.020341
0.008810
0.036400
0.088000
0.020000
0.012000
0.007271
0.011151
0.016800
0.014000
0.018600
0.059000
0.031000
0.007000
0.010300
0.012447
0.013300
−0.027000
0.175000
0.017600
0.007000
0.020000
0.010000
0.000000
0.005900
0.017000
−0.027500
0.219000
0.013000
0.011000
0.014000
−0.050000
0.000000
0.000000
0.007000
0.015000
(2-16)
where ni, nj = number of first- and second-order groups, respectively
tm1,i = first-order group contributions from Table 2-158
tm2,i = second-order group contributions from Table 2-159
−CH3
−C5H3(N)−
Six-member ring
H, D, T
He
B
C
N
O
F
Ne
Al
Si
P
S
Cl
Ar
Ti
V
Ga
Ge
As
Se
Br
Kr
Rb
Zr
Nb
Mo
Sn
Sb
Te
I
Xe
Cs
Hf
Ta
W
Re
Os
Hg
Bi
Rn
U
a
2-321
tm2,i
0.4640
12.6275
1.5656
The predicted value is 4 percent higher than the recommended experimental value of 267 K in the DIPPR 801 database.
Normal Boiling Point The normal boiling temperature Tb is the
temperature at which the vapor pressure of the liquid equals 101.325 kPa
(1.0 atm). If there are sufficient vapor pressure data available, then Tb may
be found from a regression of the data using an appropriate vapor pressure
equation [e.g., Eqs. (2-24) to (2-28)]. If two or more vapor pressure values are
available in the approximate temperature range of Tb, they can be used to
obtain Tb by using Eq. (2-2) to linearly interpolate ln P* versus 1/T values.
When one or more low-temperature vapor pressure points are available, a
common occurrence, then the method of Pailhes can be used to estimate Tb.
2-322
PHYSICAL AnD CHEMICAL DATA
TABLE 2-158
Group
First-Order Groups and Their Contributions for Melting Point *
Group
tm1,i
TABLE 2-159
Group
tm1,i
}CH3
0.4640
}COOCH2}
>CH2
0.9246
}OOCH
>CH}
0.3557
}OCH3
>C<
1.6479
}OCH2}
}CH=CH2
1.6472
}OCH<
}CH=CH}
1.6322
}OCH2F
>C=CH2
1.7899
}CH2NH2
>C=CH}
2.0018
>CHNH2
>C=C<
5.1175
}NHCH3
}CH=C=CH2
3.3439
}CH2NH}
>ACH
1.4669
>CHNH}
>AC}
0.2098
>NCH3
>ACCH3
1.8635
}NCH2}
>ACCH2}
0.4177
>ACNH2
>ACCH<
−1.7567
}C5H3(N)}
}OH
3.5979
}CH2CN
>ACOH
13.7349
}COOH
}COCH3
4.8776
}CH2Cl
}COCH2}
5.6622
>CHCl
}CHO
4.2927
>CCl}
}COOCH3
4.0823
}CHCl2
*Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697.
3.5572
4.2250
2.9248
2.0695
4.0352
4.5047
6.7684
4.1187
4.5341
6.0609
3.4100
4.0580
0.9544
10.1031
12.6275
4.1859
11.5630
3.3376
2.9933
9.8409
5.1638
}CCl3
>ACCl
}CH2NO2
>CHNO2
>ACNO2
}CH2SH
}I
}Br
}C≡CH
}C≡C}
>C=CCl}
>ACF
}CF3
}COO}
}CCl2F
}CClF2
}F (other)
}CONH2
}CON(CH3)2
}CH3S
>CH2S
tm1,i
10.2337
2.7336
5.5424
4.9738
8.4724
3.0044
4.6089
3.7442
3.9106
9.5793
1.5598
2.5015
3.2411
3.4448
7.4756
2.7523
1.9623
31.2786
11.3770
5.0506
3.1468
Second-Order Groups and Their Contributions for Melting Point*
Group
tm21,i
}CH(CH3)2
}C(CH3)3
}CH(CH3)CH(CH3)}
}CH(CH3)C(CH3)2}
}C(CH3)2C(CH3)2}
Three-member ring
Five-member ring
Six-member ring
Seven-member ring
CHn=CHm}CHp=CHk
[k, n, m, p = 0, 1, 2]
CH3CHm=CHn [m, n = 0, 1, 2]
0.0381
−0.2355
0.4401
−0.4923
6.0650
1.3772
0.6824
1.5656
6.9709
1.9913
CH2CHm=CHn [m, n = 0, 1, 2]
−0.5870
CHCHm=CHn or CCHm=CHn
[m, n = 0, 1, 2]
Alicyclic side chain: CcyclicCm
[m > 1]
CH3CH3
−0.2361
CHCHO; CCHO
Group
0.2476
1.4880
2.0547
−0.2951
CH3COCH; CH3COC
−0.2986
Ccyclic(=O)
0.7143
ACCHO
−0.6697
*Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697.
The most accurate method for prediction of normal boiling temperatures
without experimental data is the Nannoolal method.
Recommended Method Pailhes method.
Reference: Pailhes, F., Fluid Phase Equilib., 41 (1988): 97.
Classification: Group contributions.
Expected uncertainty: ~3 K (1 to 2 percent).
Applicability: Organic compounds.
Input data: Molecular structure and one measured vapor pressure value
*
Pmeas (often at a low pressure). The method requires estimation of the reduced
normal boiling point, Tbr, and Pc, which in the example below are obtained
using the Wilson-Jasperson first-order method and the Ambrose method,
respectively.
Description: A simple group contribution method is given by
log(Pc /bar) + (1 − Tbr ) x P
2
Tb = Tmeas
− 3 x p − 1.49 x p
log(Pc /bar)
where Tb = estimated normal boiling point
Pc = critical pressure estimated from group contributions
−3.1034
28.4324
0.4838
0.0127
−2.3598
−2.0198
−0.5480
0.3189
0.9124
9.5209
CHm(OH)CHn(NHp)
[m, n, p = 0, 1, 2, 3]
CHm(NH2)CHn(NH2)
[m, n = 0, 1, 2]
CHm cyclic}NHp}CHn cyclic
[m, n, p = 0, 1, 2]
CHm}O}CHn=CHp
[m, n, p = 0, 1, 2]
AC}O}CHm
[m = 0, 1, 2, 3]
CHm cyclic}S}CHn cyclic
[m, n = 0, 1, 2]
CHm=CHn}F
[m, n = 0, 1, 2]
CHm=CHn}Br
[m, n = 0, 1, 2]
ACBr
ACl
−2.8298
CH3COCH2
tm21,i
CHCOOH; CCOOH
ACCOOH
CH3COOCH; CH3COOC
COCH2COO or COCHCOO or COCCOO
CO}O}CO
ACCOO
CHOH
COH
CHm(OH)CHn(OH) [m, n = 0, 1, 2]
CHm cyclic}OH [m = 0, 1]
(2-17)
2.7826
2.5114
1.0729
0.2476
0.1175
−0.2914
−0.0514
−1.6425
2.5832
−1.5511
xP = log(1 atm/P*meas)
Tmeas = temperature at which experimental vapor pressure P*meas is
known
Example The vapor pressure of n-decylacetate (M = 200.32 kg/kmol) at 348.65 K
is 106.66 Pa. Estimate the normal boiling point of this compound, using the Paihles
method.
Structure and group contributions from Tables 2-154 and 2-157:
Wilson-Jasperson
Groups
ni
ni
DP,i
H
24
0.002793
−COO−
1
0.470
O
2
0.020341
C (alkyl)
11
0.226
C
12
0.008532
Δtci
Ambrose
Groups
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
CHARACTERIZInG AnD CORRELATInG COnSTAnTS
Group contribution calculations using Eq. (2-13) for Tbr and Eq. (2-7) for Pc :
∑ n ∆tc
i
i
= (24)(0.002793) + (2)(0.020341) + (12)(0.008532) = 0.210098
Acentric Factor The acentric factor of a compound w is defined in terms
of the reduced vapor pressure evaluated at a reduced temperature of 0.7 as
Tbr = (0.048271 + 0.210098)0.2 = 0.7629
∑n ∆
i
P ,i
ω = − log Pr*
= (1)(0.470) + (11)(0.226) = 2.956
Pc =
200.32
bar = 18.450 bar
(0.339 + 2.956)2
Calculation of auxiliary quantities:
101,325 Pa
1 atm
x P = log ∗ = log
= 2.9777
Pmeas
106.66 Pa
Calculation of normal boiling point using Eq. (2-17):
log (18.450) + (1 − 0.7629)(2.9777)
Tb
2
= (348.65)
− 3(2.9777) − 1.49(2.9777)
log(18.450)
K
Tb = 520.94 K
The estimated value is 0.7 percent higher than the DIPPR 801 recommended value of
517.15 K.
Recommended Method: Nannoolal method.
Reference: Nannoolal, Y., J. Rarey, D. Ramjugernath, and W. Cordes, Fluid
Phase Equilib., 226 (2004): 45.
Classification: Group contributions.
Expected uncertainty: ~7 K (about 2 percent).
Applicability: Organic compounds.
Input data: Ci values in Table 2-155; intramolecular group-group interactions Cij in Table 2-156; and the number of nonhydrogen atoms in the
molecule.
Description: A GC method that includes second-order corrections for
steric effects and intramolecular interactions. Tb is calculated from
(2-18)
where nhvy = number of nonhydrogen (heavy) atoms
ni = number of occurrences of group i
Ci = group contribution from Table 2-155
GI = total group-group interaction as calculated using Eq. (2-12)
and Table 2-156
−1.0000
(2-19)
Example Calculate the acentric factor of chlorobenzene with a known value for Tb.
Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and
Pc = 45.1911 bar.
Calculation of auxiliary quantities (see Eq. (2-28a) for these equations):
Tbr =
Tb 404.87
=
= 0.64
Tc 632.35
ψ = −35 +
αc =
=
Example Estimate the normal boiling point of di-isopropanolamine by using the
Nannoolal method.
Structure:
Tr = 0.7
It is primarily used as a third parameter (in addition to Tc and Pc) in CS
predictions as a measure of deviations from nonspherical molecular shape,
hence the name, suggesting molecular interactions that are not between
centers of molecules. However, as defined in Eq. (2-19), w also contains
polarity information, and it increases with increasing polarity for molecules of similar size and shape. The value of w is close to zero for small,
spherically shaped, nonpolar molecules (argon, methane, etc.). It increases
in value with larger deviations of molecular shape from spherical (longer
chain lengths, less chain branching, etc.) and with increasing molecular
polarity. When possible, w should be obtained from experimental vapor
pressure correlations by using Eq. (2-19), but an accurate estimation of w
can be made by using the critical constants and a single vapor pressure
point by application of CS vapor pressure equations.
Recommended Method 1 Definition.
Classification: Theory and empirical extension of theory.
Expected uncertainty: Within 3 percent if an experimental vapor pressure
correlation is available; within 10 percent from a predicted vapor pressure
correlation.
Applicability: Most organic compounds.
Input data: Vapor pressure correlation or Tc, Pc, and Tb if an experimental
vapor pressure correlation is unavailable.
Description: Equation (2-19) is applied directly to the appropriate vapor
pressure equation. A predictive vapor pressure equation can also be used as
in the second example.
N
∑n ⋅ C + GI
Tb i =1 i i
+ 84.3395
= 0.6583
K nhvy + 1.6868
2-323
K = 0.0838
36
36
+ 42 ⋅ ln(Tbr ) − Tbr6 = −35 +
+ 42 ⋅ ln(0.64) − (0.64)6 = 2.4312
Tbr
0.64
(3.758) K ψ + ln( PC /1.01325bar)
K ψ − ln(Tbr )
45.1911
(3.758)( 0.0838 )(2.4312) + ln
1.01325
= 7.025
(0.0838)(2.4312) − ln(0.64)
D = K (α c − 3.758) = (0.0838)(7.025 − 3.758) = 0.2738
A = 35 D = 9.581 B = −36 D = −9.855 C = α c − 42 D = −4.473
Calculation using Eq. (2-28) at Tr = 0.7:
ln( Pr ) = 9.581 −
Group contributions and values:
Group
ni
Ci
Group total
}CH3
2
177.3066
354.6132
>C(c)<(e)
4
266.8769
1067.508
}OH sec
2
390.2446
780.4892
}NH}
1
223.0992
223.0992
}OH:: }OH
2/(9 × 2)
291.7985
32.42206
}OH:: }NH}
4/(9 × 2)
286.9698
63.77107
Total
2521.902
GI
Note that the frequencies of the interaction correction terms are calculated in the
following manner: There are three interacting groups (}OH, }OH, }NH}) in the
molecule, so NG − 1 = 2. The four }OH:: }NH} interactions and two }OH:: }OH
interactions are each divided by 2 and by the number of nonhydrogen atoms nhvy = 9,
according to Eq. (2-12).
Calculation using Eq. (2-18):
2521.902
Tb
=
+ 84.3395 = 509.3
K 9 0.6583 + 1.6868
Tb = 509.3 K
This value differs by −2.4 percent from the DIPPR 801 recommended value of 521.9 K.
9.855
− 4.473 ⋅ ln(0.7) + 0.2738 ⋅ (0.7)6 = −2.870
0.7
Calculation using Eq. (2-19):
ω=−
ln( Pr )
2.870
− 1.0000 =
− 1.0000 = 0.246
2.303
2.303
This value differs by −1.5 percent from DIPPR 801 recommended value of 0.2499.
Recommended Method 2 Corresponding states.
Reference: [PGL5].
Classification: Corresponding states.
Expected uncertainty: Generally within 5 percent, worse for strongly polar
fluids.
Applicability: Most organic compounds.
Input data: Tc, Pc, and a single vapor pressure point (e.g., the normal
boiling point Tb).
Description: See Eq. (2-29) for the equations used in this method. The
vapor pressure equation is inverted to obtain the acentric factor from a
single vapor pressure point.
Example Repeat the above calculation of the acentric factor of chlorobenzene,
using the Walton-Ambrose modification of the Lee-Kesler vapor pressure equation,
Eq. (2-29).
Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and
Pc = 45.1911 bar.
2-324
PHYSICAL AnD CHEMICAL DATA
This is 3.8 percent below the DIPPR 801 database value of 1.564 × 10−10 m which was
obtained from spectral principal moments of inertia.
Calculation of auxiliary quantities:
Tbr =
Tb 404.87
=
= 0.64
Tc 632.35
τ = 1 − 0.64 = 0.36
(−5.97616)(0.36) + (1.29874)(0.36)1.5 − (0.60394)(0.36)2.5 − (1.06841)(0.36)5
f (0) =
0.64
= −3.0034
(−5.03365)(0.36) + (1.11505)(0.36)1.5 − (5.41217)(0.36)2.5 − (7.46628)(0.36)5
0.64
= −3.1788
f (1) =
(−0.64771)(0.36) + (2.41539)(0.36)1.5 − (4.26979)(0.36)2.5 − (3.25259)(0.36)5
0.64
= −0.037
f (2) =
Example Calculate the dipole moment for methanol.
Draw structure and optimize molecule by using computational chemistry software: The
dipole moment obtained from a geometry optimized with the HF/6-31G model chemistry for methanol is 2.288 D. This value is 35 percent larger than the experimental
gas-phase value of 1.700 D in the DIPPR 801 database.
Calculation using Eq. (2-29) at the normal boiling point:
ln
1.01325
= −3.798 = f (0) + ωf (1) + ω 2 f (2) = −3.0034 − 3.1788ω − 0.037ω 2
45.1911
Back solution of the quadratic equation for ω:
ω = 0.249
Radius of Gyration The radius of gyration Rg is a measure of the mass
distribution about the center of mass of a molecule. Radius Rg increases with
molecular size. It is useful in CS applications to separate molecular size
and shape effects from polar effects. It is defined in terms of the principal
moments of inertia of a molecule (A, B, and C) as
Rg =
(AB )1/2 N A
M
(2-20)
2π(ABC )1/3 N A
M
(2-21)
for planar molecules and as
Rg =
Dipole Moment The dipole moment of a molecule is the first moment
of the electric charge density expansion. All normal paraffins have a value of
zero. Charge separation within the molecule due to electronegativity differences between bonded atoms increases the dipole moment. Computational
chemistry software uses the electron density distribution of the optimized
molecule to calculate dipole moments.
Recommended Method Electron density distribution.
Classification: Computational chemistry.
Expected uncertainty: Uncertainty varies depending upon the model
chemistry chosen, but it can be as large as 60 percent.
Applicability: All molecules.
Input data: Molecular structure.
for nonplanar molecules. Radii of gyration can be calculated from these
defining equations using principal moments of inertia obtained from spectral data or from computational chemistry software.
Recommended Method Principal moments of inertia.
Classification: Computational chemistry.
Expected uncertainty: Less than 5 percent.
Applicability: All molecules.
Input data: M and molecular structure.
Description: Computational chemistry software is used to optimize the
geometry of the molecule and obtain the principal moments of inertia to be
used in Eqs. (2-20) and (2-21).
Example Calculate the radius of gyration for hydrazine.
Input information: From the DIPPR 801 database, M = 32.0452 kg/kmol. The structure of hydrazine is
Refractive Index Refractive index is the ratio of the speed of light
in a vacuum to the speed of light in the medium. The incident light is the
sodium D line (5.896 × 10−7 m). Refractive index is dimensionless and generally ranges between 1.3 and 1.5 for organic liquids.
Recommended Method Wildman-Crippen method.
Reference: Wildman, S. A., and G. M. Crippen, J. Chem. Inf. Comput. Sci. 39
(1999): 868.
Classification: Theory and group contribution.
Expected uncertainty: Generally less than 3 percent for liquids.
Applicability: Most organic molecules (currently not applicable to organic
acids).
Input data: Molecular structure, molecular weight, and density at the
desired temperature.
Description: This method is based on the Lorentz-Lorenz relation between the
molar refraction RD and the refractive index, which can be written in the form
ρ
M + 2
RD
gm ⋅ cm −3
n=
ρ
M −
RD
gm ⋅ cm −3
(2-22)
where n is refractive index at the same temperature as the density r. Wildman
and Crippen developed a GC method for RD with the atomic contributions
shown in Table 2-160 for each type of atom with its bonded neighbors.
Example Calculate the refractive index of m-ethylphenol at 298.15 K. The various types of atoms corresponding to the descriptions in Table 2-160 are identified in
the 2-D structural diagram shown here.
H2N—NH2
H1
Calculation of the principal moments of inertia: Optimizing hydrazine with HF/6-31G
model chemistry gives the following principal moments of inertia:
H1
C18
A = 12.24050 amu ⋅ Bohr2
H1
B = 72.41081 amu ⋅ Bohr2
C = 79.16893 amu ⋅ Bohr2
C18
H1
H1
C1
C1
H1
H1
C21
C18
C23
C18
H1
Conversion from atomic units to SI gives
5.29177 × 10 −11 m
A = (12.24050 amu ⋅ Bohr 2 )
Bohr
−2
1.66054 × 10 −27 kg
amu
= 5.692 × 10 −47 kg ⋅ m 2
4.65010 −48 kg ⋅ m2
= 3.367 × 10 −46 kg ⋅ m 2
B = (72.41081 amu ⋅ Bohr 2 )
amu ⋅ Bohr 2
4.65010 −48 kg ⋅ m2
−46
2
C = (79.16893 amu ⋅ Bohr 2 )
= 3.681 × 10 kg ⋅ m
2
amu ⋅ Bohr
Calculation using Eq. (2-21):
(ABC)1/3 = [(5.692 × 10−47)(3.367 × 10−46)(3.681 × 10−46)]1/3 kg ⋅ m2
= 1.918 × 10−46 kg ⋅ m2
Rg =
2π (1.918 × 10 − 46 kg ⋅ m 2 )(6.022 ⋅10 26 kmol −1 )
= 1.505 × 10 −10 m
32.0452 kg/kmol
H2
02
H1
The molecular weight of m-ethylphenol is 122.16 kg/kmol, and its liquid density at
298.15 K is given in the DIPPR database as 1.00651 g/cm3. The group contributions are
summed up as shown in this table:
Type
C1
C18
C21
C23
O2
H1
H2
Description
1° & 2° aliphatic
aromatic
4° aromatic –aliphatic C
4° aromatic –O attached
alcohol
hydrocarbon
alcohol
Group Sum
Number
2
4
1
1
1
9
1
19
Value
Contribution
2.503
3.350
3.509
3.853
0.8238
1.057
1.395
5.006
13.40
3.509
3.853
0.8238
9.513
1.395
RD
37.4998
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-160
2-325
Wildman-Crippen Contributions for Refractive Indexa
Table-specific nomenclature: e = N, O, P, S, F, Cl, Br, or I; ! = not (e.g., !e = not any of the e elements); c = aromatic carbon; n = aromatic nitrogen; o = aromatic oxygen;
A = any nonhydrogen atom; a = aromatic, not necessarily carbon; bond types are single (}), double (=), triple (#), and aromatic (:)
Type
Description
C1 1°, 2° aliphatic
C2 3°, 4° aliphatic
C3 1°, 2° aliphatic e
C4 3º, 4º aliphatic e
C5 olefin e
C6 olefin
C7 acetylene
C8 1° aromatic c
C9 1° aromatic e
C10 2° aromatic
C11 3° aromatic
C12 4° aromatic
C13 aromatic e
C14 aromatic F
C15 aromatic Cl
C16 aromatic Br
C17 aromatic I
C18 aromatic
C19 bridgehead
C20 4° aromatic
C21 4° aromatic
C22 4° aromatic
C23 4° aromatic
C24 4° aromatic
C25 4° aromatic
C26 C=C aromatic
C27 aliphatic e
CS supplemental C
H1 hydrocarbon
H2 alcohol
H3 amine/amide
H4 acid
HS supplemental H
MR
C(4H), C(3H)(C), C(2H)(2C)
C(H)(3C), C(4C)
C(3H)(e), C(2H)(2e)
C(H)(3e), C(4e)
C(=e)
C(2H)(=A), C(H)(=A), C(=A)
C(#A)
C(3H)(c)
C(3H)(ae)
C(2H)(a)
C(H)(a)
C(a)
c(!e)
c(F)
c(Cl)
c(Br)
c(I)
c(H)
c(3:a)
c(2:a)(a)
c(2:a)(C)
c(2:a)(N)
c(2:a)(O)
c(2:a)(S)
c(2:a)(=C), c(2:a)(=N, =O)
C(=C)(a)
C(4!e)
any other C
H(H), H(C)
H(O)
H(N), H(O)(N)
H(COO), H(COS), H(OO)
any other H
2.503
2.433
2.753
2.731
5.007
3.513
3.888
2.464
2.412
2.488
2.582
2.576
4.041
3.257
3.564
3.180
3.104
3.350
4.346
3.904
3.509
4.067
3.853
2.673
3.135
4.305
2.693
3.243
1.057
1.395
0.9627
1.805
1.112
Type
Description
MR
N(2H)(A)
N1 1° amine
N(H)(2A)
N2 2° amine
N(2H)(a)
N3 1° aromatic amine
N(H)(a)(A, a)
N4 2° aromatic amine
N5 imine
N(H)(=A, =a)
N6 substituted imine
N[2(=A, =a)]
N(3A)
N7 3° amine
N(a)[2(a, A)]
N8 3° aromatic amine
N9 nitrile
N(#A)
N11 aromatic N
n
N13 4° amine
N(4A,), N(=A)[2(A, a)]
NS supplemental N
any other N
O1 aromatic
o
O2 alcohol
O(H), O(2H)
O3 aliphatic ether
O[2(C, A)]
O4 aromatic ether
O(a)(A, a)
O5 oxide
O(=O, =N), O(A)(N)
O6 oxide
O(A)(S)
O7 oxide
O(A)(!N, !S)
O8 aromatic carbonyl
O(=c)
O9 aliphatic carbonyl
O(=C)[2(C, H, N, A]
O10 aromatic carbonyl
O(=C)(c)(C, H, A, a)
O11 carbonyl (e)
O(=C)(A, a)
O12 acid
O(C=O)
OS supplemental O
any other O
F fluorine
F(A)
Cl chlorine
Cl(A)
Br bromine
Br(A)
I iodine
I(A)
P phosphorous
P(A)
S1 aliphatic S
S(A)
S3 aromatic S
s(A)
pblk all remaining p-block elements
2.262
2.173
2.827
3.000
1.757
2.428
1.839
2.819
1.725
2.202
0.2604
2.134
1.080
0.8238
1.085
1.182
3.367
0.7774
0.000
3.135
0.000
0.2215
0.3890
—
0.6865
1.108
5.853
8.927
14.02
6.920
7.591
6.691
5.754
Wildman, S. A., and G. M. Crippen, J. Chem. Inf. Comput. Sci. 39 (1999): 868.
a
This value for RD is used in Eq. (2.22) to obtain
n=
with the coefficients given by
122.16 + 2(1.00651)(37.4998)
= 1.530
122.16 − (1.00651)(37.4998)
Applicability
The predicted value differs by 0.3 percent from the experimental value of 1.535 given
in the DIPPR database.
Dielectric Constant The dielectric constant is the ratio of the electric
field strength in vacuum to that in the material for the same charge
distribution. Equivalently, it is the ratio of the capacitance between two
parallel charged plates when filled with the material to that of a vacuum
with identical charges on the plates.
Recommended Method Liu method.
Reference: Liu, J-P, W. V. Wilding, N. F. Giles, and R. L. Rowley, J. Chem. Eng.
Data 55 (2010): 41–45.
Classification: QSPR.
Expected uncertainty: Generally less than 1 percent for nonpolar organic
liquids and less than 20 percent for polar organic liquids.
Applicability: Organic liquids. Not valid if the predicted dielectric constant
is greater than 50.
Input data: For hydrocarbons and nonpolar molecules, the dipole
moment μ, solubility parameter δ, and refractive index n are required. For
polar and nonhydrocarbon molecules, the van der Waals area Avdw and number of oxygen-containing groups are additionally required.
Description: The general correlation for the dielectric constant ε is
Hydrocarbons
and nonpolar
C1
0.1283
0
C2
2.8251 × 10−5
C3
0.2150
C4
−0.3416
0.5239
4.072 × 108
7.408 × 10−5
−0.3248
The summation term shown in Eq. (2.23) is only for oxygen-containing
groups in the molecule in which Gi is the contribution shown below and ki
(ki > 1) is the number of occurrences of that group in the molecule.
Group
Example
Group
Gi
Example
Gi
0.2879
–OH(na)
alcohol
0.2230
[S, N, P] = O thionyl chloride
ketone
0.3615
–OH(a)
phenol
0.0990
>C=O
0.3348
2-pyrrolidone
0.0075
>C=O ring
–OH(C < 5)* ethanol
–COO–
ester
−0.0650
–CHO
aldehyde
0.1617
–COOH
acid
−0.5900
*Applied in addition to regular −OH group for molecules with fewer than 5 C atoms.
Example Calculate the dielectric constant of salicylaldehyde at 303 K. The structure of salicylaldehyde is shown below with the two different oxygen-containing groups
and their contributions that are to be used in Eq. (2.23).
O
−1
O Groups
A
G
µ
δ
ln ε = C 0 + C1 + C 2 2 vdw −1 + C 3 1/2 -3/2 + C 4 n 2 + ∑ i
m ⋅ kmol
D
J ⋅m
ki
i
(2-23)
C0
−0.1694
HO
Group
Gi
ki
−CHO
0.1617
1
−OH(a)
0.0990
1
2-326
PHYSICAL AnD CHEMICAL DATA
Values of the input properties for Eq. (2.23) obtained from the DIPPR database are
μ = 3.08794 D, Avdw = 8.43 × 108 m2/kmol, d = 21330 J1/2∙m−3/2, n = 1.57017. Equation (2.23)
is then used to obtain the dielectric constant:
4.072
ln ε = −0.3416 + (0.5239) ( 3.08794 ) +
8.43
+ (7.408 × 10 −5 )(21330) − (0.3248)(1.57017)2 + 0.1617 + 0.0990
C = αc − 42D
B = −36D
A = 35D
Values of the constant K [Vetere, A., Ind. Eng. Chem. Res., 30 (1991): 2487]
are as follows:
Class
ln e = 2.799 and e = 16.43
A few reported experimental values are 13.9 at 293 K, 17.1 at 303 K, and 18.35 at 293.15 K.
Value
Acids
K = −0.120 + 0.025h
Alcohols
K = 0.373 − 0.030h
All other organic compounds
K = 0.0838
VAPOR PRESSURE
Liquids Vapor pressure is the equilibrium pressure at a given temperature of pure, coexisting liquid and vapor phases. The vapor pressure curve is a
monotonic function of temperature from its minimum value (the triple point
pressure) at the triple point temperature Tt, to its maximum value, Pc, at Tc.
Liquid vapor pressure data over a limited temperature range can be correlated with the Antoine equation [Antoine, C., C.R., 107 (1888): 681, 836]
In
P∗
B
= A−
T /K + C
Pa
aτ + bτ1.5 + cτ 2.5 + d τ 5
1− τ
K = 0.0838
D = (0.0838)(7.0248 − 3.758) = 0.2738
C = 7.0248 − (42)(0.2738) = −4.4729
B = −(36)(0.2738) = −9.8552
A = −(35)(0.2738) = 9.5814
Calculation using Eq. (2-28) at each T (detailed calculation shown for T = 500 K):
Tr = 500/632.35 = 0.7907
(2-25)
where τ ≡ 1 − Tr
ln Pr = 9.5814 −
or the Riedel equation [Riedel, L., Chem. Ing. Tech., 26 (1954): 679]
ln
T
T
P∗
B
= A+
+ C ln + D
K
Pa
T /K
K
aτ + bτ1.5 + cτ 2.5 + d τ5 + eτ 6
1− τ
Pr = exp(−1.7651) = 0.1712
(for alcohols)
(2-27)
B
+ C ln Tr + DTr6
Tr
(2-28)
is used with the constants for this equation determined from the following
set of relationships:
ψ = −35 +
h = Tbr
36
+ 42 ln Tbr − Tbr6
Tbr
ln ( Pc /1.01325 bar)
1 − Tbr
αc =
P = PrPc = (0.1712)(45.1911 bar) = 7.74 bar
(2-26)
Correlation of experimental data within a few tenths of a percent over the
entire fluid range can usually be obtained with either the Wagner or Riedel
equations.
Two prediction methods are recommended for liquid vapor pressure. The
first method is based on the Riedel equation; the second is a CS method.
Both methods require Tc and Pc as input, but these can be estimated by the
methods shown earlier if experimental values are unavailable.
Recommended Method 1 Riedel method.
Reference: Riedel, L., Chem. Ing. Tech., 26 (1954): 679.
Classification: Empirical extension of theory and corresponding states.
Expected uncertainty: Varies strongly depending upon relative T, but
1 percent or less above Tb is typical with uncertainties of 5 to 30 percent
near the triple point.
Applicability: Most organic compounds.
Input data: Tb, Tc, Pc.
Description: Equation (2-26) in reduced form
ln Pr = A +
9.8552
− 4.4729 ln 0.7907 + (0.2738)(0.7907) 6 = −1.7651
0.7907
E
In its original form, E in Eq. (2-26) was assigned a value of 6, but other integer values of E from 1 to 6 have been found to be more effective for different
families of chemicals in representing the vapor pressure over the whole liquid range. With the best value of E, either the Riedel or the Wagner equation
can be used to correlate most fluids over the whole liquid range, but a fifth
term is used in the Wagner equation for alcohols [Poling, B. E., Fluid Phase
Equilib., 116 (1996): 102]:
ln Pr∗ =
Tbr = 404.87/632.35 = 0.640
36
ψ = −35 +
+ 42 ln(0.640) − (0.640) 6 = 2.431
0.640
(3.758) (0.0838)(2.431) + ln (45.191/1.01325)
= 7.0248
αc =
(0.0838)(2.431) − ln (0.640)
(2-24)
Data from the triple point to the critical point can be correlated with either a
modified form of the Wagner equation [Wagner, W., A New Correlation Method
for Thermodynamic Data Applied to the Vapor-Pressure Curve of Argon, Nitrogen, and Water, J. T. R. Watson (trans. and ed.), IUPAC Thermodynamic Tables
Project Centre, London, 1977; Ambrose, D., J. Chem. Thermodyn., 18 (1986):
45; Ambrose, D., and N. B. Ghiassee, J. Chem. Thermodyn., 19 (1987): 903, 911]
ln Pr∗ =
Example Estimate the vapor pressure of chlorobenzene at 50 K intervals from
300 to 600 K.
Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and
Pc = 45.1911 bar.
Auxiliary Quantities:
3.758 K ψ + ln(Pc /1.01325 bar)
K ψ − ln Tbr
D = K (α c − 3.758)
(2-28a)
T/K
Tr
ln Pr
P/bar
PDIPPR/bar
% Error
300
350
400
450
500
550
600
0.4744
0.5535
0.6326
0.7116
0.7907
0.8698
0.9488
−7.8532
−5.5704
−3.9323
−2.7101
−1.7651
−1.0067
−0.3705
0.0176
0.172
0.886
3.01
7.74
16.51
31.20
0.0175
0.172
0.880
2.98
7.67
16.39
31.11
0.3
0.1
0.6
0.9
0.9
0.8
0.3
Recommended Method 2 Ambrose-Walton method.
References: Ambrose, D., and J. Walton, Pure & Appl. Chem., 61 (1989):
1395; Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510.
Classification: Corresponding states.
Expected uncertainty: Varies strongly with relative T, but less than
1 percent is typical above Tb if the acentric factor is known.
Applicability: Most organic compounds.
Input data: Tb, Tc, Pc, and w.
Description: The acentric factor is used to interpolate within the simplefluid and deviation terms for ln P*. The f (i) terms have been obtained from
correlations of the reference fluid vapor pressures with the Wagner vapor
pressure equation
ln Pr* = f (0) + ωf (1) + ω 2 f (2)
−5.97616 τ + 1.29874 τ1.5 − 0.60394 τ 2.5 − 1.06841τ 5
1− τ
−5.03365 τ + 1.11505 τ1.5 − 5.41217 τ 2.5 − 7.46628 τ 5
(1)
f =
1− τ
−0.64771τ + 2.41539 τ1.5 − 4.26979 τ 2.5 + 3.25259 τ 5
(2)
f =
1− τ
f (0) =
(2-29)
where t = 1 − Tr.
Example Repeat the calculation of the liquid vapor pressure of chlorobenzene at
50-K intervals from 300 to 600 K using the Ambrose-Walton method.
Input information: From the DIPPR 801 database, Tc = 632.35 K, Pc = 45.1911 bar, and
w = 0.249857.
Auxiliary quantities:
Tr = 500/632.35 = 0.7907
t = 1 − 0.7907 = 0.2093
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
Simple-fluid and deviation vapor pressure terms at each T (shown for T = 500 K):
( − 5.97616)(0.2093) + (1.29874)(0.2093)1.5 − (0.60394)(0.2093) 2.5 − (1.06841)(0.2093)5
0.7907
= −1.4405
f (0) =
( − 5.03365)(0.2093) + (1.11505)(0.2093)1.5 − (5.41217)(0.2093) 2.5 − (7.46628)(0.2093)5
0.7907
= −1.3383
Applicability: Organic compounds for which group contributions have
been regressed.
Input data: Molecular structure.
Description: GC values from Table 2-161 are directly additive for both
enthalpy of formation and absolute third-law entropies:
∆H of
f (1) =
(−0.64771)(0.2093) + (2.41539)(0.2093)1.5 − (4.26979)(0.2093) 2.5 + (3.25259)(0.2093)5
0.7907
= 0.0145
f (2) =
Calculation using Eq. (2-29):
*
ln Pr = −1.4405 + (0.249857)(−1.3383) + (0.249857)2(0.0145) = −1.774
P* = (45.1911 bar)[exp(−1.774)] = 7.667 bar
T
t
f (0)
300
350
400
450
500
550
600
0.5256
0.4465
0.3674
0.2884
0.2093
0.1302
0.0512
−5.9228
−4.3006
−3.1036
−2.1800
−1.4405
−0.8289
−0.3068
f (1)
−7.5966
−5.0017
−3.3106
−2.1576
−1.3383
−0.7318
−0.2612
f (2)
−0.3050
−0.1439
−0.0437
0.0043
0.0145
0.0036
−0.0081
ln P*r
P*/bar
P*DIPPR/
bar
% Error
−7.840
−5.559
−3.933
−2.719
−1.774
−1.012
−0.373
0.0178
0.174
0.885
2.98
7.67
16.43
31.14
0.0175
0.172
0.880
2.98
7.67
16.39
31.11
1.4
1.5
0.5
0.0
0.0
0.3
0.1
2-327
kJ/mol
N
= ∑ ni (∆H of )i
i =1
N
So
= ∑ ni (S o )i
−1 −1
J ⋅ mol K
i =1
(2-31)
where ( ∆H of )i = enthalpy of formation GC value and (So)i = entropy GC value,
both obtained from Table 2-161.
Group values in Table 2-161 are defined by the central, nonhydrogen
group and the atoms bonded to that group. Thus, C—(2H)(2C) represents
a C atom to which 2 H and 2 C atoms are bonded. For example, propane
(CH3—CH2—CH3) is composed of three groups: two C—(3H)(C) and one
C—(2H)(2C).
Example Estimate the standard and ideal gas enthalpies of formation of
o-toluidine.
Input information: Because the melting point (256.8 K) and boiling point (473.49 K)
for o-toluidine bracket 298.15 K, the standard state phase at 298.15 K and 1 bar is liquid.
Structure:
Group contributions:
Solids Below the triple point, the pressure at which the solid and vapor
phases of a pure component are in equilibrium at any given temperature is
the vapor pressure of the solid. It is a monotonic function of temperature
with a maximum at the triple point. Solid vapor pressures can be correlated
with the same equations used for liquids. Estimation of solid vapor pressure
can be made from the integrated form of the Clausius-Clapeyron equation
ln
P ∗ ∆H sub Tt
=
1−
Pt∗
RTt T
Group
ni
Cb—(H)(2Cb)
Cb—(C)(2Cb)
Cb—(N)(2Cb)
C—(3H)(C)
N—(2H)(Cb)
4
1
1
1
1
Total
DH of gas
DH of liq.
So gas
Ss liq.
13.81
23.64
−1.30
−42.26
19.25
54.57
8.16
19.16
1.50
−47.61
−11.00
−5.31
48.31
−35.61
−43.53
127.32
126.90
368.32
28.87
−19.50
−24.43
83.30
71.71
226.56
(2-30)
where Tt = triple point temperature
Pt* = triple point pressure
DHsub = enthalpy of sublimation
The liquid and solid vapor pressures are identical at the triple point. A good
vapor pressure correlation that is valid at the triple point may be used to
obtain the triple point pressure. Estimating solid vapor pressures by using
Eq. (2-30) generally requires an estimation of DHsub, and so the illustrative
example is combined with the example on enthalpy of sublimation in the
section on latent enthalpy.
THERMAL PROPERTIES
Enthalpy of Formation The standard enthalpy (heat) of formation
is the enthalpy change upon formation of 1 mole of the compound in its
standard state from its constituent elements in their standard states. Two
different standard enthalpies of formation are commonly defined based on
the chosen standard state. The standard enthalpy of formation ∆H sf uses the
naturally occurring phase at 298.15 K and 1 bar as the standard state while
the ideal gas enthalpy (heat) of formation ∆H of uses the compound in the
ideal gas state at 298.15 K and 1 bar as the standard state. In both cases,
the standard state for the elements is their naturally occurring state of
aggregation at 298.15 K and 1 atm. Sources for data include DIPPR, TRC,
SWS, JANAF, and TDB. The Domalski-Hearing method is the most accurate
general method for estimating either ∆H sf or ∆H of if the appropriate GC values are available, but a CC method is also as accurate for estimating ∆H of if
an isodesmic reaction can be formulated and used. The Domalski-Hearing
method also applies to entropies, and the entropy predictive equations are
listed in this section for convenience because they are equivalent in form to
the enthalpy equations. However, discussion and illustration of the estimation methods for entropy are delayed to the next subsection.
Recommended Method Domalski-Hearing method.
Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22
(1993): 805.
Classification: Group contributions.
Expected uncertainty: 3 percent.
Calculation from Eq. (2-31):
∆H of
kJ/mol
= 54.57
So
= 368.32
J/(mol ⋅ K)
∆H Sf
kJ/mol
= −5.31
Ss
= 226.56
J/(mol ⋅ K)
o
The recommended DIPPR 801 standard enthalpies of formation are ∆H f = 53.20 kJ/mol
s
and ∆H f = −4.72 kJ/mol. The estimated values are higher than the recommended
values by 2.6 and 12.5 percent, respectively. The recommended DIPPR 801 standard
entropies are So = 355.8 J/(mol ⋅ K) and Ss = 231.2 J/(mol ⋅ K). The estimated values differ
from these by 3.5 and −2.0 percent, respectively.
Recommended Method Isodesmic reaction.
Reference: Foresman, J. B., and A. Frisch, Exploring Chemistry with
Electronic Structure Methods, 2d ed., Gaussian Inc., Pittsburgh, Pa., 1996.
Classification: Computational chemistry.
Expected uncertainty: 5 to 10 percent depending upon the level of theory
and basis set size used.
Applicability: Compounds for which an isodesmic reaction can be
formulated.
Input data: Experimental ∆H of values for all other participants in the
isodesmic reaction.
Description: While ab initio calculations of absolute enthalpies are not
currently as accurate as GC methods, relative enthalpies of molecules calculated with the same level of theory and basis set can be very accurate, as in
the case of isodesmic reactions. An isodesmic reaction is one in which the
number and type of bonds are preserved during the reaction. For example,
the reaction of acetaldehyde with ethane to form acetone and methane is
2-328
PHYSICAL AnD CHEMICAL DATA
TABLE 2-161
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with
triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
∆Hfo
So
∆Hfs liq.
S s liq.
∆Hfs solid
S s solid
56.69
23.01
−16.89
0.00
−33.19
0.00
0.00
0.00
21.75
CH Groups
C}(3H)(C)
C}(2H)(2C)
C}(H)(3C)
}CH3 corr (tertiary)
C}(4C)
}CH3 corr (quaternary)
}CH3 corr (tert/quat)
}CH3 corr (quat/quat)
Cd}(2H)
Cd}(H)(C)
Cd}(2C)
Cd}(H)(Cd)
Cd}(C)(Cd)
Cd}(Cd)(Cb)
Cd}(H)(Cb)
Cd}(C)(Cb)
Cd}(H)(Ct)
C}(4H), Methane
Cd}(2Cb)
C}(2H)(C)(Cd)
C}(H)(2C)(Cd)
}CH3 corr (tertiary)
C}(3C)(Cd)
}CH3 corr (quaternary)
C}(H)(C)(2Cd)
C}(2H)(2Cd)
C}(2H)(Cd)(Cb)
C}(H)(C)(Cd)(Cb)
cis (unsat) corr
tert}Butyl cis corr
Ct}(H)
Ct}(C)
Ct}(Cd)
Ct}(Cb)
Ct}(Ct)
C}(2H)(C)(Ct)
C}(H)(2C)(Ct)
}CH3 corr (tertiary)
C}(3C)(Ct)
}CH3 corr (quaternary)
C}(2H)(2Ct)
C}(2C)(2Ct)
Ca
Cb}(H)(2Cb)
Cb}(C)(2Cb)
Cb}(Cd)(2Cb)
Cb}(Ct)(2Cb)
Cb}(3Cb)
C}(2C)(2Cb)
C}(2H)(C)(Cb)
C}(H)(2C)(Cb)
C}(Cb)(3C)
C}(2H)(2Cb)
C}(H)(C)(2Cb)
C}(H)(3Cb)
C}(3Cb)(C)
C}(4Cb)
Cbf}(Cbf)(2Cb)
Cbf}(Cb)(2Cbf)
Cbf}(3Cbf)
Cb}(2Cb)(Cbf)
Cb}(Cb)(2Cbf)
ortho corr, hydrocarbons
meta corr, hydrocarbons
Cyclopropane rsc (unsub)
Cyclobutane rsc
Cyclopentane rsc (unsub)
Cyclohexane rsc (unsub)
Cycloheptane rsc
Cyclooctane rsc
Cyclononane rsc
Cyclodecane rsc
−42.26
−20.63
−1.17
−2.26
19.20
−4.56
−1.80
−0.64
26.32
36.32
44.14
28.28
36.78
127.32
39.16
−53.60
0.00
−149.49
0.00
0.00
0.00
115.52
33.05
−50.84
27.74
−61.33
−47.61
−25.73
−4.77
−2.18
17.99
−4.39
−1.77
−0.64
21.75
31.05
39.16
22.18
30.42
83.30
32.38
−23.89
0.00
−98.65
0.00
0.00
0.00
86.19
28.58
−29.83
13.30
−41.92
28.28
37.95
28.28
−74.48
32.88
−20.88
−1.63
−2.26
22.13
−4.56
−1.17
−18.92
27.74
−51.97
27.74
206.92
22.18
38.58
22.18
13.30
−46.74
−29.41
−5.98
−2.34
12.47
−4.35
−2.70
−2.24
22.43
25.48
32.97
17.53
27.91
56.07
17.53
13.30
17.53
38.20
−50.38
0.00
−150.23
0.00
−53.60
42.08
31.67
−28.07
0.00
−108.20
0.00
−23.89
19.32
49.91
−24.35
−6.49
−2.34
12.51
−4.35
−5.98
−21.60
4.85
17.24
113.50
115.10
121.42
120.76
120.76
−19.70
−3.16
−2.26
5.06
0.00
101.96
26.32
39.92
17.77
25.94
42.80
−45.69
0.00
0.00
0.00
67.57
14.25
5.73
17.57
110.34
101.66
32.36
103.28
103.28
−29.41
−4.56
−41.14
0.00
142.67
13.81
23.64
24.17
24.17
21.66
26.28
48.31
−35.61
−33.85
−33.85
−36.57
−21.34
−4.52
18.28
−46.43
42.59
−48.00
−147.19
30.83
−25.73
−5.02
−2.18
20.79
−4.39
−4.77
−24.43
−24.73
−6.90
5.27
17.48
104.47
107.15
114.77
119.00
104.80
−22.13
−2.18
22.83
−4.39
−39.08
20.67
134.68
8.16
19.16
19.12
19.12
17.21
−24.81
−5.82
18.70
−26.50
−21.47
0.00
0.00
14.39
28.87
−19.50
−9.04
−9.04
47.40
−13.90
−96.10
51.97
28.12
−6.86
27.04
20.10
16.00
3.59
22.46
1.26
−0.63
115.15
110.89
26.75
0.68
26.34
40.65
52.91
51.99
0.00
15.83
11.50
−0.90
−5.54
−2.50
0.00
134.86
126.04
116.22
78.18
73.97
70.78
3.26
0.00
111.58
106.64
22.84
−1.77
23.50
38.10
50.40
50.61
0.00
0.00
51.48
42.24
10.07
15.89
2.96
−2.34
26.38
−4.35
131.08
6.53
13.90
20.27
20.07
17.03
52.81
−22.10
−3.50
21.57
−21.44
16.40
34.48
116.25
64.89
14.10
12.00
1.94
−8.77
47.93
5.00
2.00
114.43
34.00
10.94
21.75
21.75
0.00
0.00
−16.89
0.00
0.00
0.00
0.00
22.75
−5.50
−10.00
−10.00
−6.00
26.90
22.85
−12.62
−6.00
2.00
7.00
0.00
0.00
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-161
2-329
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon
with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
DHfo
DHfs liq.
So
S s liq.
DHfs solid
S s solid
CHO Groups
CO}(2H), formaldehyde
CO}(C)(CO)
CO}(H)(CO)
CO}(CO)(Cb)
CO}(O)(CO)
CO}(Cd)(O)
CO}(C)(O)
CO}(H)(O)
CO}(2O)
CO}(H)(Cd)
CO}(2Cb)
CO}(C)(Cb)
CO}(H)(Cb)
CO}(O)(Cb)
CO}(2C)
CO}(H)(C)
CO}(C)(Cd)
O}(2CO), aliphatic
O}(2CO), aromatic
O}(Cd)(CO)
O}(C)(CO)
O}(H)(CO)
O}(Cb)(CO)
O}(C)(O)
O}(H)(O)
O}(2Cd)
O}(H)(Cd)
O}(C)(Cd)
O}(2Cb)
O}(C)(Cb)
O}(H)(Cb)
O}(2C)
O}(H)(C)
Cd}(H)(CO)
Cd}(C)(CO)
Cd}(O)(Cd)
Cd}(O)(C)
Cd}(O)(H)
Ct}(CO)
Cb}(CO)(2Cb)
Cb}(O)(2Cb)
C}(2H)(2CO)
C}(CO)(3C)
C}(H)(CO)(2C)
C}(2H)(CO)(C)
C}(3H)(CO)
C}(2H)(CO)(Cd)
C}(2H)(CO)(Ct)
C}(2H)(CO)(Cb)
C}(H)(CO)(C)(Cb)
C}(H)(O)(CO)(C)
C}(4O)
C}(H)(3O)
C}(3O)(C)
C}(2O)(2C)
C}(H)(2O)(C)
C}(2H)(2O)
C}(2H)(O)(Cb)
C}(2H)(O)(Cd)
C}(H)(CO)(C)(Cb)
C}(H)(CO)(2Cb)
C}(O)(3Cb)
C}(O)(3C) (ethers, esters)
C}(H)(O)(2C) (ethers, esters)
C}(O)(3C) (alcohols, peroxides)
C}(H)(O)(2C) (alcohols, peroxides)
C}(2H)(O)(C)
C}(3H)(O)
O}(CO)(O)
C}(2C)(O)(Cb)
C}(H)(C)(2O)
−108.60
−121.29
−105.98
−112.30
−123.75
−136.73
−137.24
−124.39
−111.88
−126.96
−110.00
−148.82
−121.35
−125.00
−132.67
−124.39
224.54
−214.50
−238.30
−198.03
−188.87
−254.30
−167.00
−20.75
−72.26
−139.29
34.16
−135.04
62.59
62.59
147.03
64.31
147.03
36.03
101.71
−123.30
−155.56
−149.37
−142.42
−122.00
−153.05
−119.00
−145.22
−138.12
−140.00
−152.76
−142.42
−230.50
−220.90
−201.42
−196.02
−285.64
−165.50
−23.50
−101.75
−137.32
−129.33
−77.66
−92.55
−160.30
−101.42
−159.33
32.30
121.50
29.33
121.50
35.19
−133.72
−85.27
−104.85
−191.75
−110.83
−191.50
26.61
36.78
44.14
36.32
−61.34
−50.84
33.05
30.42
39.08
31.05
15.50
−4.75
−30.74
23.93
−0.25
−21.84
−42.26
−16.95
−25.48
−16.20
126.63
−152.46
−113.97
−114.39
−53.56
−57.78
−62.22
−33.76
−27.49
9.50
−19.46
−13.50
−26.10
−32.90
−42.26
−88.00
15.30
−43.72
39.58
127.32
37.49
−141.92
−52.80
−144.60
−43.05
43.43
127.32
10.50
−5.61
−23.06
26.15
−3.89
−24.14
−47.61
−19.62
−26.61
−11.67
123.43
−133.34
−107.74
−99.54
−41.30
−51.42
−62.89
−29.17
−28.62
0.79
−21.00
−11.13
−27.60
−35.80
−47.61
−90.00
25.80
−140.75
32.72
94.68
33.81
93.55
−117.75
−120.81
−134.10
−153.60
32.90
32.13
−123.00
−42.92
−116.00
−143.70
−160.18
−145.00
−157.95
23.72
32.13
−235.00
−207.00
38.28
38.28
−210.60
−282.15
−170.00
−30.20
−105.30
12.09
21.78
45.32
23.31
−96.20
−122.87
−199.25
−119.00
−199.66
7.82
3.14
43.89
26.78
43.89
28.62
28.62
27.53
−85.98
−24.52
39.87
83.30
27.91
32.97
25.48
144.52
8.15
1.00
−19.10
24.02
−9.83
−27.90
−46.74
24.73
56.69
−46.71
14.81
−14.39
8.08
−41.92
−29.83
28.58
−10.59
0.08
1.59
23.85
−94.68
−25.31
−122.48
−29.83
32.59
83.30
−14.39
3.72
60.46
−0.50
−20.08
−12.25
−29.08
−33.00
−46.74
−80.50
29.30
−52.50
−14.77
6.95
24.73
56.69
(Continued )
2-330
PHYSICAL AnD CHEMICAL DATA
TABLE 2-161
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon
with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
DHfo
So
DHfs liq.
S s liq.
DHfs solid
−47.61
−30.80
−14.65
−2.18
5.10
−4.39
83.30
32.38
−20.00
0.00
−87.99
0.00
−26.09
0.33
0.33
51.50
112.00
25.30
75.00
119.00
71.71
71.71
32.09
−38.62
60.58
22.05
−26.94
−46.74
−34.00
−13.90
−2.34
1.00
−4.35
−26.00
−33.31
−6.30
−46.00
47.80
101.00
18.97
S s solid
CHN and CHNO Groups
C}(3H)(N)
C}(2H)(C)(N)
C}(H)(2C)(N)
}CH3 corr (tertiary)
C}(3C)(N)
}CH3 corr (quaternary)
C}(2H)(2N)
C}(2H)(Cb)(N)
N}(2H)(C) ( first, amino acids)
N}(2H)(C) (second, amino acids)
N}(H)(2C)
N}(3C)
N}(2H)(N)
N}(H)(C)(N)
N}(2C)(N)
N}(2Cb)(N)
N}(H)(Cb)(N)
N}(2CO)(N)
N}(H)(2Cd)
N}(C)(2Cd)
N}(2H)(Cb)
N}(H)(C)(Cb)
N}(2C)(Cb)
N}(C)(2Cb)
N}(H)(2Cb)
N}(3Cb)
NI}(C)
NI}(Cb)
NA}(C)
NA}(Cb)
NA}(oxide)(C)
C}(2H)(C)(NA)
C}(H)(2C)(NA)
C}(3C)(NA)
Cd}(H)(N)
Cd}(C)(N)
Cb}(N)(2Cb)
Cb}(NO)(2Cb)
Cb}(NO2)(2Cb)
Cb}(CNO)(2Cb)
Cb}(CN)(2Cb)
Cb}(NA)(2Cb)
Cb}(H)(2NI)
CO}(H)(N)
CO}(C)(N)
CO}(Cb)(N) (amides)
CO}(Cb)(N) (amino acids)
CO}(Cd)(N)
CO}(2N)
N}(2H)(CO) (amides, ureas)
N}(2H)(CO) (amino acids)
N}(H)(C)(CO) (amides, ureas)
N}(H)(C)(CO) (amino acids)
N}(2C)(CO)
N}(H)(Cb)(CO)
N}(H)(2CO)
N}(C)(2CO)
N}(Cb)(2CO)
N−(2Cb)(CO)
N}(C)(Cb)(CO)
C}(3H)(CN), acetonitrile
C}(2H)(C)(CN)
C}(H)(2C)(CN)
C}(3C)(CN)
C}(2C)(2CN)
C}(2H)(Cd)(CN)
Cd}(H)(CN)
Ct}(CN)
C}(3H)(NO2), nitromethane
C}(2H)(2NO2), dinitromethane
C}(H)(3NO2), trinitromethane
C}(4NO2), tetranitromethane
C}(2H)(C)(NO2)
−42.26
−28.30
−16.70
−2.26
0.29
−4.56
−30.00
−24.14
19.25
19.25
67.55
116.50
47.70
89.16
120.71
127.32
42.26
−63.55
0.00
−152.59
0.00
124.40
126.90
33.96
−61.71
122.18
87.50
73.40
83.55
120.64
19.25
59.00
126.40
120.44
83.55
123.15
81.46
69.00
109.50
109.50
40.80
−20.70
−2.66
11.50
−16.00
−5.74
−1.30
21.50
−1.45
−177.63
151.00
22.55
6.30
−124.39
−133.26
50.50
97.38
−11.00
26.25
109.40
97.38
50.50
121.80
73.68
54.50
104.85
104.85
22.65
−25.70
−5.42
15.50
−15.50
−5.62
1.50
−171.80
−111.00
−63.00
−63.00
−16.28
−16.28
45.00
−20.84
−91.00
−11.64
9.12
74.04
94.52
113.50
137.96
95.31
146.65
264.60
−74.86
−58.90
−0.30
82.30
−60.50
126.90
47.01
−43.53
71.71
36.40
−24.43
−28.30
79.95
122.38
20.08
64.75
147.03
56.70
−188.00
−185.00
93.55
96.00
88.25
−190.50
−63.90
−63.90
−17.10
−17.10
62.00
56.20
158.41
284.14
203.60
40.56
66.07
81.50
116.20
66.40
117.28
250.20
−112.60
−104.90
−32.80
38.30
−93.50
0.00
0.00
39.00
48.75
70.00
57.00
103.00
103.00
−29.41
85.25
252.60
167.25
67.86
137.35
66.90
73.62
45.40
88.92
−21.60
36.55
96.50
89.30
45.40
107.50
56.69
23.01
149.62
106.02
−17.91
10.50
−13.00
−3.95
9.75
23.00
−32.50
155.69
121.20
18.65
0.25
−37.57
110.46
50.45
−194.60
−177.75
−177.75
40.00
−203.10
−65.25
−59.75
−9.80
5.50
55.00
−3.50
−30.80
64.00
69.00
18.00
33.03
60.85
72.00
69.85
69.00
102.07
92.72
171.75
−48.00
−99.00
96.15
74.57
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-161
2-331
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon
with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
DHfo
So
DHfs liq.
S s liq.
DHfs solid
S s solid
CHN and CHNO Groups
C}(H)(2C)(NO2)
C}(3C)(NO2)
C}(2H)(Cb)(NO2)
C}(H)(C)(2NO2)
C}(2C)(2NO2)
C}(H)(C)(CO)(N)
C}(2H)(CO)(N)
C}(H)(Cb)(CO)(N)
O}(C)(NO)
O}(C)(NO2)
N}(H)(C)(NO2)
N}(H)(Cb)(NO2)
N}(H)(CO)(NO2)
N}(C)(2NO2)
N}(C)(Cb)(NO2)
N}(2C)(NO)
N}(2C)(NO2)
C}(2H)(C)(N3)
C}(H)(2C)(N3)
C}(2H)(Cb)(N3)
C}(3Cb)(N3)
Cb}(N3)(2Cb)
−53.00
−36.65
−62.00
−36.80
−28.50
−18.70
−3.10
115.32
−24.23
−79.71
166.11
191.92
100.30
183.00
90.00
88.00
−82.50
−61.20
−82.76
−88.80
−77.20
−46.50
−108.96
−89.00
−76.55
−81.00
−91.50
−90.30
−11.65
−30.95
127.50
−124.00
16.50
−14.00
53.50
167.00
59.00
50.00
321.70
255.00
327.40
274.00
347.00
328.60
320.00
−4.00
24.00
150.50
55.00
40.00
346.50
303.50
CHS and CHSO Groups
C}(3H)(S)
C}(2H)(C)(S)
C}(H)(2C)(S)
}CH3 corr (tertiary)
C}(3C)(S)
}CH3 corr (quaternary)
}CH3 corr (tert/quat)
}CH3 corr (quat/quat)
C}(2H)(Cb)(S)
C}(2H)(Cd)(S)
C}(2H)(2S)
Cb}(S)(2Cb)
Cd}(H)(S)
Cd}(C)(S)
S}(C)(H)
S}(Cb)(H)
S}(2C)
S}(H)(Cd)
S}(C)(Cd)
S}(2Cd)
S}(Cb)(C)
S}(C)(S)
S}(Cb)(S)
S}(2S)
S}(2Cb)
S}(H)(S)
S}(H)(CO)
CO}(C)(S)
C}(3H)(SO)
C}(2H)(C)(SO)
C}(H)(2C)(SO)
}CH3 corr (tertiary)
C}(3C)(SO)
}CH3 corr (quaternary)
C}(2H)(Cd)(SO)
cis correction
Cb}(SO)(2Cb)
O}(SO)(H)
O}(C)(SO)
SO}(2C)
SO}(2Cb)
SO}(2O)
SO}(C)(Cb)
C}(3H)(SO2)
C}(2H)(C)(SO2)
C}(H)(2C)(SO2)
}CH3 corr (tertiary)
C}(3C)(SO2)
}CH3 corr (quaternary)
−42.26
−23.17
−5.88
−2.26
13.52
−4.56
−1.80
−0.64
−18.53
−25.93
−25.10
−4.75
36.32
45.73
18.64
48.10
46.99
25.52
54.39
102.60
76.21
27.62
57.45
12.59
102.60
7.95
−5.90
−132.67
−42.26
−29.16
127.32
41.87
−47.36
0.00
−145.38
0.00
0.00
0.00
−47.61
−26.77
−6.07
−2.18
16.69
−4.39
−1.77
−0.64
−23.82
−32.44
83.30
41.09
−16.61
0.00
−86.86
0.00
0.00
0.00
−46.74
56.69
−2.34
0.00
−4.35
−2.70
−2.24
0.00
0.00
0.00
43.72
33.05
−51.92
137.67
57.34
55.19
−5.61
31.05
−10.59
28.58
1.00
25.48
1.59
0.06
28.51
29.82
85.95
89.04
29.80
50.50
58.20
14.36
35.44
30.84
56.07
68.59
93.02
−2.26
4.56
−4.56
−27.56
4.11
15.48
−158.60
−92.60
−66.78
−62.26
−213.00
−72.00
−42.26
−27.03
−14.00
−2.26
1.52
−4.56
0.00
68.59
130.54
64.31
127.32
0.00
5.06
42.00
40.60
−152.76
−47.61
−36.88
33.81
83.30
−46.74
56.69
−2.18
0.97
−4.39
−32.63
5.27
25.44
0.00
−2.34
0.00
0.00
−4.35
0.00
0.00
5.73
7.55
0.00
0.08
75.73
−108.98
22.18
127.32
−47.61
−33.76
83.30
−46.74
−35.96
56.69
0.00
−2.18
2.00
−4.39
0.00
−2.34
3.78
−4.35
0.00
0.00
0.00
0.00
(Continued )
2-332
PHYSICAL AnD CHEMICAL DATA
TABLE 2-161
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon
with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
DHfo
So
DHfs liq.
S s liq.
DHfs solid
S s solid
CHN and CHNO Groups
}CH3 corr (quat/quat)
C}(2H)(Cd)(SO2)
C}(H)(C)(Cd)(SO2)
C}(2H)(Cb)(SO2)
C}(2H)(Ct)(SO2)
Cb}(SO2)(2Cb)
Cd}(H)(SO2)
Cd}(C)(SO2)
Ct}(SO2)
SO2}(Cd)(Cb)
SO2}(2Cd)
SO2}(2C)
SO2}(C)(Cb)
SO2}(2Cb)
SO2}(SO2)(Cb)
SO2}(2O)
SO2}(C)(Cd)
SO2}(Ct)(Cb)
O}(SO2)(H)
O}(C)(SO2)
−0.64
−29.49
−71.99
−29.80
16.36
15.48
51.58
64.01
177.10
−291.55
−306.70
−288.58
−289.10
−287.76
−325.18
−417.30
−316.80
−296.30
−158.60
−91.40
C}(3H)(F), methyl fluoride
C}(3H)(Cl), methyl chloride
C}(3H)(Br), methyl bromide
C}(3H)(I), methyl iodide
C}(C)(3F)
C}(2H)(C)(F)
C}(H)(2C)(F)
C}(3C)(F)
C}(H)(C)(2F)
C}(2C)(2F)
C}(C)(Cl)(2F)
C}(H)(C)(Cl)(F)
C}(C)(3Cl)
C}(H)(C)(2Cl)
C}(2H)(C)(Cl)
C}(2C)(2Cl)
C}(H)(2C)(Cl)
C}(3C)(Cl)
C}(C)(3Br)
C}(H)(C)(2Br)
C}(2H)(C)(Br)
C}(2C)(2Br)
C}(H)(2C)(Br)
C}(3C)(Br)
C}(C)(3I)
C}(H)(C)(2I)
C}(2H)(C)(I)
C}(2C)(2I)
C}(H)(2C)(I)
C}(3C)(I)
C}(H)(C)(Br)(Cl)
N}(C)(2F)
C}(H)(C)(Cl)(O)
C}(2H)(I)(O)
C}(C)(2Cl)(F)
C}(C)(Br)(2F)
C}(C)(2Br)(F)
C}(Br)(Cl)(F)
Cd}(H)(F)
Cd}(H)(Cl)
Cd}(H)(Br)
Cd}(H)(I)
Cd}(C)(Cl)
Cd}(2F)
Cd}(2Cl)
Cd}(2Br)
Cd}(2I)
Cd}(Cl)(F)
Cd}(Br)(F)
Cd}(Cl)(Br)
Ct}(F)
−247.00
−81.90
−37.66
14.30
−673.81
−221.12
−204.46
−202.92
−454.74
−411.39
−462.70
−271.14
−81.98
−79.10
−69.45
−79.56
−55.61
−43.70
87.37
−0.64
−49.05
−2.24
25.44
7.55
0.08
−341.14
−356.62
32.10
−305.40
−361.75
CHX and CHXO Groups
231.93
243.60
254.94
263.14
178.22
146.80
55.76
−61.10
−11.70
−709.07
135.56
164.32
74.48
169.45
−487.23
−400.37
−466.00
138.31
202.14
183.28
159.24
95.41
71.34
−24.26
233.05
−112.93
−102.60
−86.90
−101.80
−71.17
−56.78
145.91
128.45
104.27
−21.78
173.31
−42.65
113.00
−10.75
7.26
84.69
−13.46
−27.31
−7.40
108.78
33.54
228.45
177.78
48.74
68.46
−18.45
−32.64
−90.37
15.90
−322.54
−394.55
88.10
−3.21
191.21
4.14
−343.87
−165.12
4.37
50.94
102.36
−5.06
−329.90
−11.51
137.24
147.85
159.91
169.45
62.76
155.63
175.41
199.16
−235.10
175.61
177.82
188.70
141.71
149.70
−12.67
−2.23
−32.08
−85.65
3.65
24.78
48.60
66.53
170.29
−428.77
115.35
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-161
2-333
Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued )
This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon
with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen.
Group
DHfs liq.
So
DHfo
S s liq.
DHfs solid
S s solid
−191.20
−32.20
19.90
73.70
0.00
−58.41
−55.11
−419.59
−696.66
−44.06
−7.24
−92.56
−225.29
−216.67
−175.49
−117.09
−35.46
54.19
55.47
74.85
61.08
0.00
−194.00
−32.00
13.50
70.40
0.00
−74.75
39.79
43.37
54.45
6.96
25.00
14.00
6.30
0.00
0.00
18.50
40.60
83.55
0.00
0.00
0.00
112.00
6.00
−6.00
8.00
8.00
6.00
10.00
8.50
0.00
34.43
23.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
CHX and CHXO Groups
Ct}(Cl)
140.00
Ct}(Br)
151.30
Ct}(I)
35.53
Cb}(F)(2Cb)
−181.26
67.52
Cb}(Cl)(2Cb)
−17.03
77.08
Cb}(Br)(2Cb)
36.35
88.60
Cb}(I)(2Cb)
94.50
98.26
3.00
0.00
cis corr}(I)(I)
C}(2H)(CO)(Cl)
−44.26
C}(H)(CO)(2Cl)
−40.40
CO}(C)(F)
−379.84
C}(Cb)(3F)
−691.79
179.08
C}(2H)(Cb)(Br)
−29.49
C}(2H)(Cb)(I)
7.31
C}(2H)(Cb)(Cl)
−73.79
CO}(C)(Cl)
−200.54
176.66
CO}(Cb)(Cl)
CO}(C)(Br)
−148.54
CO}(C)(I)
−83.94
C}(H)(C)(CO)(Cl)
−39.88
C}(C)(CO)(2Cl)
ortho corr}(I)(I)
7.56
0.00
ortho corr}(F)(F)
20.90
0.00
ortho corr}(Cl)(Cl)
9.50
0.00
ortho corr}(alkyl)(X)
2.51
0.00
cis corr}(Cl)(Cl)
−4.00
0.00
cis corr}(CH3)(Br)
−4.00
0.00
ortho corr}(F)(Cl)
13.50
0.00
ortho corr}(F)(Br)
37.25
0.00
ortho corr}(F)(I)
85.40
0.00
meta corr}(I)(I)
0.00
0.00
meta corr}(COCl)(COCl)
0.00
0.00
ortho corr}(COCl)(COCl)
0.00
0.00
ortho corr}(F)(CF3)
111.00
0.00
meta corr}(F)(CF3)
2.00
0.00
ortho corr}(F)(CH3)
−3.30
0.00
ortho corr}(F)(F’)
8.00
0.00
ortho corr}(Cl)(Cl’)
8.00
0.00
meta corr}(F)(F)
0.00
0.00
meta corr}(Cl)(Cl)
−5.00
0.00
ortho corr}(Cl)(CHO)
−6.75
0.00
ortho corr}(F)(COOH)
20.00
0.00
ortho corr}(Cl)(COCl)
0.00
0.00
ortho corr}(F)(OH)
25.50
0.00
ortho corr}(Cl)(COOH)
0.00
0.00
ortho corr}(Br)(COOH)
0.00
0.00
ortho corr}(I)(COOH)
0.00
0.00
ortho corr}(NH2)(NH2)
−10.00
0.00
meta corr}(NH2)(NH2)
0.00
0.00
ortho corr}(OH)(Cl)
7.50
0.00
cis corr}(CH3)(I)
−4.00
0.00
*Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805.
isodesmic with 12 single bonds and 1 double bond in both reactants and
products. To use this method, one devises an isodesmic reaction involving
the compound for which ∆H of is to be determined with other compounds for
which experimental ∆H of values are available. Ab initio calculations are performed on all the participating compounds, all at the same level of theory
and basis set size, to obtain the enthalpy for each at 298.15 K. The enthalpy
of reaction is then calculated from
∆H rxn = ∑ν i H i
(2-32)
where ni = stoichiometric coefficient of i (+ for products, − for reactants).
The enthalpy of reaction is also related to DHfo by
0.00
−212.99
5.50
25.50
8.50
0.00
0.00
0.00
19.50
42.50
85.20
20.08
16.06
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
8.00
8.00
8.50
4.00
0.00
20.00
0.00
20.00
20.00
20.00
20.00
0.00
14.00
11.00
0.00
Input information: The isodesmic reaction shown above will be used. The recommended DHfo values from DIPPR 801 for the other three compounds are as follows:
Acetone
Methane
Ethane
−215.70 kJ/mol
−74.52 kJ/mol
−83.82 kJ/mol
Ab initio calculations of enthalpy: With structures optimized using HF/6-31G(d)
model chemistry and energies calculated with B3LYP/6-311+G(3df,2p), the following
enthalpies are obtained (including the zero-point energy):
Acetone
Methane
Ethane
Acetaldehyde
−5.071 × 105 kJ/mol −1.063 × 105 kJ/mol −2.095 × 105 kJ/mol −4.039 × 105 kJ/mol
Calculation using Eq. (2-32):
DHrxn = (−1.063 − 5.071 + 2.095 + 4.039) × 105 kJ/mol = − 41.67 kJ/mol
∆H rxn = ∑ν i (∆H of )i
(2-33)
Calculation using Eq. (2-33):
∆H of ,acetaldehyde = ∆H of ,acetone + ∆H of ,methane − ∆H of ,ethane − ∆H rxn
o
f
With experimental values available for all ∆H except the desired compound, its value can be back-calculated from Eq. (2-33).
Example Estimate the standard ideal gas enthalpy of formation of acetaldehyde.
∆H of ,acetaldehyde = ( − 215.70 − 74.52 + 83.82 + 41.67)
kJ
kJ
= −164.73
mol
mol
The estimated value is 1.0 percent above the DIPPR 801 recommended value of
−166.40 kJ/mol.
2-334
PHYSICAL AnD CHEMICAL DATA
Entropy Absolute or third-law entropies (relative to a perfectly ordered
crystal at 0 K) of a compound in its standard state Ss or of an ideal gas So at
298.15 K and 1 bar can be found in various literature sources (DIPPR, JANAF,
TRC, SWS, and TDB). Very good estimates for Ss or So can be obtained by using
the Domalski-Hearing method. Excellent So values can also be obtained from
statistical mechanics by using experimental vibrational frequencies or values
of the frequencies generated from computational chemistry.
The standard ∆S sf and ideal gas ∆S of entropies of formation at 298.15 K
and 1 bar are related to the standard entropies by
nA
s
s
∆S sf = Scompound
− ∑ν i Selement,
i
i =1
nA
o
s
∆S of = Scompound
− ∑ν i Selement,
i
(2-34)
i =1
where S
is the absolute entropy of element i in its standard state at
298.15 K and 1 bar.
Recommended Method Domalski-Hearing method.
Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22
(1993): 805.
Classification: Group contributions.
Expected uncertainty: 3 percent.
Applicability: Organic compounds for which group contributions have
been regressed.
Input data: Molecular structure.
Description: See description given under Enthalpy of Formation above.
s
element,i
Example Calculate So for ammonia.
Structure: NH3.
Input data: M = 17 kg/kmol. McQuarrie [McQuarrie, D. A., Statistical Mechanics,
Harper & Row, New York, 1976] gives the following 3nA − 6 + d = 12 − 6 + 0 = 6
characteristic vibrational temperatures (in K): 1360, 2330, 2330, 4800, 4880, 4880. The
characteristic rotational temperatures given by McQuarrie are QA = 13.6 K, QB = 13.6 K,
and QC = 8.92 K. For NH3, s = 3.
Vibrational contribution: The table below shows a spreadsheet calculation of the
vibrational terms inside the summation sign in Eq. (2-35).
Qj/K
Qj/(298.15 K)
1207.91
1850.16
1850.16
3688.19
3821.36
3821.36
4.051
6.205
6.205
12.370
12.817
12.817
Svib
0.08929
0.01457
0.01457
0.00006
0.00004
0.00004
Sum 0.1186
Rotational contribution:
1/2
1
(298.15 K)3π e 3
Sr
= ln ⋅
= 5.81593
R
3 (13.6 K)(13.6 K)(8.92 K)
Calculation using Eq. (2-35):
Example Estimate the standard and ideal gas entropies of formation of
o-toluidine.
Standard state entropies: Estimation of Ss and So using the Domalski-Hearing method
was illustrated above in the Enthalpy of Formation section. The standard entropies of
formation can be obtained from the values determined in that example.
Formula: C7H9N. The standard entropies of the elements from the DIPPR 801
database are as follows:
Compound
νi
Sis/[J(kmol ⋅ K)]
N2
H2
C, graphite
1/2
1.9151 × 105
9/2
1.3057 × 105
7
5740
5
1
9
10 J
∆S sf = 2.2656 − (1.9151) − (1.3057) − (7)(0.0574)
2
2
kmol ⋅ K
J
kmol ⋅ K
5
1
9
10 J
∆S of = 3.6832 − (1.9151) − (1.3057) − (7)(0.0574)
2
2
kmol ⋅ K
J
= −3.552 ⋅10 5
kmol ⋅ K
= −4.969 ⋅10 5
∆G of = ∆H of − T ∆S of
Recommended Method Statistical mechanics.
Classification: Theory and computational chemistry.
Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; uncertainty depends
upon model chemistry if frequencies are determined from computational
chemistry, but generally within about 5 percent.
Applicability: Ideal gases.
Input data: M; σ (external symmetry number); characteristic rotational
temperature(s) (ΘA for linear molecules; ΘA, ΘB, and ΘC for nonlinear
molecules); and 3nA − 6 + d characteristic vibrational temperatures Qj.
Description: For harmonic frequencies, the rigorous temperature dependence of So is given by
So 3
M Sr
= ln 6175
+
kg/kmol R
R 2
+
∑
j =1
Θ j Θ j /T
−Θ /T
− 1)−1 − ln (1 − e j )
T (e
0 nonlinear
where δ =
1 linear
1 πT 3e 3 1/2
ln
nonlinear
S r σ Θ A Θ B ΘC
and =
R Te
linear
ln
σΘ A
The calculated value differs from the DIPPR 801 recommended value of 1.927 × 105
J/(kmol ⋅ K) by 0.5 percent.
Gibbs Energy of Formation The standard Gibbs energy of formation
is the Gibbs energy change upon formation of 1 mole of the compound in its
standard state from its constituent elements in their standard states. The
standard Gibbs energy of formation DGfs uses the naturally occurring phase
at 298.15 K and 1 bar as the standard state, while the ideal gas Gibbs energy
of formation DGfo uses the compound in the ideal gas state at 298.15 K and
1 bar as the standard state. In both cases, the standard state for the elements
is their naturally occurring state of aggregation at 298.15 K and 1 bar. Sources
for data include DIPPR, TRC, JANAF, and TDB. The Gibbs energies of formation are related to the corresponding enthalpies and entropies of formation by
Entropies of formation can be calculated from these values by using Eq. (2-34):
3 n A − 6+δ
o
S 298
3
= ln (6175.17) + 5.81593 + 0.1186 = 23.277
R 2
J
o
= 1.935 × 10 5
S 298
kmol ⋅ K
(2-35)
and
∆G sf = ∆H sf − T ∆S sf
(2-36)
and predicted values of ∆G sf and ∆G of are obtained from Eq. (2-36) by estimating the enthalpies and entropies of formation as shown above.
LATEnT EnTHALPY
Enthalpy of Vaporization The enthalpy (heat) of vaporization DHυ
is the difference between the molar enthalpies of the saturated vapor and
saturated liquid at a temperature between the triple point and critical point
(at the corresponding vapor pressure). Variable ∆Hυ is related to the vapor
pressure P* by the thermodynamically exact Clapeyron equation
∆H υ = − R ∆Zυ
d ln P ∗
d ln P ∗
= RT 2 ∆Zυ
dT
d (1/T )
(2-37)
where ∆Zυ = ZG − ZL, ZG = Z of saturated vapor, and ZL = Z of saturated liquid.
Experimental heats of vaporization can be effectively correlated with
2
∆H υ = A (1 − Tr ) B + CTr + DTr
+ ETr3
(2-38)
A simple method for obtaining DHυ at one temperature from a known
value at a reference temperature, say at the normal boiling point, is to truncate Eq. (2-38) after the B term, set B = 0.38, and take a ratio of the ∆Hυ values
at the two conditions to give the Watson [Thek, R. E., and L. I. Stiel, AIChE J.,
12 (1966): 599; 13 (1967): 626] correlation
1 − Tr
∆H υ = ∆H υ , ref
1 − Tr , ref
0.38
(2-39)
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
If an accurate correlation for P* and accurate values for ZG and ZL are
available, Eq. (2-37) is the preferred method for obtaining enthalpies of
vaporization. Otherwise, the CS methods shown below should be used.
Recommended Method 1 Vapor pressure correlation.
Classification: Extension of theory.
Expected uncertainty: The uncertainty varies significantly with temperature and with the quality and temperature range of the vapor pressure data
used in the correlation.
Applicability: Organic compounds for which group contributions have
been regressed.
Input data: Correlations for P*, ZG, and ZL.
Description: An expression for DHυ can be obtained from Eq. (2-37) by
using an appropriate vapor pressure correlation. If one differentiates the
Riedel vapor pressure correlation, Eq. (2-26), in accordance with Eq. (2-37),
one obtains the heat of vaporization as
DHυ = R DZυ (−B + CT + DET E+1)
(2-40)
The ZG and ZL values can be evaluated using the methods given in the
section on densities below.
Example Calculate DHυ for anisole at 452 K.
Input data: The vapor pressure coefficients in the DIPPR 801 database for Eq. (2-26)
are
A = 128.06
B = −9307.7
C = −16.693
D = 0.014919
E=1
The vapor pressure at 452 K is therefore
P∗
9307.7
− 16.693 ln ( 452 ) + 0.014919 (452)1 = 12.155
ln = 128.06 −
Pa
452
2-335
Auxiliary quantities: From the previous example, the reduced temperature variables
are
Tr = 0.7
t = 1 − 0.7 = 0.3
Calculation using Eq. (2-41):
∆H υ
= 7.08(0.3)0.354 + 10.95 (0.35017)(0.3)0.456 = 6.838
RTc
J
kJ
∆H υ = (6.838) 8.314
(645.6 K) = 36.70
mol ⋅ K
mol ⋅ K
This value is 2.2 percent below the DIPPR 801 recommended value of 37.51 kJ/(mol ⋅ K).
Enthalpy of Fusion The enthalpy (heat) of fusion DHfus is the difference between the molar enthalpies of the equilibrium liquid and solid at the
melting temperature and 1.0 atm pressure. There is no generally applicable,
high-accuracy estimation method for DHfus, but the GC method of Chickos
can be used to obtain approximate results if the melting temperature is
known.
Recommended Method Chickos method.
Reference: Chickos, J. S., C. M. Braton, D. G. Hesse, and J. R. Liebman, J. Org.
Chem., 56 (1991): 927.
Classification: QSPR and group contributions.
Expected uncertainty: Considerable variation but generally less than
50 percent.
Applicability: Only valid at the melting temperature. The method is based
on the DSfus between a solid at 0 K and the liquid at the Tm so no solid-solid
transitions are taken into account. Values of DHfus will be overestimated if
there are solid-solid transitions for the actual material.
Input data: Tm and molecular structure.
Description:
P ∗ = exp (12.155) ⋅ Pa = 1.901 × 10 5 Pa
Determine DZ: Required data from the DIPPR 801 database for this calculation are
Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017. These values are used to determine the
reduced conditions,
Tr =
452
= 0.7
645.6
Pr =
no nonaromatic rings
0
a=
N
N
N
35.19
+
4.289(
−
3
)
nonaromatic rings
R
CR
R
0.1901
= 0.045
4.25
and the values of ZG and ZL from the Lee-Kesler corresponding states method as discussed in the section on density. Interpolation of the Pr values in Tables 2-169 and 2-170
at a Tr of 0.7 gives
ZG(0) = 0.9904 +
0.045 - 0.010
(0.9504 − 0.9904) = 0.9554
0.050 - 0.010
ZG(1) = − 0.0064 +
0.045 − 0.010
( − 0.0507 + 0.0064) = −0.0452
0.050 − 0.010
ZG = ZG(0) + ω ZG(1) = 0.9554 + (0.35017)( − 0.0452) = 0.94
At this low pressure, ZL is very small compared to ZG and may be neglected; so
DZV = ZG − ZL = 0.94
Calculation using Eq. (2-40):
J
2
∆H υ = 8.314
(0.94)[9307.7 − (16.693) (452) + (0.014919) (1)(452) ]
mol ⋅ K
= 37.59
kJ
mol ⋅ K
This value is 0.2 percent higher than the value of 37.51 kJ/(mol ⋅ K) obtained from
the DIPPR 801 database.
Recommended Method 2 Corresponding states correlation.
Reference: [PGL5], p. 7.18.
Classification: Corresponding states.
Expected uncertainty: Less than about 6 percent.
Applicability: Organic compounds.
Input data: Tc, Pc, and w.
Description: The following correlation is used:
∆H υ
= 7.08τ 0.354 + 10.95ωτ 0.456
RTc
where τ = 1 − Tr
Example Repeat the above calculation for anisole’s DHυ at 452 K.
Input data: Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017.
∆H fus
∆S fus Tm
=
= (Tm /K) (a + b)
J/mol J/(mol ⋅ K) K
ng
ns
nf
i =1
j =1
k =1
b = ∑ Ng i ∆si + ∑ Ns jCs j ∆s j + ∑ Nf kCt k ∆s k
(2-42)
(2-43)
(2-44)
where Ngi = number of C—H groups of type i bonded to other carbon
atoms
ng = number of different nonring or aromatic C—H groups bonded
to other carbon atoms
Nsj = number of C—H groups of type j bonded to at least one
functional group or atom
ns = number of different nonring or aromatic C—H groups bonded
to at least one functional group or atom
Nf k = number of functional groups of type k
nf = number of different functional groups or atoms
t = total number of functional groups or atoms with the
exception that F atoms count as one regardless of number of
occurrences
Csj = value from Table 2-162 for C—H group j bonded to at least one
functional group or atom
Ctk = value from Table 2-163 for functional group k
NR = number of nonaromatic rings
NCR = number of —CH2— groups in nonaromatic ring(s) required to
form cyclic paraffin of same ring size(s)
Dsi = contribution from Table 2-162 for group i
Dsk = contribution from Table 2-163 for group k
Note that nonaromatic ring —CH2 groups are accounted for in the a term
and are not included in the b term.
Example Calculate DHfus at the melting point for (a) benzothiophene, (b)
furfuryl alcohol, and (c) cis-crotonaldehyde.
Structures:
(2-41)
2-336
PHYSICAL AnD CHEMICAL DATA
TABLE 2-162
Cs (C}H) Group Values for Chickos Estimation* of DHfus
Group
Description
Group
Ds
Cs
}CH3
methyl
1.0
>CH2
methylene
1.0
>CH}
secondary C
0.69
>C<
tertiary C
0.67
CH2=
terminal alkene
1.0
}CH=
alkene
3.23
>C=
subst. alkene
1.0
≡CH
term. alkyne
1.0
≡C}
alkyne
1.0
*Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927.
18.33
9.41
−16.91
−38.70
14.56
4.85
−11.38
10.88
2.18
}CHAr
}CAr}
}CAr}
}CAr}
>CrH}
>Cr <
}CrH=
>Cr=
≡Cr} or =Cr=
Description
aromatic C
ar. C bonded to paraffinic C
ar. C bonded to olefinic C or non-C group
ar. C bonded to acetylinic C
ring structure
ring structure
ring structure
ring structure
ring structure
(a) t = 1 (1 total “functional group”), so the C1 column in Table 2-163 is used.
NR = 1
Group
=CH}
=C}
=C}
=CH}
=CH}
}S}
NCR = 5
a = 35.19 + (5 − 3)(4.289) = 43.77
Description
N
C
aromatic (Ng type)
ring (Ng type)
ring (Ns type)
ring (Ng type)
ring (Ns type)
ring
4
1
1
1
1
1
1
1
0.86
1
0.62
1
Tm = 258.52 K
Cs
Ds
1.0
1.0
1.0
1.0
0.76
1.0
0.62
0.86
1.0
6.44
−10.33
−4.27
−2.51
−15.98
−32.97
−4.35
−11.72
−5.36
from DIPPR 801 database
DHfus = (Tm/K)(a + b) J/mol = (258.52)(43.77 + 3.51) J/mol = 12.22 kJ/mol
Ds
Total
6.44
−11.72
−11.72
−4.35
−4.35
2.18
25.76
−11.72
−10.08
−4.35
−2.70
2.18
Total −0.91
This value is 7 percent lower than the DIPPR 801 recommended value of 13.13 kJ/mol.
(c) t = 1
a=0
NR = 0
Group
Description
N
C
Ds
Total
}CH3
=CH}
=CH}
}CHO
nonring (Ng type)
nonring (Ng type)
nonring (Ns type)
aldehyde
1
1
1
1
1
1
3.23
1
18.33
4.85
4.85
19.66
18.33
4.85
15.67
19.66
Total
Tm = 304.5 K
from DIPPR 801 database
DHfus = (Tm /K)(a + b) J/mol = (304.5)(43.77 − 0.91) J/mol = 13.05 kJ/mol
This value is 10 percent higher than the DIPPR 801 recommended value of 11.83 kJ/mol.
(b) t = 2 (2 total “functional groups”), so the C2 column in Table 2-163 is used.
NR = 1
Group
=CH}
=CH}
=C<
=O}
}CH2}
}OH
NCR = 5
a = 35.19 + (5 − 3)(4.289) = 43.77
Description
ring (Ng type)
ring (Ns type)
ring (Ns type)
ring ether
Ns type
alcohol
N
C
2
1
1
1
1
1
1
0.62
0.86
1
1
12.6
Total
−4.35
−4.35
−11.72
1.34
9.41
1.13
−8.70
−2.70
−10.08
1.34
9.41
14.24
Group
Ct (Functional) Group Values for Chickos Estimation*
Description
C1
C2
}OH
alcohol
1.0
12.6
}OH
phenol
1.0
1.0
}O}
nonring ether
1.0
1.0
}O}
ring ether
1.0
1.0
nonring ketone
1.0
1.0
>C=O
>C=O
ring ketone
1.0
1.0
}CHO
aldehyde
1.0
1.0
}COOH
acid
1.0
1.83
}COO}
ester
1.0
1.0
aliphatic
1.0
1.0
}NH2
}NH2
aromatic
1.0
1.0
>NH
nonring
1.0
1.0
>NH
ring
1.0
1.0
>N}
nonring
1.0
1.0
>N}
ring
1.0
1.0
=N}
ring
1.0
1.0
=N}
aromatic
1.0
1.0
}CN
nitrile
1.0
1.4
}NO2
nitro
1.0
1.0
}CONH2
primary amide
1.0
1.0
}CONH}
secondary amide
1.0
1.0
}SH
1.0
1.0
}S}
nonring
1.0
1.0
}S}
ring
1.0
1.0
nonring
1.0
1.0
}SO2
}F
on aliph. C
1.0
1.0
}F
on olefinic C
1.0
1.0
}F
on ring C
1.0
1.0
}Cl
1.0
2.0
}Br
1.0
1.0
}I
1.0
1.0
*Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927.
C3
C4
Ds
18.9
1.0
1.0
1.0
26.4
1.0
1.0
1.0
1.13
16.57
1.09
1.34
3.14
−1.88
19.66
14.90
3.68
16.23
15.48
−2.18
1.84
−15.90
−17.07
1.67
7.32
9.62
17.36
26.19
−0.42
17.99
7.20
2.18
3.26
14.73
13.01
15.90
8.37
17.95
16.95
1.88
1.0
1.72
1.0
1.0
1.0
0.36
1.0
1.0
1.0
2.0
1.0
1.0
1.0
1.0
1.93
0.82
from DIPPR 801 database
DHfus = (Tm/K)(a + b) J/mol = (158.38)(0 + 58.51) J/mol = 9.27 kJ/mol
This value is 5 percent higher than the DIPPR 801 recommended value of 8.86 kJ/mol.
Ds
Total 3.51
TABLE 2-163
of DH fus
Tm = 158.38 K
58.51
Enthalpy of Sublimation The enthalpy (heat) of sublimation DHsub is
the difference between the molar enthalpies of the equilibrium vapor and
solid along the sublimation curve below the triple point. The effects of pressure on DHsub and melting temperature are very small so that Tt and the normal melting point are nearly equal and
DHsub(Tt) = DHυ (Tt) + DHfus(Tt)
(2-45)
Equation (2-45) can be used to estimate DHsub at the triple point if DHυ is
accurately known at Tt. Because DHυ is usually obtained from Eq. (2-37),
DHυ(T) correlations may be less accurate near Tt where P*(Tt) is very small
and difficult to measure. In this case, it is better to estimate DHsub directly by
using the following recommended method. DHsub is only a weak function of
temperature and can generally be treated as a constant from the triple point
temperature down to the first solid-solid phase transition.
Recommended Method Goodman method.
Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley,
Int. J. Thermophys. 25 (2004): 337.
Classification: QSPR and group contributions.
Expected uncertainty: 6 percent.
Applicability: Organic compounds for which group contributions have
been regressed.
Input data: Molecular structure and radius of gyration RG.
Description:
N
N
N
R
n
∆H sub (Tt )
= 698.04 + 3.83798 × 1012 G + ∑ ni ai + ∑ ni2βi + ∑ i f i
m i =1
RK
n
i =1 x
i =1
(2-46)
where ai = GC values from Table 2-164
bi = nonlinear corrections for >CH2 and Ar—CH = groups
fi = halogen corrections
nx = total number of all halogen and hydrogen atoms attached to C
and Si atoms
Example Calculate DHsub and the solid vapor pressure for 1,2,3-trichlorobenzene
at 301.15 K.
Structure:
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-164
Group Contributions and Corrections* for DHsub
Group
Description
736.5889
561.3543
111.0344
−800.517
572.6245
541.2918
117.9504
626.7621
348.8092
763.284
1317.056
911.2903
970.4474
3278.446
2402.093
Nonlinear terms
>C=O
}COO}
}COOH
}NH2
}NH}
>N}
}NO2
}SH
}S}
}SS}
}F
}Cl
}Br
>Si<
>Si(O})}
9.5553
−2.21614
Description
ai
ketone
ester
acid
primary amine
sec. amine
tertiary amine
nitro
thiol/mercaptan
sulfide
disulfide
fluoride
chloride
bromide
silane
siloxane
1816.093
2674.525
5006.188
2219.148
1561.222
325.9442
3661.233
1921.097
1930.84
2782.054
626.4494
1243.445
669.9302
−83.7034
−16.0597
Halogen correction terms
bi
methylene
aromatic C
>CH2
Ar}CH=
Group
ai
methyl
methylene
secondary C
tertiary C
terminal alkene
alkene
substituted alkene
aromatic C
subst. aromatic C
furan O
pyridine N
thiophene S
ether
alcohol
aldehyde
}CH3
>CH2
>CH}
>C<
CH2=
}CH=
>C=
Ar }CH=
Ar >C=
Ar }O}
Ar }N=
Ar }S}
}O}
}OH
}COH
2-337
fi
F fraction
Cl fraction
Br fraction
}F
}Cl
}Br
−1397.4
−1543.66
5812.49
*Goodman, B., et al., Int. J. Thermophys., 25 (2004): 337.
Group contributions:
2
Linear groups
A4 /T
A2 /T
C Po = A0 + A1
+ A3
cosh(A4 /T )
sinh(A2 /T )
Nonlinear and correction terms
Group
ni
ai
Group
ni
bi
Ar}CH=
3
626.7621
Ar }CH=
3
−2.21614
Ar >C=
3
348.8092
}Cl
3
}Cl
3
nx
6
1243.445
(2-48)
fi
−1543.66
and a polynomial form (generally fourth-order)
∑ ni ai = 6657.049
C Po =
4
∑ AT
i
(2-49)
i
i = 0
i
Input data: The value of RG from the DIPPR 801 database is 4.455 × 10−10 m.
Calculation using Eq. (2-46):
∆H sub (Tt )
= 698.04 + (3.838 × 1012 )(4.455 × 10 −10 )
RK
3
+ 6657.05 + (3 2 )(−2.21614) + (−1543.66)
6
kJ
kJ
= 68.78
∆H sub (Tt ) = (8273 K) 0.008314
mol ⋅ K
mol
The estimated value is 5.6 percent above the DIPPR 801 recommended value of
65.11 kJ/mol.
Estimate the solid vapor pressure at 301.15 K: The solid vapor pressure can be
calculated from Eq. (2-30) by using the estimated DHsub and one additional solid
vapor pressure point. In this example the triple point temperature and vapor pressure
(Tt = 325.65 K; Pt* = 182.957 Pa) from the DIPPR 801 database are used in Eq. (2-30):
ln
2
Ideal gas heat capacities may also be estimated from several techniques, of
which two of the most accurate and commonly used are recommended here.
Recommended Method 1 Statistical mechanics.
Reference: Rowley, R. L., Statistical Mechanics for Thermophysical Property
Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994.
Classification: Theory and computational chemistry.
Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; accuracy depends
upon model chemistry if frequencies are determined from computational
chemistry, but generally within 3 percent.
Applicability: Ideal gases.
Input data: 3nA − 6 + d vibrational frequencies nj, or the corresponding
characteristic vibrational temperatures Qj. The two are related by
(2-50)
Qj = hnj /k
Description: For harmonic frequencies, the rigorous temperature dependence of C Po is given by
68.78 kJ/mol
P∗
1 − 325.65 = −2.067
=
182.957 Pa [0.008314 kJ/(mol ⋅ K)](325.65 K) 301.15
2
P* = (182.957 Pa) [exp(−2.067)] = 23.16 Pa
The estimated value is 0.3 percent above the DIPPR 801 recommended value of 23.09 Pa.
HEAT CAPACITY
Θ /T
C Po 8 − δ 3 n A −6+δ Θ j e j
=
+ ∑ Θ j /T
2
R
2
T
−
e
(
1)
j =1
0
δ =
1
nonlinear
linear
(2-51)
Example Calculate the ideal gas heat capacity of ammonia at 300 K.
The isobaric heat capacity CP is defined as the energy required to change the
temperature of a unit mass (specific heat) or mole (molar heat capacity) of
the material by one degree at constant pressure. Typical units are J/(kg ⋅ K).
Gases The isobaric heat capacity of a gas is related rigorously to the
ideal gas value C Po by
2
P ∂ V
C P = C Po − T ∫ 2 dP
0 ∂T
P
(2-47)
The second term, giving the deviation of the real fluid heat capacity from the
ideal gas value, can be neglected at low to moderate pressures, or it can be
calculated directly from an appropriate EoS.
Ideal gas heat capacities are available from several sources (DIPPR,
JANAF, TRC, and SWS). Two common correlating equations for C Po are the
Aly-Lee equation [Aly, F. A., and L. L. Lee, Fluid Phase Equilib., 6 (1981): 169]
Structure:
Input data: McQuarrie (McQuarrie, D. A., Statistical Mechanics, Harper & Row, New
York, 1976) gives the following 3nA − 6 + d = 12 − 6 + 0 = 6 characteristic vibrational
temperatures (in K): 1360, 2330, 2330, 4800, 4880, and 4880. Alternatively, a computational chemistry package gives the following scaled frequencies for HF/6-31G+ model
chemistry (1013 Hz): 3.24, 4.97, 4.97, 9.90, 10.26, and 10.26.
Calculation: The table on the left uses the experimental Q values to determine the
individual terms in the summation of Eq. (2-51). The table on the right uses the scaled
frequencies from computational chemistry software and Eq. (2-50) to obtain Q values
and the individual terms in Eq. (2-51).
2-338
PHYSICAL AnD CHEMICAL DATA
HF/6-31G+ scaled frequencies*
Experimental frequencies
Q/K
1360
2330
2330
4800
4880
4880
Q/(300 K)
4.533
7.767
7.767
16.000
16.267
16.267
Term
nscaled/10 Hz
Q/K
0.2256
0.0256
0.0256
0.0000
0.0000
0.0000
3.24
4.97
4.97
9.90
10.26
10.26
1555.0
2385.3
2385.3
4751.4
4924.2
4924.2
13
Q/(300 K)
5.183
7.951
7.951
15.838
16.414
16.414
Term
0.1524
0.0223
0.0223
0.0000
0.0000
0.0000
Sum: 0.2768
Sum: 0.1970
*Empirical scaling factors have been developed for each model chemistry to help
correct theoretical frequencies for anharmonic effects [Scott, A. P., and L. Radom,
J. Phys. Chem., 100 (1996): 16502].
Danner, AIChE J., 23 (1977): 944] and thermodynamic differentiation. The
Ruzicka-Domalski method is generally accurate at low temperature, but the
cubic behavior can overestimate the temperature rise at higher temperatures. The Lee-Kesler method is accurate for nonpolar and slightly polar
fluids, but has less accuracy for strongly polar or associating fluids.
Recommended Method 1 Ruzicka-Domalski.
References: Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22
(1993): 597, 619.
Classification: Group contributions.
Expected uncertainty: 4 percent.
Applicability: Organic compounds for which group values are available.
Input data: Molecular structure and Table 2-166 values.
Description: Groups are summed to find the temperature coefficients for
a cubic polynomial correlation:
From experimental frequencies:
T
T
= A+ B
+ D 100 K
R
100 K
Cp
8
J
J
C Po = + 0.2768 R = (4.2768) 8.3143
= 35.56
2
mol ⋅ K
mol ⋅ K
N
A = ∑ ni ai
From computational chemistry frequencies:
i =1
8
J
J
C Po = + 0.197 R = (4.197) 8.3143
= 34.90
2
mol ⋅ K
mol ⋅ K
The value calculated from experimental frequencies is 0.1 percent lower than the
DIPPR 801 recommended value of 35.61 J/(mol ⋅ K); the value calculated from frequencies generated from computational chemistry software is 2.0 percent lower than the
DIPPR 801 value.
Recommended Method 2 Benson method as implemented in CHETAH
program.
References: Benson, S. W., et al., Chem. Rev., 69 (1969): 279; CHETAH
Version 8.0: The ASTM Computer Program for Chemical Thermodynamic
and Energy Release Evaluation (NIST Special Database 16).
Classification: Group contributions.
Expected uncertainty: 4 percent.
Applicability: Ideal gases of organic compounds.
Input data: Table 2-165 group values at the seven specified temperatures.
Description: Groups are summed at each individual temperature:
N
C Po = ∑ ni ⋅ (C op )i
(2-52)
N
B = ∑ ni bi
i =1
2
(2-53)
N
D = ∑ ni di
(2-54)
i =1
where ni = number of occurrences of group i and ai, bi, di = individual group
contributions.
Example Estimate the liquid heat capacity for 2-methyl-2-propanol at 340 K.
Structure:
Group contributions:
Group
ni
C } (3C, O) (alcohol)
O } (H)(C)
C } (3H)(C)
1
1
3
ai
−44.690
12.952
3.8452
Sum −20.202
i =1
where ni = number of occurrences of group i and (C Po )i = individual group
contribution. Either Eq. (2-48) or Eq. (2-49) can be used to interpolate
between the discrete temperatures.
J
C p = 8.3143
mol ⋅ K
= 254.16
Example Calculate the ideal gas heat capacity of isoprene (2-methyl-1,3-butadiene)
at 400 K.
Structure:
bi
di
31.769
−10.145
−0.33997
−4.8791
2.6261
0.19489
20.604
−1.668
2
304 − 1.668 340
−20.202 + 20.604
100
100
J
mol ⋅ K
This value is 0.7 percent higher than the DIPPR 801 recommended value of
252.40 J/(mol ⋅ K).
Group identification and values:
Group
No.
Value, J/(mol ⋅ K)
Contribution, J/(mol ⋅ K)
=CH2
2
26.62
=C}(2C)
1
19.3
53.24
19.3
}CH3}(=C)
1
32.82
32.82
=CH}(C)
1
21.05
Recommended Method 2 Lee-Kesler.
References: [PGL5]
Classification: Corresponding states.
Expected uncertainty: 4 percent.
Applicability: Organic compounds other than those that are strongly
polar or associate.
Input data: Tc, w, and the ideal gas heat capacity at the same temperature.
Description: The isobaric liquid heat capacity is calculated at the reduced
temperature Tr using
21.05
Total
Cp
126.41
R
=
C op
R
+ 1.586 +
6.3(1 − Tr )1/3 0.4355
0.49
+ ω 4.2775 +
+
1 − Tr
1 − Tr
Tr
(2-55)
The value of 126.4 J/(mol ⋅ K) is 3.1 percent below the DIPPR 801 recommended value
of 130.4 J/(mol ⋅ K).
Example Calculate the isobaric liquid heat capacity for 1,4-dioxane at 320 K.
Liquids Liquid isobaric heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many
compounds. Usually liquid heat capacity is correlated as a function of temperature with a polynomial equation; a third-order polynomial is usually
adequate.
Estimation of liquid heat capacity can be done by using a number of
methods [Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993):
597, 619; Chueh, C. F., and A. C. Swanson, Chem. Eng. Prog., 69, 7 (1973): 83;
Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510; Tarakad, R. R., and R. P.
Auxiliary data: From the DIPPR 801 database: Tc = 597.0 K, w = 0.2793, and
C /R = 11.94. The reduced temperature is therefore Tr = (320 K)/(597.0 K) = 0.536.
From Eq. (2.55),
o
p
Cp
R
= 11.94 + 1.586 +
1/3
0.49
6.3 (1 − 0.536 )
0.4355
+ (0.2793) 4.2775 +
+
= 18.58
1 − 0.536
0.536
1 − 0.536
and Cp = 154.5 J/(mol ∙ K). This is 4.6 percent below the DIPPR recommended value of
162.0 J/(mol ∙ K).
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-165
2-339
Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity
Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide;
Nim = imino.
Group
298 K
400 K
500 K
600 K
800 K
1000 K
1500 K
45.17
45.17
45.17
45.17
45.21
45.17
45.17
45.17
45.17
45.17
45.17
45.17
45.17
45.17
54.5
54.5
54.5
54.5
54.42
54.54
54.54
54.54
54.54
54.5
54.5
54.5
54.5
54.5
61.83
61.83
61.83
61.83
61.95
61.83
61.83
61.83
61.83
61.83
61.83
61.83
61.83
61.83
73.59
73.59
73.59
73.59
73.67
73.59
73.59
73.59
73.59
73.59
20.59
19.42
17.12
20.59
38.51
37.67
35.79
28.76
38.93
53.16
22.35
20.93
19.25
22.35
39.77
39.35
38.3
31.27
40.18
56.93
23.02
21.89
20.59
23.02
40.6
40.18
39.85
33.32
41.02
59.86
24.28
23.32
26.58
24.28
37.8
39.14
38.17
40.18
40.98
40.98
63.71
40.18
41.9
39.77
38.01
39.35
39.47
36.84
38.34
41.73
39.72
41.36
40.1
38.72
40.85
45.46
46.34
43.2
47.3
49.35
49.77
72.58
47.3
48.1
46.46
45.46
46.46
46.5
44.58
45.84
51.32
46.97
48.3
47.17
45.92
50.98
51.74
51.65
47.26
52.74
55.25
55.25
78.82
52.74
52.49
51.07
51.03
51.49
51.61
49.94
51.15
59.23
52.24
53.29
52.49
51.28
59.48
36.63
35.12
32.57
35.16
36.54
35.5
36.38
34.28
33.7
31.77
40.73
41.11
38.09
40.18
41.06
40.35
41.44
39.6
38.97
35.41
42.9
43.99
41.44
42.7
43.53
43.11
44.24
42.65
42.07
38.97
25.53
36.75
27.17
19.97
33.07
32.23
27.17
27.63
34.11
34.58
33.99
27.63
38.47
30.43
25.2
35.58
34.32
30.43
31.56
36.5
37.34
36.71
28.46
37.51
31.69
26.71
35.58
34.49
31.23
33.32
33.91
37.51
36.67
CH3 Groups
CH3}(Cb)
CH3}(CO)
CH3}(Ct)
CH3}(C)
CH3}(N)
CH3}(O)
CH3}(PO)
CH3}(P)
CH3}(P=N)
CH3}(Si)
CH3}(SO2)
CH3}(SO)
CH3}(S)
CH3}(=C)
25.91
25.91
25.91
25.91
25.95
25.91
25.91
25.91
25.91
25.91
25.91
25.91
25.91
25.91
32.82
32.82
32.82
32.82
32.65
32.82
32.82
32.82
32.82
32.82
32.82
32.82
32.82
32.82
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
39.35
73.59
Ct Groups
Ct}(Cb)
Ct}(Ct)
Ct}(C)
Ct}(=C)
CtBr
CtCl
CtF
CtH
CtI
Ct(CN)
10.76
14.82
13.1
10.76
34.74
33.07
28.55
22.06
35.16
43.11
14.82
16.99
14.57
14.82
36.42
35.16
31.65
25.07
36.84
47.3
14.65
18.42
15.95
14.65
37.67
36.42
33.99
27.17
38.09
50.65
41.77
37.04
64.04
CH2 Groups
CH2}(2CO)
CH2}(2C)
CH2}(2O)
CH2}(2=C)
CH2}(Cb,O)
CH2}(Cb,SO2)
CH2}(Cb,S)
CH2}(Cb,=C)
CH2}(C,Cb)
CH2}(C,CO)
CH2}(C,Ct)
CH2}(C,N)
CH2}(C,O)
CH2}(C,SO2)
CH2}(C,SO)
CH2}(C,S)
CH2}(C,=C)
CH2}(=C,O)
CH2}(=C,SO2)
CH2}(=C,SO)
CH2}(=C,S)
16.03
23.02
11.85
19.67
15.53
15.53
38.09
19.67
24.45
25.95
20.72
21.77
20.89
17.12
19.05
22.52
21.43
19.51
20.34
18.42
22.23
26.66
29.09
21.18
28.46
26.26
27.5
49.02
28.46
31.85
32.23
27.46
28.88
28.67
24.99
26.87
29.64
28.71
29.18
28.51
26.62
28.59
CH}(2C,Cb)
CH}(2C,CO)
CH}(2C,Ct)
CH}(2C,N)
CH}(2C,O)
CH}(2C,SO2)
CH}(2C,S)
CH}(2C,=C)
CH}(3C)
CH}(C,2O)
20.43
18.96
16.7
19.67
20.09
18.5
20.3
17.41
19
22.02
27.88
25.87
23.48
26.37
27.79
26.16
27.25
24.74
25.12
23.06
C}(2C,2O)
C}(3C,Cb)
C}(3C,CO)
C}(3C,Ct)
C}(3C,N)
C}(3C,O)
C}(3C,SO2)
C}(3C,SO)
C}(3C,S)
C}(3C,=C)
C}(4C)
19.25
19.72
9.71
0.33
18.42
18.12
9.71
12.81
19.13
16.7
18.29
19.25
28.42
18.33
7.33
25.95
25.91
18.33
19.17
26.25
25.28
25.66
32.15
34.53
31.48
35.16
34.66
34.66
57.43
35.16
37.59
36.42
33.19
34.74
34.74
31.56
33.28
36
34.83
36.21
34.95
29.05
34.45
59.65
60.28
60.28
57.6
59.44
61.11
60.11
CH Groups
33.07
30.89
28.67
31.81
33.91
31.65
32.57
30.72
30.01
27.67
44.7
46.55
47.22
46.76
C Groups
23.02
33.86
23.86
14.36
30.56
30.35
23.86
20.26
31.18
31.1
30.81
31.94
34.45
33.99
(Continued )
2-340
PHYSICAL AnD CHEMICAL DATA
TABLE 2-165
Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )
Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide;
Nim = imino.
Group
298 K
400 K
500 K
600 K
800 K
1000 K
1500 K
25.32
Aromatic (Cb and Cp Groups)
Cb}(Cb)
Cb}(CO)
Cb}(Ct)
Cb}(C)
Cb}(N)
Cb}(O)
Cb}(Si)
Cb}(SO2)
Cb}(SO)
Cb}(S)
Cb}(=C)
Cb}(=Nim)
CbBr
CbCl
CbF
CbH
CbI
Cb(CHN2)
Cb(CN)
Cb(N3)
Cb(NCO)
Cb(NCS)
Cb(NO2)
Cb(SO2OH)
Cp}(2Cb,Cp)
Cp}(3Cp)
Cp}(Cb,2Cp)
13.94
11.18
15.03
11.18
16.53
16.32
11.18
11.18
11.18
16.32
15.03
16.53
32.65
30.98
26.37
13.56
33.49
47.3
41.86
34.74
55.25
32.23
38.93
65.42
12.56
8.37
12.56
17.66
13.14
16.62
13.14
21.81
22.19
13.14
13.14
13.14
22.19
16.62
21.81
36.42
35.16
31.81
18.59
37.25
20.47
15.4
18.33
15.4
24.86
25.95
15.4
15.4
15.4
25.95
18.33
24.86
39.35
38.51
35.58
22.85
40.18
22.06
17.37
19.76
17.37
26.45
27.63
17.37
17.37
17.37
27.63
19.76
26.45
41.44
40.6
38.09
26.37
41.44
24.11
20.76
22.1
20.76
27.33
28.88
20.76
20.76
20.76
28.88
22.1
27.33
43.11
42.7
41.02
31.56
43.11
24.91
22.77
23.48
22.77
27.46
28.88
22.77
22.77
22.77
28.88
23.48
27.46
43.95
43.53
42.7
35.2
43.95
48.14
52.74
55.67
59.86
62.79
64.04
70.32
74.51
79.95
82.88
50.23
79.49
15.49
12.14
15.49
59.44
84.51
17.58
14.65
17.58
66.56
97.61
19.25
16.74
19.25
76.18
109.25
21.77
19.67
21.77
80.37
113.31
23.02
21.35
23.02
=C}(2C)
=C}(CO,O)
=C}(C,Cb)
=C}(C,CO)
=C}(C,O)
=C}(C,SO2)
=C}(C,S)
=C}(C,=C)
=CC}(=C,O)
=CH}(Cb)
=CH}(CO)
=CH}(Ct)
=CH}(C)
=CH}(O)
=CH}(SO2)
=CH}(S)
=CH}(=C)
=CH2
=C=
17.16
23.4
18.42
22.94
17.16
15.49
14.65
18.42
18.42
18.67
31.73
18.67
17.41
17.41
12.72
17.41
18.67
21.35
16.32
19.3
29.3
22.48
29.22
19.3
26.04
14.94
22.48
22.9
24.24
37.04
24.24
21.05
21.05
19.55
21.05
24.24
26.62
18.42
22.02
32.44
25.87
31.98
22.02
38.51
17.12
25.87
26.29
31.06
40.31
31.06
27.21
27.21
28.63
27.21
31.06
35.58
20.93
24.28
33.57
27.21
33.53
24.28
44.62
18.46
27.21
27.21
34.95
43.45
34.95
32.02
32.02
32.94
32.02
34.95
42.15
22.19
25.45
34.03
27.71
34.32
25.45
47.47
20.93
27.71
27.71
37.63
46.21
37.63
35.37
35.37
36.29
35.37
37.63
47.17
23.02
O}(2C)
O}(2O)
O}(2=C)
O}(Cb,CO)
O}(CO,O)
O}(C,Cb)
O}(C,CO)
O}(C,O)
O}(C,=C)
O}(=C,CO)
OH}(Cb)
OH}(CO)
OH}(C)
OH}(O)
O(CN)}(Cb)
O(CN)}(C)
O(CN)}(=C)
O(NO2)}(C)
O(NO)}(C)
(CO)Cl}(C)
(CO)H}(Cb)
(CO)H}(CO)
14.23
15.49
14.02
8.62
1.51
2.6
11.64
15.49
12.72
6.03
18
15.95
18.12
21.64
34.74
41.86
54.42
39.93
38.09
42.28
33.53
28.13
15.49
15.49
16.32
11.3
6.28
3.01
15.86
15.49
13.9
12.47
18.84
20.85
18.63
24.24
15.49
15.49
17.58
13.02
9.63
4.94
18.33
15.49
14.65
16.66
20.09
24.28
20.18
26.29
15.91
15.49
18.84
14.32
11.89
7.45
19.8
15.49
15.49
18.79
21.77
26.54
21.89
27.88
18.42
17.58
21.35
16.24
15.28
11.89
20.55
17.58
17.54
20.8
25.12
30.01
25.2
29.93
19.25
17.58
22.6
17.5
17.33
14.99
21.05
17.58
18.96
21.77
27.63
32.44
27.67
31.44
48.3
43.11
46.04
44.2
32.78
55.5
46.88
49.39
48.77
37.25
65.3
50.23
51.9
59.48
41.4
68.61
55.67
55.67
68.56
47.84
72.75
58.18
57.76
74.01
50.73
24.07
25.03
25.03
24.07
40.73
85.81
=C=,=C},=CH}Groups
20.89
31.31
24.82
31.02
20.89
33.32
16.03
24.82
24.82
28.25
38.8
28.25
24.32
24.32
24.82
24.32
28.25
31.44
19.67
26.62
28.13
28.13
41.77
41.77
40.27
40.27
41.77
55.21
23.86
Oxygen Groups
20.09
20.09
37.34
33.65
34.2
60.69
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-165
2-341
Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )
Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide;
Nim = imino.
Group
298 K
400 K
500 K
600 K
800 K
1000 K
40.52
40.52
40.52
48.77
21.05
46.71
46.71
46.71
63.12
26.32
51.07
51.07
51.07
74.68
29.54
55.25
85.64
49.52
68.98
82.88
77.86
46.71
57.85
77.44
74.93
68.52
57.3
57.35
59.86
56.09
54.42
59.9
58.18
56.72
53.75
68.23
53.41
46.88
69.07
48.39
63.21
54.42
74.17
56.3
59.86
59.02
56.51
58.18
55.67
53.16
47.72
46.88
43.95
48.56
56.93
88.66
52.07
70.99
86.23
82.88
52.03
63.46
84.14
80.79
76.06
65.26
64.88
67.81
64.04
63.62
68.15
66.14
64.25
58.81
74.93
59.82
56.09
89.66
53.12
71.24
87.9
85.39
53.24
65.84
87.9
83.72
79.99
69.95
70.32
73.67
69.9
69.49
73.8
72
69.36
61.62
79.53
64.38
74.93
54.83
69.9
59.31
79.7
57.72
62.37
61.53
59.86
61.11
59.44
57.76
51.9
51.49
49.39
52.74
78.28
58.64
74.51
61.95
81.58
56.93
63.62
62.79
61.53
62.79
61.53
60.69
55.25
54.83
53.16
55.67
17.29
26.16
34.45
27.33
29.05
24.99
20.3
20.93
17.66
45.63
21.35
30.93
28.59
13.94
26.29
14.57
29.3
33.78
34.7
33.78
38.93
22.35
28.34
21.89
28.42
37.8
28.59
30.93
27.46
22.1
22.94
20.05
50.9
28.3
33.28
33.07
16.91
30.1
17.75
32.65
39.39
41.69
39.39
43.95
23.82
28.71
23.4
28.76
38.47
34.91
38.68
27.92
22.14
27.08
21.43
53.54
32.98
34.28
36.21
18.21
32.36
18.96
34.74
43.83
46.97
43.83
48.14
23.9
29.51
1500 K
Oxygen Groups
(CO)H}(C)
(CO)H}(N)
(CO)H}(O)
(CO)H}(=C)
CO}(Cb)(O)
29.43
29.43
29.43
24.32
9.12
32.94
32.94
32.94
30.22
11.51
CBr}(3C)
CBr3}(C)
CCl}(3C)
CCl2}(2C)
CCl3}(C)
CClF2}(C)
CF}(3C)
CF2}(2C)
CF3}(Cb)
CF3}(C)
CF3}(S)
CH2Br}(Cb)
CH2Br}(C)
CH2Br}(=C)
CH2Cl}(C)
CH2F}(C)
CH2I}(Cb)
CH2I}(C)
CH2I}(O)
CHBr}(2C)
CHBrCl}(C)
CHCl}(2C)
CHCl}(C,O)
CHCl2}(C)
CHF}(2C)
CHF2}(C)
CHI}(2C)
CHI2}(C)
CI}(3C)
=CBr2
=CBrCl
=CBrF
=CCl2
=CClF
=CF2
=CHBr
=CHCl
=CHF
=CHI
39.35
72.12
36.96
51.07
68.23
57.35
28.46
39.01
52.32
53.16
41.36
30.51
38.09
40.6
37.25
33.91
33.91
38.51
34.41
37.38
51.9
35.45
37.67
50.65
30.56
41.44
38.64
56.93
41.15
51.49
50.65
45.21
47.72
43.11
40.6
33.91
33.07
28.46
36.84
47.72
78.65
43.87
62.29
75.35
67.39
37.09
46.97
64.04
62.79
54.46
46.46
46.04
47.72
44.79
41.86
45.17
46.04
43.91
44.62
58.6
42.7
41.44
58.6
37.84
50.23
45.67
63.42
49.18
55.25
53.16
50.23
52.32
48.97
46.04
39.77
38.51
35.16
41.86
CH2(N3)}(C)
=CH(N3)
N}(2C,Cb)
N}(2C,CO)
N}(2C,SO2)
N}(2C,SO)
N}(2C,S)
N}(3C)
N}(Cb,2CO)
N}(C,2CO)
Nb pyrid}N
NF2}(C)
NH}(2Cb)
NH}(2CO)
NH}(2C)
NH}(Cb,CO)
NH}(C,Cb)
NH}(C,CO)
NH}(C,N)
NH2}(Cb)
NH2}(CO)
NH2}(C)
NH2}N
=Naz}(C)
=Naz}(N)
64.46
54.42
2.6
13.02
25.2
17.58
15.99
14.57
4.1
4.48
10.88
26.5
9.04
15.03
17.58
2.39
15.99
2.76
20.09
23.94
17.04
23.94
25.53
11.3
8.87
36.92
36.92
36.92
39.77
16.65
Halide Groups
52.74
82.92
47.72
66.76
79.95
73.25
42.7
53.24
72
68.65
62.08
52.2
52.74
54.42
51.49
50.23
53.7
54
51.19
50.06
63.3
48.89
43.95
64.46
43.83
57.35
50.9
69.61
54.08
58.18
56.51
53.58
55.67
52.74
50.23
44.37
43.11
39.77
45.63
Nitrogen Groups
8.46
19.17
26.58
24.61
21.64
19.09
12.81
12.99
13.48
34.58
13.06
23.19
21.81
6.32
20.47
6.49
24.28
27.25
24.03
27.25
30.98
17.16
17.5
13.69
23.52
31.56
25.62
25.99
22.73
17.71
18.04
15.95
40.9
17.29
28.05
25.66
9.96
23.9
10.3
27.21
30.64
29.85
30.64
35.16
20.59
23.06
27.21
39.97
37.67
51.4
51.4
55.25
(Continued )
2-342
PHYSICAL AnD CHEMICAL DATA
TABLE 2-165
Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )
Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide;
Nim = imino.
Group
298 K
400 K
500 K
600 K
800 K
1000 K
1500 K
Nitrogen Groups
=NazH
=Nim}(Cb)
=Nim}(C)
=NimH
18.33
12.56
10.38
12.35
20.47
22.77
24.86
28.34
31.06
13.98
19.17
16.53
27
17.96
32.27
19.21
38.22
19.25
41.52
S}(2Cb)
S}(2C)
S}(2S)
S}(2=C)
S}(Cb,S)
S}(C,Cb)
S}(C,S)
S}(C,=C)
SH}(Cb)
SH}(CO)
SH}(C)
SO}(2Cb)
SO}(2C)
SO2}(2Cb)
SO2}(2C)
SO2}(2=C)
SO2}(Cb,SO2)
SO2}(Cb,=C)
SO2}(C,Cb)
S(CN)}(Cb)
S(CN)}(C)
S(CN)}(=C)
8.37
20.89
19.67
20.05
12.1
12.64
21.89
17.66
21.43
31.94
24.53
23.94
37.17
34.99
48.22
48.22
41.06
41.4
41.61
39.77
46.88
59.44
8.41
20.76
20.93
23.36
14.19
14.19
22.69
21.26
22.02
33.86
25.95
38.05
41.98
46.17
50.1
50.1
48.14
48.14
48.14
11.47
21.22
21.77
26.33
17.37
16.91
23.06
24.15
25.24
34.2
28.38
47.93
45.17
62.54
59.77
59.77
61.66
61.16
60.74
15.91
22.65
22.19
33.24
20.01
19.34
22.52
24.57
29.26
35.58
30.56
47.97
45.96
66.39
64.38
64.38
65.76
65.8
65.38
19.72
23.98
22.6
40.73
21.35
20.93
21.43
24.57
32.82
34.49
32.27
47.09
46.76
66.81
66.47
66.47
67.1
66.64
66.64
113.23
−39.64
134.95
198.62
219.72
47.72
61.95
52.7
45.21
50.19
80.79
36.21
61.62
41.4
72.42
43.11
51.90
51.49
56.93
56.93
64.04
70.74
80.79
85.81
66.22
54
63.67
101.3
46.71
74.47
55.84
77.52
60.69
74.17
117.2
53.96
83.72
66.39
86.48
66.14
82.08
129.76
58.81
90.46
73.75
99.58
72
92.84
146.09
64.92
99.54
82.92
108.41
79.11
99.2
156.13
67.77
104.48
87.32
50.23
56.09
61.11
68.65
73.67
63.21
69.28
72.83
78.19
80.37
84.76
90.41
93.51
97.11
98.74
−11.05
−7.03
−7.95
−10.88
−12.64
−16.37
−14.56
−7.87
−6.2
−7.41
−9.63
18.09
−19.25
−10.88
−5.78
−5.57
−6.78
−8.63
24.35
−23.86
0.84
−10.97
−5.44
−5.99
−6.91
−15.91
−17.33
−12.56
−3.77
−16.74
−15.91
−2.89
−15.32
−15.32
−6.4
4.6
−1.21
−5.36
−11.72
−12.26
−10.88
9.21
−12.01
−11.3
3.6
−18.46
−18.46
−1.8
9.21
0.33
−4.35
−8.08
−9.46
−10.05
17.58
−9.08
−7.53
5.4
−23.32
−23.32
35.33
Sulfur Groups
9.38
21.01
21.35
23.15
15.57
15.53
23.06
23.27
23.32
33.99
27.25
40.6
43.95
56.72
55.88
55.88
56.59
55.88
56.3
Boron and Silicon Groups
Si}(4C)
SiH3}(C)
154.5
171.2
252.91
Monovalent Ligands
CH2(CN)}(C)
CH2(NCS)}(C)
CH2(NO2)}(C)
CH(CN)}(2C)
CH(NO2)}(2C)
CH(NO2)2}(C)
C(CN)}(3C)
C(CN)2}(2C)
C(NO2)}(3C)
=CH(CHN2)
=CH(CN)
=CH(NCS)
=CH(NO2)
=C(CN)2
105.9
3,4 Member Ring Corrections
cyclobutane ring
cyclobutene ring
cyclopropane ring
ethylene oxide ring
ethylene sulfide ring
thietane ring
trimethylene oxide ring
−19.3
−10.59
−12.77
−8.37
−11.93
−19.21
−19.25
−16.28
−9.17
−10.59
−11.72
−10.84
−17.5
−20.93
1,4 dioxane ring
cyclohexane ring
cyclohexene ring
cyclopentadiene ring
cyclopentane ring
cylopentene ring
furan ring
piperidine ring
pyrrolidine ring
tetrahydrofuran ring
thiacyclohexane ring
thiolane ring
thiophene ring
−19.21
−24.28
−17.92
−14.44
−27.21
−25.03
−20.51
−24.7
−25.83
−25.12
−26.04
−20.51
−20.51
−20.8
−17.16
−12.72
−11.85
−23.02
−22.39
−18
−19.67
−23.36
−24.28
−17.83
−19.55
−19.55
−13.14
−7.91
−8.79
−12.56
−11.13
−16.37
−17.58
−2.8
−5.11
−6.36
5,6 Member Ring Corrections
−15.91
−12.14
−8.29
−8.96
−18.84
−20.47
−15.07
−12.14
−20.09
−20.09
−9.38
−15.4
−15.4
13.81
3.39
−1.55
−4.52
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-165
2-343
Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued )
Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide;
Nim = imino.
Group
298 K
400 K
500 K
600 K
800 K
1000 K
−1.63
−1.63
−1.63
−1.63
−1.63
−1.26
2.93
3.68
−1.09
−1.09
−1.09
−1.09
−1.09
1500 K
7 and 8 Member Ring Corrections
cycloheptane ring
cyclooctane ring
−38.01
−44.16
Gauche and 1,5 Repulsion Corrections
but-2-ene structure C}C=C}C
but-3-ene structure C}C}C=C
cis- between 2 t-butyl groups
cis- involving 1 t-butyl group
cis-(not with t-butyl group)
ortho- between Cl atoms
ortho- between F atoms
other ortho- (nonpolar-nonpolar)
−5.61
−5.61
−5.61
−5.61
−5.61
−2.09
−4.56
−4.56
−4.56
−4.56
−4.56
5.02
−0.84
5.65
4.69
−3.39
−3.39
−3.39
−3.39
−3.39
2.09
−0.42
5.44
−2.55
−2.55
−2.55
−2.55
−2.55
−2.51
1.26
4.9
2.76
−0.21
*Benson, S. W., et al., Chem. Rev., 69 (1969): 279.
†
CHETAH Version 8.0: The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16).
TABLE 2-166
Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method*
Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond;
Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom.
Group Definition
a
b
d
T range (K)
Group Definition
Hydrocarbon Groups
C}(3H,C)
C}(2H,2C)
C}(H,3C)
C}(4C)
=C}(2H)
=C}(H,C)
=C}(2C)
=C}(H,=C)
=C}(C,=C)
C}(3H,=C)
C}(2H,C,=C)
C}(H,2C,=C)
C}(3C,=C)
C}(2H,2=C)
Ct}(H)
Ct}(C)
=C=
Ct}(Cb)
Cb}(H)
Cb}(C)
Cb}(=C)
Cb}(Cb)
C}(2H,C,Ct)
C}(3H,Ct)
C}(3H,Cb)
C}(2H,C,Cb)
C}(H,2C,Cb)
C}(3C,Cb)
C}(2H,2Cb)
C}(H,3Cb)
=C}(H,Cb)
=C}(C,Cb)
Cp}(Cp,2Cb)
Cp}(2Cp,Cb)
Cp}(3Cp)
3.8452
2.7972
−0.42867
−2.9353
4.1763
4.0749
1.9570
3.6968
1.0679
3.8452
2.0268
−0.87558
−4.8006
1.4973
9.1633
1.4822
3.0880
12.377
2.2609
1.5070
−5.7020
5.8685
2.0268
3.8452
3.8452
1.4142
−0.10495
1.2367
−18.583
−46.611
3.6968
1.0679
−3.5572
−11.635
26.164
−0.33997
−0.054967
0.93805
1.4255
−0.47392
−1.0735
−0.31938
−1.6037
−0.50952
−0.33997
−0.20137
0.82109
2.6004
−0.46017
−4.6695
1.0770
−0.62917
−7.5742
−0.2500
−0.13366
5.8271
−0.86054
−0.20137
−0.33997
−0.33997
0.56919
1.0141
−1.3997
11.344
24.987
−1.6037
−0.50952
2.8308
6.4068
−11.353
15.423
−8.9527
8.5430
10.880
9.6663
9.6663
−2.0600
6.3944
10.784
0.037620
13.532
7.2295
8.7956
7.1564
7.6646
9.3249
−9.2464
10.550
2.6966
−0.35391
−1.8601
−1.8601
5.3281
−0.10298
−2.4754
5.6204
−3.2794
0.41759
−0.19165
−0.84442
−2.0750
−1.2478
b
d
T range (K)
Halogen Groups
0.19489
0.10679
0.0029498
−0.085271
0.099928
0.21413
0.11911
0.55022
0.33607
0.19489
0.11624
0.18415
−0.040688
0.52861
1.1400
−0.19489
0.25779
1.3760
0.12592
0.011799
−1.2013
−0.063611
0.11624
0.19489
0.19489
0.0053465
−0.071918
0.41385
−1.4108
−3.0249
0.55022
0.33607
−0.39125
−0.78182
1.2756
80–490
80–490
85–385
145–395
90–355
90–355
140–315
130–305
130–305
80–490
90–355
110–300
165–295
130–300
150–275
150–285
140–315
230–550
180–670
180–670
230–550
295–670
90–355
80–490
80–490
180–470
180–670
220–295
300–420
375–595
130–305
130–305
250–510
370–510
385–480
=C}(Cl,F)
Cb}(F)
Cb}(Cl)
Cb}(Br)
Cb}(I)
C}(Cb,3F)
C}(2H,Cb,Cl)
7.8204
3.0794
4.5479
2.2857
2.9033
7.4477
16.752
C}(3H,N)
C−(2H,C,N)
C}(2H,Cb,N)
C}(H,2C,N)
C}(3C,N)
N}(2H,C)
N}(2H,Cb)
N}(H,2C)
N}(3C)
N}(H,C,Cb)
N}(2C,Cb)
N}(C,2Cb)
Cb}(N)
N}(2H,N)
N}(H,C,N)
N}(2C,N)
N}(H,Cb,N)
C}(2H,C,CN)
C}(3C,CN)
=C}(H,CN)
Cb}(CN)
C}(2H,C,NO2)
O}(C,NO2)
Cb}(NO2)
N}(H,2Cb) (pyrrole)
Nb}(2Cb)
3.8452
2.4555
2.4555
2.6322
1.9630
8.2758
8.2758
−0.10987
4.5942
0.49631
−0.23640
4.5942
−0.78169
6.8050
1.1411
−1.0570
−0.74531
11.976
2.5774
9.0789
1.9389
18.520
−2.0181
15.277
−7.3662
0.84237
2.8647
−1.9986
−0.42564
0.08488
0.41360
0.41360
−0.82721
0.19403
0.33288
−0.92054
0.80145
0.15892
0.24596
0.27199
0.82003
0.44241
125–345
125–345
245–310
180–355
140–360
140–360
275–360
168–360
190–420
245–340
240–420
180–420
165–415
120–300
120–240
155–300
O}(H,C)
O}(H,C) (diol)
O}(H,Cb) (diol)
O}(H,Cb)
C–(3H,O)
C–(2H,C,O)
C–(2H,Cb,O)
C–(2H,=C,O)
C}(H,2C,O) (alcohol)
C}(H,2C,O) (ether, ester)
C}(3C,O) (alcohol)
C}(3C,O) (ether, ester)
O}(2C)
O}(C,Cb)
O}(2Cb)
C}(2H,2O)
−0.69005
0.46959
0.22250
2.2573
2.9763
−0.92230
−6.7938
0.19165
−0.0055745
−0.0097873
−0.40942
−0.62960
0.39346
1.2520
120–240
210–365
230–460
245–370
250–320
210–365
245–345
0.19489
−0.24054
−0.24054
0.45109
0.31086
0.035272
0.035272
0.89325
0.55316
−0.57161
−2.5258
0.55316
−0.25287
0.15634
−0.69350
−0.71494
−0.53306
0.52358
−0.58466
0.32986
−0.47276
1.05080
−1.83980
0.71161
−0.68137
−0.20336
80−490
190–375
190–375
240–370
255–375
185–455
185–455
170–400
160–360
240–380
285–390
160–360
240–455
215–465
205–300
205–300
295–385
185–345
295–345
195–345
265–480
190–300
180–350
280–415
255–450
210–395
2.6261
0.54075
0.54075
−0.87263
0.19489
−0.27140
−4.9593
−4.9593
0.69508
−0.016124
−4.8791
−0.44354
0.37860
−1.44210
0.31655
−0.31693
155–505
195–475
195–475
285–400
80–490
135–505
260–460
260–460
185–460
130–170
200–355
170–310
130–350
320–350
300–535
170–310
Nitrogen Groups
Halogen Groups
C}(C,3F)
C}(2C,2F)
C}(C,3Cl)
C}(H,C,2Cl)
C}(2H,C,Cl)
C}(2H,=C,Cl)
C}(H,2C,Cl)
C}(2H,C,Br)
C}(H,2C,Br)
C}(2H,C,I)
C}(C,2Cl,F)
C}(C,Cl,2F)
C}(C,Br,2F)
=C}(H,Cl)
=C}(2F)
=C}(2Cl)
a
−0.33997
1.0431
1.0431
−2.0135
−1.7235
−0.18365
−0.18365
0.73024
−2.2134
3.4617
16.260
−2.2134
1.5059
−0.72563
3.5981
4.0038
3.6258
−2.4886
3.5218
−0.86929
3.0269
−5.4568
10.505
−4.4049
6.3622
1.25560
Oxygen Groups
12.952
5.2302
5.2302
−7.9768
3.8452
1.4596
−35.127
−35.127
2.2209
0.98790
−44.690
−3.3182
5.0312
−22.5240
−4.5788
1.0852
−10.145
−1.5124
−1.5124
8.10450
−0.33997
1.4657
28.409
28.409
−1.4350
0.39403
31.769
2.6317
−1.5718
13.1150
0.94150
1.5402
(Continued )
2-344
PHYSICAL AnD CHEMICAL DATA
TABLE 2-166
Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method* (Continued )
Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond;
Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom.
Group Definition
a
b
d
T range (K)
Group Definition
a
Oxygen Groups
C}(2C,2O)
Cb}(O)
C}(3H,CO)
C}(2H,C,CO)
C}(H,2C,CO)
C}(3C,CO)
CO}(H,C)
CO}(H,=C)
CO}(H,Cb)
CO}(2C)
CO}(C,=C)
CO}(C,Cb)
CO}(H,O)
CO}(C,O)
CO}(=C,O)
CO}(O,CO)
O}(C,CO)
O}(H,CO)
=C}(H,CO)
=C}(C,CO)
Cb}(CO)
CO}(Cb,O)
−12.955
−1.0686
3.8452
6.6782
3.92380
−2.2681
−3.82680
−8.00240
−8.00240
5.4375
41.507
−47.21100
13.11800
29.24600
41.61500
23.99000
−21.43400
−27.58700
−9.01080
−12.81800
12.15100
16.58600
9.10270
3.52210
−0.33997
−2.44730
−2.12100
1.75580
7.67190
3.63790
3.63790
0.72091
−32.632
24.36800
16.12000
3.42610
−12.78900
6.25730
−4.01640
−0.16485
15.14800
15.99700
−1.67050
5.44910
−1.53670
−0.79259
0.19489
0.47121
0.49646
−0.25674
−1.27110
−0.15377
−0.15377
−0.18312
6.0326
−2.82740
−5.12730
−2.89620
0.53631
−3.24270
3.05310
2.74830
−3.04360
−3.05670
−0.12758
−2.68490
275–335
285–530
80–490
180–465
185–375
225–360
180–430
220–430
220–430
185–380
275–355
300–465
280–340
180–445
195–350
320–345
175–440
230–500
195–355
195–430
175–500
175–500
0.19489
−0.08349
−0.31234
−0.72356
−0.75674
0.47368
0.47368
0.45625
0.45625
0.17938
0.45625
−0.06131
80–490
130–390
150–390
190–365
260–375
130–380
130–380
165–390
165–390
170–350
165–390
205–345
Sulfur Groups
C}(3H,S)
C}(2H,C,S)
C}(H,2C,S)
C}(3C,S)
Cb}(S)
S}(H,C)
S}(H,Cb)
S}(2C)
S}(2Cb)
S}(C,S)
S}(Cb,S)
S}(2Cb) (thiophene)
3.84520
1.54560
−1.64300
−5.38250
−4.45070
10.99400
10.99400
9.23060
9.23060
6.65900
9.23060
3.84610
−0.33997
0.88228
2.30700
4.50230
4.43240
−3.21130
−3.21130
−3.00870
−3.00870
−1.35570
−3.00870
0.36718
*Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619.
Solids Solid heat capacity increases with increasing temperature and
is proportional to T 3 near absolute zero. The heat capacity at a solid-solid
phase transition becomes large, and there can be a substantial difference
in the heat capacity of the two equilibrium solid phases that exist on either
side of the transition temperature. The heat capacity generally rises steeply
with increasing temperature near the triple point.
For a quick estimation of solid heat capacity specifically at 298.15 K,
the very simple modification of Kopp’s rule [Kopp, H., Ann. Chem. Pharm.
(Liebig), 126 (1863): 362] by Hurst and Harrison [Hurst, J. E., and B. K.
Harrison, Chem. Eng. Comm., 112 (1992): 21] can be used. At other temperatures and to obtain the temperature dependence of the solid heat capacity,
the method given below by Goodman et al. should be used.
Recommended Method 1 Goodman method.
Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley,
J. Chem. Eng. Data, 49 (2004): 24.
Classification: Group contributions.
Expected uncertainty: 10 percent.
Applicability: Organic compounds for which group values are available.
Input data: Molecular structure and Table 2-167 group values.
Description:
CP
A T
=
J/(mol ⋅ K) 1000 K
b
d
T range (K)
Ring Strain Contributions
4.4297
−4.3392
1.2313
−2.8988
−0.33642 −2.8663
0.21983 −1.5118
−2.0097
−0.72656
−11.460
4.9507
−4.1696
0.52991
5.9700
−3.7965
0.21433 −2.5214
−1.2086
−1.5041
−5.6817
1.5073
−14.885
7.4878
−8.9683
6.4959
−7.2890
3.1119
−8.7885
8.2530
−12.914
13.583
−6.1414
3.5709
−3.6501
2.4707
−6.3861
2.6257
−6.8984
0.66846
−3.9271
−0.29239
−19.687
8.8265
−0.67632 −1.4753
61.213
−30.927
1.0222
0.75099
0.70123
0.28172
0.14758
−0.74754
−0.018423
0.74612
0.63136
0.42863
−0.19810
−1.0879
−1.5272
−0.43040
−2.4573
−4.0230
−0.48620
−0.60531
−0.19578
−0.070012
0.048561
−1.4031
−0.13087
3.2269
155–240
140–300
180–300
135–365
145–485
270–300
295–320
175–310
140–300
160–320
220–300
260–330
170–300
205–320
200–310
275–330
170–395
280–375
250–320
235–485
210–425
315–485
315–485
310–485
15.281
12.703
25.681
−2.3360
1.3109
−7.0966
−0.13720
−1.18130
0.14304
195–330
170–400
265–370
6.8459
−7.0148
−2.3985
9.6704
3.2842
−13.017
−5.8759
7.3764
−0.48585
−2.8138
−5.8260
3.7416
1.2408
−2.1901
0.10253
0.11376
1.2681
−0.15622
135–325
185–300
175–300
190–305
160–320
295–325
−0.73127
−3.2899
−12.766
−1.3426
0.38399
5.2886
0.40114
0.089358
−0.59558
200–320
170–390
295–340
Example Estimate the solid heat capacity for p-cresol at 307.93 K.
Structure:
Group contributions:
Group
ni
1
4
2
1
}CH3
Ar }CH=
Ar >C=
}OH
ai
0.20184
0.082478
0.012958
0.10341
bi
0
−0.00033
0
0
From Eq. (2-57):
A = exp [6.7796 + 0.20184 + (4) (0.082478) + (2)(0.012958)
+ 0.10341+ (4)2 (−0.00033)] = 1694.9
From Eq. (2-56):
0.79267
N
N
A = exp 6.7796 + ∑ ni ai + ∑ ni2βi
i =1
i =1
Hydrocarbons (ring strain)
cyclopropane
cyclobutane
cyclopentane (unsub)
cyclopentane (sub)
cyclohexane
cycloheptane
cyclooctane
spiropentane
cyclopentene
cyclohexene
cycloheptene
cyclooctene
cyclohexadiene
cyclooctadiene
cycloheptatriene
cyclooctatetraene
indan
1H-indene
tetrahydronaphthalene
decahydronaphthalene
hexahydroindan
dodecahydrofluorene
tetradecahydrophenanthrene
hexadecahydropyrene
Nitrogen compounds
ethyleneimine
pyrrolidine
piperidine
Oxygen compounds
ethylene oxide
trimethylene oxide
1,3-dioxolane
furan
tetrahydrofuran
tetrahydropyran
Sulfur compounds
thiacyclobutane
thiacyclopentane
thiacyclohexane
(2-56)
CP =
(2-57)
where ni = number of occurrences of group i
ai = individual group i contribution
bi = nonlinear correction terms for chain and aromatic carbons
1694.9
J
J
= 159.1
(307.93) 0.79267
1000
mol ⋅ K
mol ⋅ K
This value is 2.5 percent higher than the DIPPR 801 recommended value of 155.2 J/(mol ⋅ K).
Recommended Method 2 Modified Kopp’s rule.
Reference: Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362; Hurst,
J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21.
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
2-345
TABLE 2-167 Group Values and nonlinear Correction Terms for Estimation of Solid Heat Capacity
with the Goodman et al.* Method
Group
Description
ai
}CH3
>CH2
>CH}
>C<
CH2=
}CH=
>C=
=C=
#CH
#C}
Ar }CH=
Ar >C=
Ar }O}
Ar }N=
Ar >N}
Ar }NH}
Ar }S}
}O}
}OH
}COH
>C=O
}COO}
}COOH
}COOCO}
methyl
methylene
secondary C
tertiary C
terminal alkene
alkene
subst. alkene
allene
terminal alkyne
alkyne
arom. C
subst. arom. C
furan O
pyridine N
subst. pyrrole N
pyrrole N
thiophene S
ether
alcohol
aldehyde
ketone
ester
acid
anhydride
0.20184
0.11644
0.030492
−0.04064
0.18511
0.11224
0.028794
0.053464
−0.02914
0.13298
0.082478
0.012958
0.066027
0.056641
0.008938
−0.05246
0.090926
0.064068
0.10341
0.15699
0.12939
0.13686
0.21019
0.33091
Group
}CO3}
}NH2
>NH
>N}
=NH
#N
}N=N}
}NO2
}N=C=O
}SH
}S}
}SS}
=S
>S=O
}F
}Cl
}Br
}I
>Si<
>Si(O})}
cyc >Si(O})}
P(=O)(O})3
>P}
>P(=O)}
Description
ai
carbonate
primary amine
secondary amine
tertiary amine
double -bond NH
nitrile
diazide
nitro
isocyanate
thiol/mercaptan
sulfide
disulfide
sulfur double bond
sulfoxide
fluoride
chloride
bromide
iodide
silane
linear siloxane
cyclic siloxane
phosphate
phosphine
phosphine oxide
0.2517
0.056138
−0.00717
−0.01661
0.17689
0.015355
0.3687
0.23327
0.2698
0.21123
0.14232
0.31457
0.13753
0.040002
0.15511
0.16995
0.19112
0.11318
0.12213
0.10125
0.063438
0.15016
0.069602
0.21875
Nonlinear Terms
Groups
Usage
bi
Methylene
Aromatic carbon
>CH2
−0.00188
Ar=CH}
−0.00033
*Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 24.
Classification: Group contributions.
Expected uncertainty: 10 percent.
Applicability: At 298.15 K; organic compounds that are solids at 298.15 K.
Input data: Compound chemical formula and element contributions of
Table 2-168.
Description:
N
CP
= ∑ nE ∆ E
J/(mol ⋅ K) E = 1
C
C P , m = ∑ x iC P ,i
DEnSITY
Structure: C12H8S.
Group values from Table 2-168:
DS = 12.36
Calculation using Eq. (2-54):
CP = (12)(10.89) + (8)(7.56) + (1)(12.36) = 203.52 J/(mol ⋅ K)
TABLE 2-168 Element Contributions to Solid Heat Capacity for the
Modified Kopp’s Rule*†
Element
DE
Element
DE
Element
DE
C
H
O
N
S
F
Cl
Br
I
Al
B
10.89
7.56
13.42
18.74
12.36
26.16
24.69
25.36
25.29
18.07
10.10
Ba
Be
Ca
Co
Cu
Fe
Hg
K
Li
Mg
Mn
32.37
12.47
28.25
25.71
26.92
29.08
27.87
28.78
23.25
22.69
28.06
Mo
Na
Ni
Pb
Si
Sr
Ti
V
W
Zr
All others
29.44
26.19
25.46
31.60
17.00
28.41
27.24
29.36
30.87
26.82
26.63
*Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362.
†
Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21.
(2-59)
i =1
This neglects the excess heat capacity, which, if available, can be added to
the mole fraction average to improve the estimated value.
Example Estimate the solid heat capacity at 298.15 K for dibenzothiophene.
DH = 7.56
Mixtures The molar heat capacity of liquid and vapor mixtures can be
estimated as a mole fraction average of the pure-component values
(2-58)
where N = number of different elements in compound
nE = number of occurrences of element E in compound
DE = contribution of element E from Table 2-168
DC = 10.89
This value is 2.5 percent higher than the DIPPR 801 recommended value of 198.45
J/(mol ⋅ K).
Density is defined as the mass of a substance per unit volume. Density is
given in kg/m3 in SI units, but lbm/ft3 and g/cm3 are common AES and cgs
units, respectively. Other commonly used forms of density include molar
density (density divided by molecular weight) in kmol/m3, relative density
(density relative to water at 15°C), and the older term specific gravity (density relative to water at 60°F). Often the inverse of density, specific volume,
and the inverse of molar density, molar volume, are correlated and used to
convey equivalent information.
Gases Gases/vapors are compressible and their densities are strong
functions of both temperature and pressure. Equations of state (EoS) are
commonly used to correlate molar densities or molar volumes. The most
accurate EoS are those developed for specific fluids with parameters
regressed from all available data for that fluid. Super EoS are available for
some of the most industrially important gases and may contain 50 or more
constants specific to that chemical. Different predictive methods may be
used for gas densities depending upon the conditions:
1. At very low densities (high temperatures, generally above the critical,
and very low pressures, generally below a few bar), the ideal gas EoS
Z ≡
PV
=1
RT
(2-60)
may be applied.
2. At moderate densities (below 40 percent of the critical density), the
virial equation truncated after the second virial coefficient
Z =1+
B (T )
V
(2-61)
2-346
PHYSICAL AnD CHEMICAL DATA
may be used. Second virial coefficients B(T) are available in the DIPPR 801
database for many chemicals and can be estimated using the Tsonopoulos
method.
Recommended Method Tsonopoulos method.
Reference: Tsonopoulos, C., AIChE J., 20 (1974): 263; 21 (1975): 827; 24
(1978): 1112.
Classification: Corresponding states.
Expected uncertainty: 8 percent for B(T).
Applicability: Nonpolar organic compounds and some classes of polar
compounds.
Input data: Class of fluid, w, Pc, Tc, and m.
Description:
BPc
= B (0) + ωB (1) + B (2)
RTc
(2-62)
where
B (0) = 0.1445 −
0.330 0.1385 0.0121 0.000607
−
−
−
Tr3
Tr8
Tr
Tr2
(2-63)
(2-64)
a b
−
Tr6 Tr8
2
µ
P
T
µ r = c c
D bar K
3. For higher gas densities, the Lee-Kesler method described below
provides excellent predictions for nonpolar and slightly polar fluids.
Extended four-parameter corresponding-states methods are available for
polar and slightly associating compounds.
Recommended Method Lee-Kesler method.
Reference: Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510.
Classification: Corresponding states.
Expected uncertainty: 1 percent except near the critical point where errors
can be up to 30 percent.
Applicability: Nonpolar and moderately polar compounds. An extended
Lee-Kesler method, not described here, may be used for polar and slightly
associating compounds [Wilding, W. V., and R. L. Rowley, Int. J. Thermophys.,
8 (1986): 525].
Input data: Tc, Pc, w, Z(0), Z(1).
Description:
Z = Z(0) + wZ(1)
0.331 0.423 0.008
B = 0.0637 + 2 − 3 − 8
Tr
Tr
Tr
(1)
B (2) =
r = V −1 = 0.86 kmol/m3 is much less than 40 percent of the critical density (the
DIPPR 801 recommended value for the critical density is 13.8 kmol/m3).
(2-65)
where Z = compressibility factor
Z(0) = compressibility factor of simple fluid obtained from Table 2-169
Z(1) = deviation from simple fluid obtained from Table 2-170
Analytical expressions for Z(0) and Z(1) can also be generated by using
Z (0) = Z0
−2
(2-66)
and m = dipole moment. The values of a and b used in Eq. (2-65) depend
upon the class of fluid, as given in the table below:
Class
a
b
Nonpolar fluids
Ketones, aldehydes,
nitriles, ethers, esters,
NH3, H2S, HCN
Monoalkylhalides,
mercaptans, sulfides
1-Alcohols except methanol
Methanol
0
−21.4mr − 4.308 × 1019mr8
0
0
−2.188 × 1016mr4 − 7.831 × 1019mr8
0
0.0878
0.0878
0.00908 + 69.57mr
0.0525
Example Estimate the molar volume of ammonia at 430 K and 2.82 MPa.
Input properties: Recommended values from the DIPPR 801 database are Tc = 405.65 K,
Pc = 11.28 MPa, m = 1.469 D, and w = 0.252608.
Reduced conditions:
Tr = (430 K)/(405.65 K) = 1.06
Pr = (2.82 MPa)/(11.28 MPa) = 0.25
Z (1) =
Z1 − Z0
0.3978
(2-68)
where Z0 and Z1 are determined from
Zi =
PrVr
B C
D
c
γ
−γ
= 1 + + 2 + 5 + 3 4 2 β + 2 exp 2
Tr
Vr Vr Vr Tr Vr Vr
Vr
b2 b3 b4
− −
Tr Tr2 Tr3
c c
C = c1 − 2 + 32
Tr Tr
d
D = d1 + 2
Tr
B = b1 −
(2-69)
as applied to the simple reference fluid and to the acentric reference fluid
(n-octane), respectively. The constants for Eq. (2-69) for the two reference
fluids are given in Table 2-171.
Example Estimate the molar volume of saturated n-decane vapor at 540.5 K.
Input properties: Recommended values from the DIPPR 801 database are Tc = 617.7 K,
Pc = 2.11 MPa, P*(540.5 K) = 0.6799 MPa, and w = 0.492328.
Reduced conditions:
mr = (1.469)2(112.8)/(405.65)2 = 0.0014793
Second virial coefficient from Eqs. (2-63) to (2-66):
(2-67)
Tr = (540.5 K)/(617.7 K) = 0.875 and Pr = (0.6799 MPa)/(2.11 MPa) = 0.322
LK compressiblity factor: Since vapor phase values are needed, the appropriate values from Tables 2-169 and 2-170 that can be used to double-interpolate are as follows:
B(0) = 0.1445 – 0.330/1.06 – 0.1385/(1.06)2 − 0.0121/(1.06)3 − 0.000607/(1.06)8 = −0.301
B(1) = 0.0637 + 0.331/(1.06)2 − 0.423/(1.06)3 − 0.008/(1.06)8 = −0.00189
a = (−21.4)(0.0014793) − (4.308 × 1019)(0.0014793)8 = −0.033
b=0
B(2) = (−0.033)/(1.06)6 = −0.023
From Eq. (2-62) :
BPc/(RTc) = −0.301 − (0.252608)(0.00189) − 0.023 = −0.324
B = (−0.324)[0.008314 m3 ⋅ MPa/(kmol ⋅ K)](405.65 K)/(11.28 MPa) = −0.097 m3/kmol
Molar volume from Eq. (2-61) :
3
m 3 ⋅ MPa
0.0083143
(430 K) −0.097 m
kmol ⋅ K
RT
B
m3
kmol
V=
1+ =
= 1.162
1+
P V
2.82 M Pa
V
kmol
Note that the ideal gas value, 1.268 m3/kmol, deviates by 9.1 percent from this
more accurate value. The truncated virial EoS should be valid for this density since
Z(0)
Tr\Pr
0.85
0.90
Z(1)
0.2
0.8810
0.9015
0.4
0.2
Tr\Pr
(0.7222)
0.7800
0.85
0.90
−0.0715
−0.0442
0.4
(−0.1503)
−0.1118
Double linear interpolation within these values gives Z(0) = 0.8058 and Z(1) = −0.1025.
From Eq. (2-67):
Z = 0.8058 + (0.492328)(−0.1025) = 0.7553
Note: If the analytical form available in Eq. (2-69) is used, the following more accurate
values are obtained: Z(0) = 0.8131, Z(1) = − 0.1067, and Z = 0.7606.
Molar volume:
ZRT
V=
=
P
m 3 ⋅ MPa
(0.7553) 0.0083143
(540.5 K)
kmol ⋅ K
0.6799 M Pa
= 4.992
m3
kmol
4. Cubic EoS can be used to obtain both vapor and liquid densities as an alternative
method to those mentioned above.
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-169
2-347
Simple Fluid Compressibility Factors Z(0)
Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J.
Thermophys., 8(1987):717].
Tr\Pr
0.010
0.050
0.100
0.200
0.400
0.600
0.800
1.000
1.200
1.500
2.000
3.000
5.000
7.000
10.000
0.30
0.35
0.40
0.45
0.0029
0.0026
0.0024
0.0022
0.0145
0.0130
0.0119
0.0110
0.0290
0.0261
0.0239
0.0221
0.0579
0.0522
0.0477
0.0442
0.1158
0.1043
0.0953
0.0882
0.1737
0.1564
0.1429
0.1322
0.2315
0.2084
0.1904
0.1762
0.2892
0.2604
0.2379
0.2200
0.3470
0.3123
0.2853
0.2638
0.4335
0.3901
0.3563
0.3294
0.5775
0.5195
0.4744
0.4384
0.8648
0.7775
0.7095
0.6551
1.4366
1.2902
1.1758
1.0841
2.0048
1.7987
1.6373
1.5077
2.8507
2.5539
2.3211
2.1338
0.50
0.0021
0.0103
0.0207
0.0413
0.0825
0.1236
0.1647
0.2056
0.2465
0.3077
0.4092
0.6110
1.0094
1.4017
1.9801
(0.9741)
(0.8699)
0.9804
0.0098
0.0195
0.0390
0.0778
0.1166
0.1553
0.1939
0.2323
0.2899
0.3853
0.5747
0.9475
1.3137
1.8520
(0.0020)
(0.9000)
(0.7995)
0.9849
0.0093
0.0186
0.0371
0.0741
0.1109
0.1476
0.1842
0.2207
0.2753
0.3657
0.5446
0.8959
1.2398
1.7440
(0.0019)
(0.9211)
(0.8405)
0.9881
0.9377
0.0178
0.0356
0.0710
0.1063
0.1415
0.1765
0.2113
0.2634
0.3495
0.5197
0.8526
1.1773
1.6519
(0.0018)
(0.0089)
(0.8707)
(0.7367)
0.9904
0.9504
0.8958
0.0344
0.0687
0.1027
0.1366
0.1703
0.2038
0.2538
0.3364
0.4991
0.8161
1.1241
1.5729
(0.0086)
(0.0172)
(0.7805)
0.9598
0.9165
0.0336
0.0670
0.1001
0.1330
0.1656
0.1981
0.2464
0.3260
0.4823
0.7854
1.0787
1.5047
(0.0085)
(0.0169)
(0.8181)
(0.6122)
0.9669
0.9319
0.8539
0.0661
0.0985
0.1307
0.1626
0.1942
0.2411
0.3182
0.4690
0.7598
1.0400
1.4456
(0.0168)
(0.0332)
(0.6659)
(0.4746)
0.9436
0.8810
0.0661
0.0983
0.1301
0.1614
0.1924
0.2382
0.3132
0.4591
0.7388
1.0071
1.3943
(0.0336)
(0.7222)
(0.5346)
0.9015
0.7800
0.1006
0.1321
0.1630
0.1935
0.2383
0.3114
0.4527
0.7220
0.9793
1.3496
(0.0364)
(0.0685)
(0.6040)
(0.4034)
0.9115
0.8059
0.6635
0.1359
0.1664
0.1963
0.2405
0.3122
0.4507
0.7138
0.9648
1.3257
(0.7350)
(0.1047)
(0.4499)
0.8206
0.6967
0.1410
0.1705
0.1998
0.2432
0.3138
0.4501
0.7092
0.9561
1.3108
(0.0822)
(0.1116)
0.4853)
0.8338
0.7240
0.5580
0.1779
0.2055
0.2474
0.3164
0.4504
0.7052
0.9480
1.2968
(0.1312)
(0.1532)
0.7360
0.5887
0.1844
0.2097
0.2503
0.3182
0.4508
0.7035
0.9442
1.2901
0.1959
0.2154
0.2538
0.3204
0.4514
0.7018
0.9406
1.2835
0.2901
0.4648
0.5146
0.6026
0.6880
0.7443
0.7858
0.8438
0.8827
0.9103
0.9308
0.9463
0.9583
0.9678
0.9754
0.9865
0.9941
0.9993
1.0031
1.0057
1.0097
1.0115
0.2237
0.2370
0.2629
0.4437
0.5984
0.6803
0.7363
0.8111
0.8595
0.8933
0.9180
0.9367
0.9511
0.9624
0.9715
0.9847
0.9936
0.9998
1.0042
1.0074
1.0120
1.0140
0.2583
0.2640
0.2715
0.3131
0.4580
0.5798
0.6605
0.7624
0.8256
0.8689
0.9000
0.9234
0.9413
0.9552
0.9664
0.9826
0.9935
1.0010
1.0063
1.0101
1.0156
1.0179
0.3229
0.3260
0.3297
0.3452
0.3953
0.4760
0.5605
0.6908
0.7753
0.8328
0.8738
0.9043
0.9275
0.9456
0.9599
0.9806
0.9945
1.0040
1.0106
1.0153
1.0221
1.0249
0.4522
0.4533
0.4547
0.4604
0.4770
0.5042
0.5425
0.6344
0.7202
0.7887
0.8410
0.8809
0.9118
0.9359
0.9550
0.9827
1.0011
1.0137
1.0223
1.0284
1.0368
1.0401
0.7004
0.6991
0.6980
0.6956
0.6950
0.6987
0.7069
0.7358
0.7761
0.8200
0.8617
0.8984
0.9297
0.9557
0.9772
1.0094
1.0313
1.0463
1.0565
1.0635
1.0723
1.0741
0.9372
0.9339
0.9307
0.9222
0.9110
0.9033
0.8990
0.8998
0.9112
0.9297
0.9518
0.9745
0.9961
1.0157
1.0328
1.0600
1.0793
1.0926
1.1016
1.1075
1.1138
1.1136
1.2772
1.2710
1.2650
1.2481
1.2232
1.2021
1.1844
1.1580
1.1419
1.1339
1.1320
1.1343
1.1391
1.1452
1.1516
1.1635
1.1728
1.1792
1.1830
1.1848
1.1834
1.1773
(0.9648)
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.93
0.95
0.97
0.98
0.9922
0.9935
0.9946
0.9954
0.9959
0.9961
0.9963
0.9965
0.9725
0.9768
0.9790
0.9803
0.9815
0.9821
0.9528
0.9573
0.9600
0.9625
0.9637
0.9174
0.9227
0.9253
0.8398
(0.1703)
0.99
0.9966
0.9826
0.9648
0.9277
0.8455
0.7471
0.6138
(0.2324)
1.00
1.01
1.02
1.05
1.10
1.15
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.20
2.40
2.60
2.80
3.00
3.50
4.00
0.9967
0.9968
0.9969
0.9971
0.9975
0.9978
0.9981
0.9985
0.9988
0.9991
0.9993
0.9994
0.9995
0.9996
0.9997
0.9998
0.9999
1.0000
1.0000
1.0000
1.0001
1.0001
0.9832
0.9837
0.9842
0.9855
0.9874
0.9891
0.9904
0.9926
0.9942
0.9954
0.9964
0.9971
0.9977
0.9982
0.9986
0.9992
0.9996
0.9998
1.0000
1.0002
1.0004
1.0005
0.9659
0.9669
0.9679
0.9707
0.9747
0.9780
0.9808
0.9852
0.9884
0.9909
0.9928
0.9943
0.9955
0.9964
0.9972
0.9983
0.9991
0.9997
1.0001
1.0004
1.0008
1.0010
0.9300
0.9322
0.9343
0.9401
0.9485
0.9554
0.9611
0.9702
0.9768
0.9818
0.9856
0.9886
0.9910
0.9929
0.9944
0.9967
0.9983
0.9994
1.0002
1.0008
1.0017
1.0021
0.8509
0.8561
0.8610
0.8743
0.8930
0.9081
0.9205
0.9396
0.9534
0.9636
0.9714
0.9775
0.9823
0.9861
0.9892
0.9937
0.9969
0.9991
1.0007
1.0018
1.0035
1.0043
0.7574
0.7671
0.7761
0.8002
0.8323
0.8576
0.8779
0.9083
0.9298
0.9456
0.9575
0.9667
0.9739
0.9796
0.9842
0.9910
0.9957
0.9990
1.0013
1.0030
1.0055
1.0066
0.6353
0.6542
0.6710
0.7130
0.7649
0.8032
0.8330
0.8764
0.9062
0.9278
0.9439
0.9563
0.9659
0.9735
0.9796
0.9886
0.9948
0.9990
1.0021
1.0043
1.0075
1.0090
2-348
PHYSICAL AnD CHEMICAL DATA
TABLE 2−170
Acentric Deviations Z (1) from the Simple Fluid Compressibility Factor
Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J.
Thermophys., 8(1987):717].
Tr\Pr
0.010
0.050
0.100
0.200
0.400
0.600
0.800
1.000
1.200
1.500
0.30
0.35
0.40
0.45
−0.0008
−0.0009
−0.0010
−0.0009
−0.0040
−0.0046
−0.0048
−0.0047
−0.0081
−0.0093
−0.0095
−0.0094
−0.0161
−0.0185
−0.0190
−0.0187
−0.0323
−0.0370
−0.0380
−0.0374
−0.0484
−0.0554
−0.0570
−0.0560
−0.0645
−0.0738
−0.0758
−0.0745
−0.0806
−0.0921
−0.0946
−0.0929
−0.0966
−0.1105
−0.1134
−0.1113
−0.1207
−0.1379
−0.1414
−0.1387
−0.0009
−0.0045
−0.0090
−0.0181
−0.0360
−0.0539
−0.0716
−0.0893
(−0.0457)
(−0.2270)
−0.0172
−0.0343
−0.0513
−0.0682
−0.0164
−0.0326
−0.0487
−0.0309
2.000
3.000
5.000
7.000
10.000
−0.2407
−0.2738
−0.2799
−0.2734
−0.3996
−0.4523
−0.4603
−0.4475
−0.5572
−0.6279
−0.6365
−0.6162
−0.7915
−0.8863
−0.8936
−0.8606
−0.1069 −0.1330
−0.1762 −0.2611
−0.4253
−0.5831
−0.8099
−0.0849
−0.1015 −0.1263
−0.1669 −0.2465
−0.3991
−0.5446
−0.7521
−0.0646
−0.0803
−0.0960 −0.1192
−0.1572 −0.2312
−0.3718
−0.5047
−0.6928
−0.0461
−0.0611
−0.0759
−0.0906 −0.1122
−0.1476 −0.2160
−0.3447
−0.4653
−0.6346
−0.0294
−0.0438
−0.0579
−0.0718
−0.0855 −0.1057
−0.1385 −0.2013
−0.3184
−0.4270
−0.5785
−0.0417
−0.0550
−0.0681
−0.0808 −0.0996
−0.1298 −0.1872
−0.2929
−0.3901
−0.5250
−0.0526
−0.0648
−0.0767 −0.0940
−0.1217 −0.1736
−0.2682
−0.3545
−0.4740
−0.0509
−0.0622
−0.0731 −0.0888
−0.1138 −0.1602
−0.2439
−0.3201
−0.4254
−0.0604
−0.0701 −0.0840
−0.1059 −0.1463
−0.2195
−0.2862
−0.3788
−0.0602
−0.0687 −0.0810
−0.1007 −0.1374
−0.2045
−0.2661
−0.3516
−0.0607
−0.0678 −0.0788
−0.0967 −0.1310
−0.1943
−0.2526
−0.3339
−0.0623
−0.0669 −0.0759
−0.0921 −0.1240
−0.1837
−0.2391
−0.3163
−0.0641
−0.0661 −0.0740
−0.0893 −0.1202
−0.1783
−0.2322
−0.3075
−0.0680
−0.0646 −0.0715
−0.0861 −0.1162
−0.1728
−0.2254
−0.2989
−0.0879
−0.0223
−0.0062
0.0220
0.0476
0.0625
0.0719
0.0819
0.0857
0.0864
0.0855
0.0838
0.0816
0.0792
0.0767
0.0719
0.0675
0.0634
0.0598
0.0565
0.0497
0.0443
−0.0609 −0.0678
−0.0473 −0.0621
0.0227 −0.0524
0.1059 0.0451
0.0897 0.1630
0.0943 0.1548
0.0991 0.1477
0.1048 0.1420
0.1063 0.1383
0.1055 0.1345
0.1035 0.1303
0.1008 0.1259
0.0978 0.1216
0.0947 0.1173
0.0916 0.1133
0.0857 0.1057
0.0803 0.0989
0.0754 0.0929
0.0711 0.0876
0.0672 0.0828
0.0591 0.0728
0.0527 0.0651
−0.0824
−0.0778
−0.0722
−0.0432
0.0698
0.1667
0.1990
0.1991
0.1894
0.1806
0.1729
0.1658
0.1593
0.1532
0.1476
0.1374
0.1285
0.1207
0.1138
0.1076
0.0949
0.0849
−0.1672
−0.1615
−0.1556
−0.1370
−0.1021
−0.0611
−0.0141
0.0875
0.1737
0.2309
0.2631
0.2788
0.2846
0.2848
0.2819
0.2720
0.2602
0.2484
0.2372
0.2268
0.2042
0.1857
−0.2185
−0.2116
−0.2047
−0.1835
−0.1469
−0.1084
−0.0678
0.0176
0.1008
0.1717
0.2255
0.2628
0.2871
0.3017
0.3097
0.3135
0.3089
0.3009
0.2915
0.2817
0.2584
0.2378
−0.2902
−0.2816
−0.2731
−0.2476
−0.2056
−0.1642
−0.1231
−0.0423
0.0350
0.1058
0.1673
0.2179
0.2576
0.2876
0.3096
0.3355
0.3459
0.3475
0.3443
0.3385
0.3194
0.2994
−0.1608
−0.1834
−0.1879
−0.1840
(−0.0740)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.93
0.95
0.97
0.98
−0.0314
−0.0043
−0.0086
(−0.0009)
(−0.1438)
(−0.2864)
−0.0205
−0.0041
−0.0082
(0.0008)
(0.0949)
(−0.1857)
−0.0137
−0.0772
−0.0078
−0.0156
(−0.0008)
(0.0039)
(−0.1262)
(−0.2424)
−0.0093
−0.0064
−0.0044
−0.0029
−0.0019
−0.0015
−0.0012
−0.0010
−0.0009
−0.0507
−0.1161
−0.0148
(−0.0038)
(−0.0075)
(−0.1685)
−0.0339
−0.0744
−0.0143
−0.0282
(−0.0037)
(−0.0072)
(−0.1298)
(−0.2203)
−0.0228
−0.0152
−0.0099
−0.0075
−0.0062
−0.0050
−0.0044
−0.0487
−0.1160
−0.0272
−0.0401
(−0.0073)
(−0.0139)
(−0.1682)
(−0.2185)
−0.0319
−0.0205
−0.0154
−0.0126
−0.0101
−0.0090
−0.0715
−0.0268
−0.0391
(−0.0144)
(−0.1503)
(−0.1692)
−0.0442
−0.1118
−0.0396
−0.0503
(−0.0179)
(−0.0286)
(−0.1580)
(−0.1464)
−0.0326
−0.0262
−0.0208
−0.0184
−0.0763
−0.1662
−0.0514
(−0.0340)
(−0.0424)
(−0.1418)
−0.0589
−0.1110
−0.0540
(−0.0444)
(−0.0490)
(−0.1532)
−0.0450
−0.0390
−0.0770
−0.1647
(−0.0714)
(−0.0643)
−0.0641
−0.1100
(−0.0828)
0.99
−0.0008
−0.0039
−0.0079
−0.0161
−0.0335
−0.0531
−0.0796
(−0.1621)
1.00
1.01
1.02
1.05
1.10
1.15
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.20
2.40
2.60
2.80
3.00
3.50
4.00
−0.0007
−0.0006
−0.0005
−0.0003
0.0000
0.0002
0.0004
0.0006
0.0007
0.0008
0.0008
0.0008
0.0008
0.0008
0.0008
0.0007
0.0007
0.0007
0.0006
0.0006
0.0005
0.0005
−0.0034
−0.0030
−0.0026
−0.0015
0.0000
0.0011
0.0019
0.0030
0.0036
0.0039
0.0040
0.0040
0.0040
0.0040
0.0039
0.0037
0.0035
0.0033
0.0031
0.0029
0.0026
0.0023
−0.0069
−0.0060
−0.0051
−0.0029
0.0001
0.0023
0.0039
0.0061
0.0072
0.0078
0.0080
0.0081
0.0081
0.0079
0.0078
0.0074
0.0070
0.0066
0.0062
0.0059
0.0052
0.0046
−0.0140
−0.0120
−0.0102
−0.0054
0.0007
0.0052
0.0084
0.0125
0.0147
0.0158
0.0162
0.0163
0.0162
0.0159
0.0155
0.0147
0.0139
0.0131
0.0124
0.0117
0.0103
0.0091
−0.0285
−0.0240
−0.0198
−0.0092
0.0038
0.0127
0.0190
0.0267
0.0306
0.0323
0.0330
0.0329
0.0325
0.0318
0.0310
0.0293
0.0276
0.0260
0.0245
0.0232
0.0204
0.0182
−0.0435
−0.0351
−0.0277
−0.0097
0.0106
0.0237
0.0326
0.0429
0.0477
0.0497
0.0501
0.0497
0.0488
0.0477
0.0464
0.0437
0.0411
0.0387
0.0365
0.0345
0.0303
0.0270
−0.0588
−0.0429
−0.0303
−0.0032
0.0236
0.0396
0.0499
0.0612
0.0661
0.0677
0.0677
0.0667
0.0652
0.0635
0.0617
0.0579
0.0544
0.0512
0.0483
0.0456
0.0401
0.0357
−0.1118
−0.1072
−0.1021
−0.0838
−0.0373
0.0332
0.1095
0.2079
0.2397
0.2433
0.2381
0.2305
0.2224
0.2144
0.2069
0.1932
0.1812
0.1706
0.1613
0.1529
0.1356
0.1219
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-171 Constants for the Two Reference Fluids Used in
Lee-Kesler Method*
Constant
b1
b2
b3
b4
c1
c2
c3
c4
d1 × 104
d2 × 104
b
g
2-349
Tr = (353.15 K)/(405.65 K) = 0.871
Simple reference fluid
Acentric reference fluid
0.1181193
0.265728
0.154790
0.030323
0.0236744
0.0186984
0.0
0.042724
0.155488
0.623689
0.65392
0.060167
0.2026579
0.331511
0.027655
0.203488
0.0313385
0.0503618
0.016901
0.041577
0.48736
0.0740336
1.226
0.03754
α = {1 + [0.48 + (1.574) (0.252608) − (0.176) (0.252608)2] [1 − (0.871)0.5]}2 = 1.119
Rearrange and solve Eq. (2-70) for V:
P=
RT
aα
−
V − b V (V + b)
PV 3 − RTV 2 + (aα − bRT − Pb2)V − abα = 0
or
3
m3 V
V
− 0.029
41.352 3
m /mol
mol m 3 /mol
2
m6 V
−10
+ 4.037 × 10 −6
− 1.25 × 10 = 0
mol 2 m 3 /mol
Vapor root (initial guess of V = 7.1 × 10−7 m3/mol from ideal gas equation):
*Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510.
Vvap = 5.395 × 10−4 m3/mol
and rvap = 1/Vvap = 1.854 kmol/m3
Liquid root (initial guess of V = 2.72 × 10−5 m3/mol from 1.05b):
Recommended Method Cubic EoS.
Classification: Empirical extension of theory.
Expected uncertainty: Varies depending upon compound and conditions,
but a general expectation is 10 to 20 percent.
Applicability: Nonpolar and moderately polar compounds.
Input data: Tc, Pc, w.
Description: The more common cubic EoS can be written in the form
a α (Tr )
V
V
−
Z=
V − b V 2 + δV + ε RT
Vliq = 4.441 × 10−5 m3/mol
The corresponding values and equation for the Peng-Robinson EoS are
a = 4.611 × 106 cm6 ⋅ bar/mol2
P=
or
(2-70)
353.15 K, using the Soave and Peng-Robinson EoS.
Required properties: Recommended values in the DIPPR 801 database are
w = 0.252608
P*(353.15 K) = 41.352 bar (vapor pressure at 353.15 K)
EoS parameters (shown for Soave EoS):
2
bar ⋅ cm 3
0.42748 83.145
(405.65 K)
6
mol ⋅ K
0.42748 (RTc )
= 4.311 × 10 6 cm ⋅ bar
a=
=
112.8 bar
Pc
mol 2
2
0.08664 (RTc )
b=
=
Pc
bar ⋅ cm 3
0.08664 83.145
(405.65 K)
mol ⋅ K
cm 3
= 25.906
112.8 bar
mol
TABLE 2-172
EoS
RT
aα
−
V − b V 2 + 2bV − b 2
PV 3 + (bP − RT)V 2 + (aα − 2bRT − 3Pb2)V + (bP 3 + RTb2 − abα) = 0
m3 V
V
− 0.0284
41.352 3
m /mol
mol m 3 /mol
2
m6 V
−10
+ 3.651 × 10 −6
− 1.018 × 10 = 0
mol 2 m 3 /mol
Solve for the two physical roots of this equation:
Vvap = 5.286 × 10−4 m3/mol and rvap = 1.892 kmol/m3
Vliq = 3.914 × 10−5 m3/mol and rliq = 25.55 kmol/m3
The liquid density calculated from the Soave EoS is 24.2 percent below the DIPPR 801
recommended value of 29.69 kmol/m3; that calculated from the Peng-Robinson EoS is
13.9 percent below the recommended value.
Liquids For most liquids, the saturated molar liquid density r can be
effectively correlated with
ρ=
Example Estimate the molar density of liquid and vapor saturated ammonia at
Pc = 112.8 bar
b = 23.262 cm3/mol α = 1.103
3
where a, b, d, and e are constants that depend upon the model EoS chosen,
as does the temperature dependence of the function α(Tr). Definitions of
these constants and α(Tr) for some of the more commonly used EoS models
are shown in Table 2-172. The corresponding relations for many other EoS
models in this same form are available [Soave, G., Chem. Eng. Sci., 27 (1972):
1197]. The independent parameters a and b in these models can be
regressed from experimental data to correlate densities or can be obtained
from known critical constants to predict density data.
Of the cubic EoS given in Table 2-172, the Soave and Peng-Robinson
are the most accurate, but there is no general rule for which EoS produces the best estimated volumes for specific fluids or conditions. The
Peng-Robinson equation has been better tuned to liquid densities, while
the Soave equation has been better tuned to vapor-liquid equilibrium and
vapor densities. In solving the cubic equation for volume, a convenient initial guess to find the vapor root is the ideal gas value, while an initial value
of 1.05b is convenient to locate the liquid root.
Tc = 405.65 K
rliq = 1/Vliq = 22.516 kmol/m3
and
A
D
B [1+(1−T /C ) ]
(2-71)
adapted from the Rackett prediction equation [Rackett, H. G., J. Chem. Eng.
Data, 15 (1970): 514]. The regression constants A, B, and D are determined
from the nonlinear regression of available data, while C is usually taken as
the critical temperature. The liquid density decreases approximately linearly from the triple point to the normal boiling point and then nonlinearly
to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range
of temperature.
The recommended method for estimation of saturated liquid density for
pure organic compounds is the Rackett prediction method.
Recommended Method Rackett method.
Reference: Rackett, H. G., J. Chem. Eng. Data, 15 (1970): 514.
Classification: Corresponding states.
Expected uncertainty: 15 percent as purely predictive equation; 2 percent
if a liquid density value is available.
Relationships for Eq. (2-70) for Common Cubic EoS
d
e
α(Tr)
van der Waals*
0
0
1
Relich-Kwong†
0
0
Tr−0.5
Soave‡
b
0
[1 + (0.48 + 1.574w − 0.176w2)(1 − Tr0.5)]2
Peng-Robinson§
2b
−b2
[1 + (0.37464 + 1.54226w − 0.2699w2)(1 − Tr0.5)]2
*van der Waal, J. H., Z. Phys. Chem., 5 (1890): 133.
†
Redlich, O., and J. N. S. Kwong, Chem. Rev., 44 (1949): 233.
‡
Soave, G., Chem. Eng. Sci., 27 (1972): 1197.
§
Peng, D. Y., and D. B. Robinson, Ind. Eng. Chem. Fundam., 15 (1976): 59.
aPc/(RTc)2
bPc/(RTc)
0.42188
0.42748
0.42748
0.45724
0.125
0.08664
0.08664
0.0778
2-350
PHYSICAL AnD CHEMICAL DATA
Applicability: Saturated liquid densities of organic compounds.
Input data: Tc, Pc, and Zc (or, equivalently, Vc).
Description: A predictive form of the equation is given by
RT
1
= V = c Zcq
ρ
Pc
Example Estimate the density of solid naphthalene at 281.46 K.
Required properties: The recommended values from the DIPPR 801 database for Tt
and the liquid density at Tt are
where q = 1 + (1 − Tr )
(2-72)
When one or more liquid density data points are available, Zc in Eq. (2-72)
can be replaced with an adjustable parameter fitted from the data (ZRA
in the notation of Spencer and Danner [Spencer, C. F., and R. P. Danner,
J. Chem. Eng. Data 17 (1972): 236]). This produces densities in good agreement with experiment and permits accurate interpolation of the densities
over most of the liquid temperature range, but it does not give the correct
critical density unless ZRA = Zc.
Example Estimate the saturated liquid density of acetonitrile at 376.69 K.
Required properties: The recommended values from the DIPPR 801 database are
Tc = 545.5 K
rL(Tt) = 7.6326 kmol/m3
Tt = 353.43 K
2/7
Pc = 4.83 MPa
Zc = 0.184
Calculate supporting quantities:
From Eq. (2-73):
281.46 K
kmol
kmol
ρs = 1.28 − 0.16
7.6326 3 = 8.797 3
353.43 K
m
m
The estimated value is 4.3 percent lower than the DIPPR 801 recommended value of
9.1905 kmol/m3.
Mixtures Both liquid and vapor densities can be estimated using purecomponent CS and EoS methods by treating the fluid as a pseudo-pure
component with effective parameters calculated from the pure-component
parameters using ad hoc mixing rules.
To apply the Lee-Kesler CS method to mixtures, pseudo-pure fluid constants are required. One of the simplest set of mixing rules for these quantities is [Prausnitz, J. M., and R. D. Gunn, AIChE J., 4 (1958): 430, 494; Joffe, J.,
Ind. Eng. Chem. Fundam., 10 (1971): 532]:
Tr = (376.69 K)/(545.5 K) = 0.691
C
Tc = ∑ x iTc ,i
q = 1 + (1 − 0.691)2/7 = 1.715
Calculate saturated liquid density from Eq. (2-72):
C
∑x Z
i
Pc =
4.83 × 10 6 Pa
(0.184)− 1.715 = 19.42 kmol
ρ=
m3
Pa ⋅ m 3
8.314
(545.5
K)
mol ⋅ K
RTc
(2-75)
i =1
ω = ∑ xiωi
1/1.798
(2-76)
i =1
The procedures are identical to those for pure components with the replacement of Tc, Pc, and w with the effective mixture values obtained from the
above equations.
To use a cubic EoS for a mixture, mixing rules are used to calculate
effective mixture parameters in terms of the pure-component values.
Although more complex mixing rules may improve prediction accuracy,
the simple forms recommended here provide reasonable accuracy without
adjustable parameters:
= 0.202
C
b = ∑ x i bi
(2-77)
i =1
6
×
4.83
10
Pa
(0.202)−1.715 = 16.577 kmol
ρ=
m3
Pa ⋅ m 3
(545.5 K)
8.314
mol ⋅ K
2
The value obtained by the modified Rackett method is 0.9 percent below the DIPPR 801
recommended value. Note, however, that with ZRA = 0.202 instead of Zc, Eq. (2-72) gives
rc = 5.28 kmol/m3 instead of rc = Pc/(ZcRTc) = 5.79 kmol/m3.
Solids Solid density data are sparse and usually available only within
a narrow temperature range. For most solids, density decreases approximately linearly with increasing temperature. No accurate method for prediction of solid densities is available, but an approximate correlation has
been found between the density of the liquid phase at the triple point and
the solid that is stable at the triple point conditions.
Recommended Method Goodman method.
Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley,
J. Chem. Eng. Data, 49 (2004): 1512.
Classification: Empirical correlation.
Expected uncertainty: 6 percent.
Applicability: Organic compounds; applicable to the stable solid phase at
the triple point temperature Tt; applicable T range is from Tt down to either
the first solid-phase transition temperature or to approximately 0.3Tt.
Input data: Liquid density at the triple point.
Description: The density for the solid phase that is stable at the triple
point has been correlated as a function of temperature and the liquid density at Tt as
T
ρs = 1.28 − 0.16 ρL (Tt )
Tt
∑x V
C
q = 1 + (1 – 0.546)2/7 = 1.798
4.83 × 10 6 Pa
Z RA =
Pa ⋅ m 3
kmol
(545.5
K)
18.919
8.314
kmol ⋅ K
m3
c ,i
i =1
C
i c ,i
The estimated density is 16 percent above the DIPPR 801 value of 16.73 kmol/m3.
Calculate rsat from Eq. (2-72) with a known liquid density: Kratzke and Muller
[Kratzke, H., and S. Muller, J. Chem. Thermo., 17 (1985): 151] reported an experimental
density of 18.919 kmol/m3 at 298.08 K. Use of this experimental value in Eq. (2-72) to
calculate ZRA gives
Tr = (298.08 K)/(545.5 K) = 0.546
(2-74)
i =1
(2-73)
C
(2-78)
aα = ∑ x i (ai α i )1/2
i =1
Mixture calculations are then identical to the pure-component calculations
using these effective mixture parameters for the pure-component aα and b
values.
The modified Rackett method has also been extended to liquid mixtures
[Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972): 236] using
the following combining and mixing rules as modified by Li [Li, C. C., Can. J.
Chem. Eng., 19 (1971): 709]:
Tc ,ij = Tc ,iTc , j
φi =
x iVc ,i
C
∑x V
j c, j
C
C
Tc = ∑ ∑ φi φ jTc ,ij
(2-79)
i =1 j =1
j =1
Recommended Method Spencer-Danner-Li mixing rules with Rackett
equation.
References: Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972):
236; Li, C. C., Can. J. Chem. Eng., 19 (1971): 709.
Classification: Corresponding states.
Expected uncertainty: About 7 percent on average; higher near the Tc of
any of the components.
Applicability: Saturated (at the bubble point) liquid mixtures.
Input data: Tc, Vc, and xi.
Description: The predictive form of the equation is given by
C xT q
1
= V = R ∑ i c ,i Z RA
ρ
i =1 Pc ,i
q = 1.0 + (1.0 − Tr )2/7
(2-80)
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
where
C
Z RA = 0.29056 − 0.08775 ∑ x i ω i
and
Tr =
i =1
T
Tc
(2-81)
2-351
Input data: Tc, Pc, and M.
Description: The correlation for viscosity as a function of reduced
temperature is
46.1Tr0.618 - 20.4 exp( - 0.449Tr ) + 19.4 exp( − 4.058 Tr ) + 1
ηo
=
2.173424 × 1011 (Tc /K)1/6 (M /g ⋅ mol −1 )−1/2 (Pc / Pa)−2/3
Pa ⋅ s
Example Estimate the saturated liquid density of a liquid mixture of 50 mol%
ethane(1) and 50 mol% n-decane(2) at 377.6 K.
Required properties: The recommended values from the DIPPR 801 database for the
required properties are as follows:
Example Estimate the low-pressure vapor viscosity of propane at 353 K.
Required constants: The DIPPR 801 database recommends the following values:
Tc = 369.83 K
Tc/K
Vc /(m3 ⋅ kmol−1)
Pc /bar
w
Ethane
305.32
0.1455
48.72
0.0995
Decane
617.7
0.617
21.1
0.4923
(2-83)
Pc = 4.248 MPa
M = 44.0956 g/mol
Reduced temperature:
Tr = (353 K)/(369.83 K) = 0.9545
Calculation using Eq. (2-83):
Auxiliary quantities from Eq. (2-79):
φ1 =
(0.5) (0.1455)
= 0.191;
(0.5)(0.1455) + (0.5)(0.617)
(46.1) (0.9545)0.618 − 20.4 exp[ − (0.449) (0.9545)] + 19.4 exp[ − 4.058(0.9545)] + 1
ηo
=
Pa ⋅ s
(2.173424 × 1011 ) (369.83) −1/6 (44.0956) −1/2 (4.248 × 10 6 )−2/3
= 9.84 × 10 −6
φ2 = 0.809
This value is 1.5 percent higher than the DIPPR 801 recommended value of
9.70 × 10−6 Pa ⋅ s.
Tc ,12 = (305.32 K) (617.7 K) = 434.3 K
Tc
= φ12Tc ,1 + 2φ1φ2Tc ,12 + φ22Tc ,2
K
= (0.191)2 (305.32) + (2)(0.191)(0.809)(434.3) + (0.809)2 (617.7)
Recommended Method 2 Reichenberg method.
Reference: Reichenberg, D., AIChE J., 21 (1975): 181.
Classification: Group contributions and corresponding states.
Expected uncertainty: 5 percent.
Applicability: Nonpolar and polar organic and inorganic vapors.
Input data: Tc, Pc, M, m, and molecular structure.
Description: The temperature dependence of the viscosity is given by
Tc = 549.68 K
Calculations from Eqs. (2-80) and (2-81):
Tr = (377.6 K)/(549.63 K) = 0.687 q = 1 + (1 − 0.687)2/7 = 1.718
1 + 270(µ ∗r ) 4
ATr2
ηo
=
Pa ⋅ s [1 + 0.36 Tr (Tr − 1)]1/6 Tr + 270(µ ∗r ) 4
ZRA = 0.29056 − 0.08775[(0.5)(0.0995) + (0.5)(0.4923)] = 0.2646
m 3 ⋅ bar (0.5)(305.32 K) (0.5) (617.7 K)
m3
1.718
+
V = 0.08314
(0.2646) = 0.151
K ⋅ kmol 48.72 bar
21.1 bar
kmol
The experimental value [Reamer, H. H., and B. H. Sage, J. Chem. Eng.
Data, 7 (1962): 161] is 0.149 m3/kmol, and the error in the estimated value
is 1.3 percent.
where the parameter A is determined from group contributions and the
modified reduced dipole µ∗r is found from
µ∗r = 52.46mr
ηo =
AT B
1 + C /T + D /T 2
(2-82)
Over smaller temperature ranges, parameters C and D may not be necessary as ln(h) is often reasonably linear with ln(T). Care should be taken in
extrapolating using Eq. (2-82) as there can be unintended mathematical
poles where the denominator approaches zero.
Numerous methods have been developed for estimation of vapor viscosity.
For nonpolar vapors, the Yoon-Thodos CS method works well, but for polar
fluids the Reichenberg method is preferred. Both methods are illustrated
below.
Recommended Method 1 Yoon-Thodos method.
Reference: Yoon, P., and G. Thodos, AIChE J., 16 (1970): 300.
Classification: Corresponding states.
Expected uncertainty: 5 percent.
Applicability: Nonpolar and slightly polar organic vapors.
(2-85)
and Eq. (2-66).
For organic compounds, A is found from the group values Ci, listed in
Table 2-173, using
VISCOSITY
Viscosity is defined as the shear stress per unit area at any point in a
confined fluid, divided by the velocity gradient in the direction perpendicular to the direction of flow. The absolute viscosity h is the shear stress
at a point, divided by the velocity gradient at that point. The SI unit of
viscosity is Pa ⋅ s [1 kg/(m ⋅ s)], but the cgs units of poise (P) [1 g/(cm ⋅ s)]
and centipoise (cP = 0.01 P) are also frequently used (1 cP = 1 mPa ⋅ s).
The kinematic viscosity n is defined as the ratio of the absolute viscosity
to density at the same temperature and pressure. The SI unit for n is m2/s,
but again cgs units are very common and n is often given in stokes (1 St =
1 cm2/s) or centistokes (1 cSt = 0.01 cm2/s).
Gases Experimental data for gases and vapors at low density are often
correlated with
(2-84)
A = 10
M
−7 kg/kmol
1/2
(Tc /K)
(2-86)
N
∑n C
i
i
i =1
For inorganic gases, A is obtained from
M 1/2 P 2/3 T −1/6
c
c
A = 1.6104 × 10 −10
g/mol Pa K
TABLE 2-173
Group
(2-87)
Reichenberg* Group Contribution Values
Ci
Group
}CH3
9.04
}F
>CH2
6.47
}Cl
>CH}
2.67
}Br
>C<
−1.53
}OH alcohol
=CH2
7.68
>O
=CH}
5.53
>C=O
>C=
1.78
}CHO
≡CH
7.41
}COOH
≡C}
5.24
}COO} or HCOO}
>CH2 ring
6.91
}NH2
>CH} ring
1.16
>NH
>C< ring
0.23
=N} ring
=CH} ring
5.90
}CN
>C= ring
3.59
>S ring
*Reichenberg, D., AIChE J., 21 (1975): 181.
Ci
4.46
10.06
12.83
7.96
3.59
12.02
14.02
18.65
13.41
9.71
3.68
4.97
18.13
8.86
2-352
PHYSICAL AnD CHEMICAL DATA
Example Estimate the low-pressure vapor viscosity of ethyl acetate at 401.25 K.
Required constants: The DIPPR 801 database recommends the following values:
Tc = 523.3 K
M = 88.1051 g/mol
Pc = 3.88 MPa
where rc = Pc /(ZcRTc) and
m = 1.78 D
T
ξ = 2173.4 c
K
Supporting quantities:
Structural groups:
M
kg/kmol
−1/2
Pc
MPa
−2/3
(2-93)
Example Estimate the vapor viscosity of CO2 at 350 K and 20 MPa if h° = 0.0174
mPa ⋅ s and Z = 0.4983 (estimated from Lee-Kesler method, see section on density).
Required properties: From the DIPPR 801 database,
M = 44.01 kg/kmol
Group
ni
Ci
Contribution
—CH3
2
9.04
18.08
>CH2
1
6.47
6.47
—COO—
1
13.41
13.41
Total
Zc = 0.274
Auxiliary quantities:
ρc =
37.96
ρr =
From Eqs. (2-66) and (2-85):
µ∗r = 52.46
Tc = 304.21 K
Pc = 7.383 MPa
m = 0 D (nonpolar)
x = (2173.4)(304.21)1/6 (44.01)−1/2(7.383)−2/3 = 224.1
Tr = (401.25 K)/(523.3 K) = 0.767
7.383 MPa
kmol
= 10.654 3
0.274 [0.008314 m 3 MPa/(K ⋅ kmol)](304.21 K)
m
20 MPa
ρ
P
=
=
= 1.295
ρc ZRT ρc 0.4983[0.008314m 3 ⋅ MPa/(K ⋅ kmol)](350 K) (10.654 m 3 ⋅ kmol)
Calculation using Eq. (2-88) for nonpolar fluids:
(1.78)2 (38.8)
= 0.024
(523.3) 2
1/4
η− ηo
+ 1
224.1
mPa ⋅ s
From Eq. (2-86):
= 1.0230 + 0.23364(1.295) + 0.58533(1.295) 2
− 0.40758(1.295) 3 + 0.093324(1.295) 4 = 1.684
(88.1051)1/2 (523.3)
A = 10
= 1.294 × 10 −5
37.96
−7
η=
Calculation using Eq. (2-84):
1.684 4 − 1
mPa ⋅ s + 0.0174 mPa ⋅ s = 0.0489 mPa ⋅ s
224.1
This differs from the experimental value of 0.0473 mPa ⋅ s by 3.4 percent.
(1.294 × 10 −5 ) (0.767) 2
1 + (270) (0.024) 4
ηo
=
= 1.003 × 10 −5
1/6
Pa ⋅ s [1 + (0.36) (0.767) (0.767 − 1)] 0.767 + (270) (0.024) 4
The estimated value is 1.5 percent lower than the DIPPR 801 recommended value of
1.018 × 10−5 Pa ⋅ s.
The dependence of viscosity upon pressure is principally a density effect. Estimation of vapor viscosity at elevated pressures is commonly done by correlating density
deviations from the low-pressure values estimated. Several methods are available, but
the method developed by Jossi et al. and extended to polar fluids by Stiel and Thodos is
relatively accurate and easy to apply.
Recommended Method Jossi-Stiel-Thodos method.
References: Stiel, L. I., and G. Thodos, AIChE J., 10 (1964): 26; Jossi, J. A., L. I.
Stiel, and G. Thodos, AIChE J., 8 (1962): 59.
Classification: Empirical correlation and corresponding states.
Expected uncertainty: 9 percent—often less for nonpolar gases, larger for
polar gases.
Applicability: Nonassociating gases; rr < 2.6.
Input data: M, Tc, Pc, Zc, m, ho (low-pressure viscosity at same T may be
estimated by using methods given above), and r (may be calculated from T
and P by using density methods given above).
Description: Deviation of h from the low-pressure value ho is given by one
of the following correlations depending upon its polarity and reduced density range:
For nonpolar gases, 0.1 < rr < 3.0:
η− ηo
ξ + 1
mPa ⋅ s
1/6
1/4
= 1.0230 + 0.23364 ρr + 0.58533ρr2 − 0.40758ρ3r + 0.093324 ρr4
(2-88)
Liquids Liquid viscosity can be correlated as a function of temperature
for low pressures. Usually the correlation is based on the Andrade equation
[Andrade, E. N. da C., Nature, 125 (1930): 309]
ln ( η) = A +
(2-94)
or an extension of it. For example, the DIPPR 801 database uses the equation
ln ( η) = A +
B
+ C ln T + DT E
T
(2-95)
which is analogous to the Riedel [Riedel, L., Chem. Ing. Tech., 26 (1954): 83]
vapor pressure equation.
Currently the most accurate method for predicting pure liquid viscosity
is the GC method by Hsu et al. It has been found that most liquids have a
viscosity between 0.15 mPa ⋅ s (or cP) and 0.55 mPa ⋅ s at the normal boiling
point, and this “rule” can be used as a valuable criterion to validate estimated viscosities as a function of temperature.
Recommended Method Hsu method.
Reference: Hsu, H.-C., Y.-W. Sheu, and C.-H. Tu, Chem. Eng. J., 88 (2002): 27.
Classification: Group contributions.
Expected uncertainty: 20 percent.
Applicability: Organic liquids; Tr < 0.75.
Input data: Pc and molecular structure.
Description: The temperature dependence of the liquid viscosity is given by
N
∑ ci N
N
P
η N
ln
= ∑ ai + T ∑ bi + i =1 2 + ∑ di ln c
mPa ⋅ s i =1
T
i =1 bar
i =1
For polar gases, rr ≤ 0.1:
η− η
1.111
mPa ⋅ s ξ = 1.656ρr
B
T
o
(2-89)
(2-96)
where Pc is critical pressure and ai, bi, ci, and di are the group contributions
obtained from Table 2-174.
For polar gases, 0.1 < rr ≤ 0.9:
η− ηo
1.739
mPa ⋅ s ξ = 0.0607 (9.045ρr + 0.63)
(2-90)
Example Estimate the liquid viscosity of benzotrifluoride at 303.15 K.
Structural information:
For polar gases, 0.9 < rr ≤ 2.2:
η− ηo
log 4 − log
ξ = 0.6439 − 0.1005ρr
mPa ⋅ s
(2-91)
For polar gases, 2.2 < rr ≤ 2.6:
η− ηo
3
2
log 4 − log
ξ = 0.6439 − 0.1005ρr − 0.000475(ρr − 10.65)
mPa ⋅ s
(2-92)
Group
>C<
(=CH})A
(=C<)A
(—F)3
Number
1
5
1
1
a
1.0031
−0.8570
0.7896
1.5394
Total −0.9529
100b
0.0001c
d
−0.3677
−0.0098
−0.0231
0.8465
0.4067
−6.0316
2.4376
−0.9222
17.8121
23.0463
1.1972
0.1311
0.1928
−2.9915
−0.9460
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-174
Group Contributions for the Hsu et al. Method*
Table-specific nomenclature: R = in nonaromatic ring, A = in aromatic ring, RC = attached to nonaromatic ring, AC = attached
to aromatic ring, X = halogen, (−X)n = n X atoms attached to same C atom
Group
a
100b
0.0001c
d
−1.0563
−0.2382
0.0060
0.4028
−0.3677
−0.2656
0.1612
0.4305
−0.1106
−0.0111
−0.1778
0.7637
−0.0120
1.7694
−0.0098
−0.0231
0.0444
0.0683
1.2165
−0.8665
0.8928
0.7556
1.4157
4.5094
−6.0316
0.9860
1.9408
3.1287
4.4245
0.3265
0.8437
7.2433
2.0143
19.0452
2.4376
−0.9222
8.1690
8.8426
34.2857
−14.7474
−0.0019
−0.1765
0.0751
0.6679
1.1972
−0.4417
0.2507
1.0465
−24.1836
25.0542
−1.5184
8.5951
−0.3677
13.3885
0.1311
0.1928
−0.4351
−0.1685
−11.6500
−2.7574
−0.5310
−1.0010
−0.3645
2.4275
0.8509
−0.3634
0.6362
−0.4377
0.0985
−0.2847
0.0872
−0.2612
0.1142
−0.2405
0.0413
−0.1841
−0.1693
−0.0113
−0.2162
0.0006
1.5834
0.0111
0.2848
1.0614
0.1801
0.1322
0.0427
0.0779
−0.0965
−0.3285
1.2621
0.5248
−1.2592
0.6232
9.5499
13.8366
29.8404
78.5417
77.1759
23.2329
50.0840
17.2243
2.9405
−4.3145
6.4296
3.7241
6.7008
3.8828
27.4079
12.6878
20.0309
9.4694
1.9325
5.4231
34.5474
7.2831
9.3746
49.1049
12.9392
15.8672
12.1837
4.4123
6.0066
1.9387
23.1473
14.2694
−23.9353
27.5184
−1.0300
0.3418
0.4246
0.9650
−6.9285
−0.0172
−1.0539
0.7139
0.1149
8.3131
0.5389
0.2386
0.7348
−12.4994
0.0002
1.1139
0.0279
0.6071
0.4686
0.8717
−0.4244
3.6587
2.1486
2.8583
2.8987
−0.0701
−0.0948
0.9549
0.3464
0.1148
1.3950
3.7646
0.8329
7.7525
−0.2126
−0.1723
0.4842
−0.0180
0.2208
0.5975
−0.2774
0.0432
26.4615
0.1316
1.5664
−4.5188
0.6712
0.1910
7.0544
5.7804
6.1893
23.2752
14.9707
14.0415
31.8007
20.9135
394.1670
45.5193
60.8742
−62.0987
37.9465
12.0578
0.1336
1.6467
0.4718
1.0653
0.1171
−0.0031
0.0001
1.8795
0.3530
1.2172
−4.6399
1.2353
1.9199
−0.0276
C, H Groups
CH4
}CH3
}CH2}
>CH}
>C<
=CH2
=CH}
=C<
≡CH
≡C}
(}CH2})R
(>CH})R
(=CH})R cycloalkene
(>C<)R spirocyclane
(=CH})A
(=C<)A cycloalkene
(=C<)A bi/terphenyl
(=C<)A naphthalene
(=C<)A turpentine
(=C<)A tetralin
−1.7296
0.0570
−0.1497
−2.2942
1.0031
0.9256
1.3365
−3.5020
87.6040
−91.6154
6.0416
−33.8745
1.2028
−56.2158
−0.8570
0.7896
2.0973
0.4392
27.3350
14.2586
}OH primary for C<3
}OH primary for C>2
}OH secondary
}OH tertiary
(}OH)RC
}OH polyhydric
(}OH)AC
}OH alkoxyalcohol
}O}
(}O})R
(}O})AC
}CHO
>CO
(>CO)R
HCOOH
}COOH for C<7
}COOH for C>6
HCOO}
}COO} for C<8
}COO} for C>7
>CHO}
}(CO)}O}(CO)} anhydride
}O}(CO)}O} carbonate
(>NO)R
}NO2
=CHNO2
(}NO2)AC
}S}
}SH primary
}SH secondary
}SH tertiary
}CSO} for C<13
}CSO} for C>12
>SO
5.7852
1.4351
−2.6895
−18.5630
16.7808
−0.0125
−2.0856
−2.6991
−0.7185
−29.8045
−2.3454
−0.8288
−2.6622
45.9143
−2.7291
−4.0451
−0.6721
−3.3731
−0.0635
−2.5390
−5.4872
−11.8236
−8.0314
−16.9531
−13.0333
−1.9653
−1.2954
−3.2767
−2.1030
−0.2481
−12.3498
−15.2678
3.7475
−32.8607
O, S Groups
N, X Groups
}NH2
}NH}
}N<
(}NH2)AC
(}NH})AC
(}N<)AC
HCONH2
HCONH}
HCON<
}CONH2
}CONH}
}COONH2
}COONH}
(>NH)R
−1.1345
−6.9489
−2.1403
−6.3646
−1.7592
−1.2982
−1.5435
−8.1097
−122.3280
−6.7363
8.9977
17.8400
−10.1316
−0.1589
(Continued )
2-353
2-354
PHYSICAL AnD CHEMICAL DATA
TABLE 2-174
Group Contributions for the Hsu et al. Method* (Continued )
Table-specific nomenclature: R = in nonaromatic ring, A = in aromatic ring, RC = attached to nonaromatic ring, AC = attached
to aromatic ring, X = halogen, (−X)n = n X atoms attached to same C atom
Group
a
100b
0.0001c
d
0.1120
−0.1324
−0.0086
−0.3851
−0.1934
−1.0770
−0.3220
−0.4130
−0.0623
0.2607
−1.1189
0.8465
−0.2352
−0.3682
−0.5629
0.0109
0.1403
−0.6623
−0.3420
−0.1635
−0.2787
−0.0245
−0.0470
6.98437
7.7955
8.6310
3.0118
3.7798
0.1882
8.8683
13.3194
4.1382
11.3406
1.3134
17.8121
−0.1505
4.6451
3.6831
5.9474
10.3743
−2.4228
1.4253
3.0150
4.3362
7.2061
8.2815
0.9719
0.6293
−0.6443
0.5524
−0.4748
1.2223
0.1702
−1.1972
−0.2644
1.8461
2.6681
−2.9915
−0.2893
−0.0751
0.3613
−14.5771
−1.1972
0.7385
73.6293
0.0621
0.5635
−18.9106
0.4485
N, X Groups
(=N})R
}C≡N
(}C≡N)AC
}Cl primary
=CHCl
(}Cl)2
(}Cl)3
(}Cl)4
(}Cl)AC
}F primary
(}F)2
(}F)3
(}F)AC
(}F)(}Cl)
(}F)(}Cl)2
(}F)2(}Cl)
(}F)2(}Cl)2
}Br primary
}Br secondary
(}Br)AC
}I primary
(}I)AC
}(CO)}Cl
−4.7601
−2.7194
0.9435
−1.7997
1.5851
−3.0561
−1.3357
4.2070
−0.3083
−9.4982
−10.3980
1.5394
0.4079
−0.8565
−3.4552
54.2824
−2.1710
−0.7586
−279.0030
−8.1919
−1.4672
70.9918
−2.3300
*Hsu, H.-C., Y.-W. Sheu, and C.-H. Tu, Chem. Eng. J., 88 (2002): 27
Supporting values:
Pc = 32.1 MPa
Calculation using Eq. (2-96):
η
230,463
= exp −0.9529 + (0.004067)(303.15) +
− 0.9460 ln(32.1) = 0.610
mPa ⋅ s
(303.15) 2
The estimated value is 20 percent higher than the DIPPR 801 value of 0.509 mPa ⋅ s.
Note that when the calculation is repeated at the normal boiling point (375.2 K), one
obtains 0.343 mPa ⋅ s which is within the range of the aforementioned empirical rule.
Liquid Mixtures Most methods for estimating liquid mixture viscosity
interpolate between the pure-component values at the same temperature.
The Grunberg-Nissan equation [Grunberg, L., and A. H. Nissan, Nature, 164
(1949): 799]
C
ln η = ∑ x i ln ηi +
i
C
viscosity of organic mixtures without any mixture data. It can estimate mixture viscosity to a limited accuracy, but it is limited in scope by the small
number of group contributions currently available.
Recommended Method UNIFAC-VISCO method.
Reference: Chevalier, J. L., P. Petrino, and Y. Gaston-Bonhomme, Chem.
Eng. Sci., 43 (1988): 1303; Gaston-Bonhomme, Y., P. Petrino, and J. L. Chevalier, Chem. Eng. Sci., 49 (1994): 1799.
Classification: Group contributions.
Expected uncertainty: 20 percent.
Applicability: Organic liquids.
Input data: Molecular structure; pure-component molar volumes and
viscosities at the mixture temperature.
Description: Liquid mixture viscosity can be estimated in a manner similar to the UNIFAC method employed for mixture excess Gibbs energy and
activity coefficients. The primary equation is
ηi
V gE gE
η C
⋅ i + c − r
ln
= x i ln
mPa ⋅ s ∑
mPa ⋅ s Vm RT RT
i =1
C
1
∑ ∑ x i x j Gij
2 i =1 j =1
(2-97)
is commonly used for nonaqueous mixtures. The parameter Gij generally
must be regressed from an experimental mixture viscosity. However, Gij can
be set to zero for hydrocarbon mixtures with expected errors in the mixture
viscosity of about 15 percent.
Estimation of liquid mixture viscosity without any mixture data is
difficult because the viscosity is strongly affected by large molecular size differences and strong cross-interactions between different types of molecules.
The UNIFAC-VISCO method described below can be used to predict liquid
(2-98)
where Vm is the mixture molar volume and Vi is the pure-component molar
volume of component i. The combinatorial and residual excess Gibbs
energies are calculated as in the standard UNIFAC method for activity
coefficients (see [PGL5]) and for brevity is not shown here. However, the
group interactions ymn are calculated using the interaction parameters αmn
obtained from Table 2-175 in the equation
α
ψ mn = exp − mn
298.15
TABLE 2-175 UnIFAC-VISCO* Group Interaction Parameters `mn
m/n
CH2
CH3
CH2cy
CHar
Cl
CO
COO
OH
CH3OH
CH2
CH3
CH2cy
CHar
Cl
CO
COO
OH
CH3OH
0
−709.5
−538.1
−623.7
−710.3
586.2
541.6
−634.5
−526.1
66.53
0
187.3
237.2
375.3
−21.56
−44.25
1209.0
653.1
224.9
−130.7
0
50.89
−163.3
740.6
416.2
−138
751.3
406.7
−119.5
8.958
0
−139.8
−117.9
−36.17
197.7
51.31
60.30
82.41
251.4
177.2
0
−4.145
240.5
195.7
−140.9
859.5
11.86
−125.4
128.4
−404.3
0
22.92
664.1
−22.59
1172.0
−172.4
−165.7
−49.85
−525.4
29.20
0
68.35
−286.2
498.6
594.4
694.4
419.3
960.2
221.5
186.8
0
−23.91
−219.7
−228.7
−381.53
−88.81
−165.4
55.52
69.62
416.4
0
*Chevalier, J. L., P. Petrino, and Y. Gaston-Bonhomme, Chem. Eng. Sci., 43 (1988): 1303; Gaston-Bonhomme, Y., P.
Petrino, and J. L. Chevalier, Chem. Eng. Sci., 49 (1994): 1799.
(2-99)
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
Example Estimate the viscosity of a mixture of 51.13 mol% ethanol(1) and
48.87 mol% benzene(2) at 298.15 K.
Required input: Values from the DIPPR 801 database for the pure components
at 298.15 K are h1 = 1.0774 mPa ⋅ s, h2 = 0.5997 mPa ⋅ s, V1 = 0.05862 m3/kmol, and
V2 = 0.08948 m3/kmol.
Groups, area fractions, and volume fractions:
Group
R
Q
N1
N2
CH3
0.9011
0.8480
1
0
CH2
0.6744
0.5400
1
0
CHar
0.5313
0.4000
0
6
OH
1.0000
1.2000
1
0
r2
q2
Group
r1
q1
CH3
0.9011
0.848
0
0
CH2
0.6744
0.54
0
0
CHar
0
0
3.1878
2.4
OH
1
1.2
0
0
2.588
3.1878
2.4
Total 2.5755
2-355
Group fractions in pure components:
Ethanol
Group
N
X
XQ
Q
lng
CH3
CH2
CHar
OH
1
1
0
1
0.3333
0.3333
0.0000
0.3333
0.283
0.180
0.000
0.400
0.3277
0.2087
0.0000
0.4637
0.5306
−0.9405
0.2095
0.6179
Sum 3
0.863
Benzene
Group
CH3
CH2
CHar
OH
N
X
XQ
Q
lng
0
0
6
0
0
0
1
0
0
0
0.4
0
0
0
1
0
0.257
−0.728
0.000
2.270
Sum 6
0.4
The pure-component Q and ln g equations are the same as shown above for the
mixture groups.
UNIFAC residual term:
where in the above table
N
qi = ∑ N i ,k Qk
and
k =1
θ1 =
4
∑x q
i
ri = ∑ N i ,k Rk
k =1
(0.5113) (2.588)
=
= 0.53
(0.5113) (2.588) + (0.4887) (2.4)
x 1 q1
2
g rE
4
= ∑ x i ∑ N m ,i (ln γ m − ln γ m ,i ) = 0.3425
RT i =1 m=1
N
where Nm and ln gm refer to the mixture and Nm,i and ln gm,i refer to the pure-component
values.
Mixture volume:
θ2 = 0.47
i
2
m3
m3
Vm = ∑ x iVi = 0.5113 0.05862
+ 0.4887 0.08948
kmol
kmol
i =1
i =1
φ1 =
x 1 r1
4
∑x r
(0.5113)(2.5755)
=
= 0.458
(0.5113)(2.5755) + (0.4887)(3.1878)
φ2 = 0.542
= 0.07370
i i
i =1
Using Eq. (2-98):
UNIFAC combinatorial term:
2
2
E
C
m3
kmol
η
0.05862
= 0.5113 ln 1.0774
ln
0.07370
mPa ⋅ s
g
φ
θ
= ∑ x i ln i + 5∑ x i qi ln i = 0.124
RT i =1
xi
φi
i =1
0.08948
+ 0.124 − 0.3425 = −0.4523
+ 0.4887 ln 0.5997
0.07370
Group interactions:
h = exp(−0.4523) mPa ⋅ s = 0.636 mPa ⋅ s
αmn
m/n group
CH3
CH2
CHar
OH
CH3
CH2
CHar
OH
0
66.53
237.2
1209
−709.5
0
−623.7
−634.5
−119.5
406.7
0
197.7
594.4
498.6
419.3
0
ymn
m/n group
CH3
CH2
CHar
OH
CH3
CH2
CHar
OH
1.000
0.800
0.451
0.017
10.801
1.000
8.100
8.399
1.493
0.256
1.000
0.515
0.136
0.188
0.245
1.000
The αmn values were obtained from Table 2-175, and ymn values were calculated from
Eq. (2-99).
Group fractions in the mixture:
Group
N
X
XQ
Q
ln g
CH3
0.5113
0.1145
0.097083
0.17370
0.293
CH2
0.5113
0.1145
0.061822
0.11061
−0.873
CHar
2.9322
0.6565
0.262618
0.46988
0.066
OH
0.5113
0.1145
0.137382
0.24581
1.077
Sum 4.4661
0.558905
The estimated value is 6.6 percent below the reported experimental value of
0.681 mPa ⋅ s [Kouris, S., and C. Panayiotou, J. Chem. Eng. Data, 34 (1989): 200].
THERMAL COnDUCTIVITY
Thermal conductivity, k, is a measure of the rate at which heat conducts
through the material and is defined as the proportionality constant in Fourier’s law of heat conduction that relates the gradient of temperature to
the heat flux or flow per unit area. In SI, it has the units of W/(m ⋅ K). The
conduction mechanism in gases is primarily via molecular collisions, and k
increases with increasing temperature (increasing molecular velocity). The
temperature dependence of low-pressure, gas-phase thermal conductivity is
adequately correlated with
k=
AT B
C
1+
T
In dense media such as liquids, energy transfers more efficiently through the
intermolecular force fields than through collisions. As a result, liquid thermal conductivity generally decreases with increasing temperature (except
for water, aqueous solutions, and a few multihydroxy and multiamine compounds), corresponding to the decrease in density with increased temperature. The temperature dependence of liquid thermal conductivity at low to
moderate pressures has been found to be well correlated by [Jamieson, D. T.,
J. Chem. Eng. Data 24 (1979): 244]
k = A (1 + Bτ1/3 + C τ 2/3 + Dτ)
Here Θ m =
X mQm
4
∑X Q
i
i =1
i
4
4
Θψ
and ln γ m = Qm 1 − ln ∑ Θi ψ i ,m − ∑ 4 i m ,i
1
i
1
i
=
=
∑ Θ j ψ j ,i
i =1
(2-100)
(2-101)
where t = 1 – T/TC. For nonassociating liquids, this equation can be simplified to two parameters by setting C = 1 − 3B and D = 3B, generally without much loss in accuracy. Below or near the normal boiling point, the
2-356
PHYSICAL AnD CHEMICAL DATA
temperature dependence of liquid thermal conductivity is nearly linear for
modest temperature ranges and can be represented by
(2-102)
k = A − BT
where B is generally in the range of 1 × 10−4 to 3 × 10−4 W/(m ⋅ K2).
Gases Methods for estimating low-pressure gas thermal conductivities
are based on kinetic theory and generally correlate the dimensionless group
kM/hCu (M = molecular weight, h = viscosity, Cu = isochoric heat capacity),
known as the Eucken factor. The method of Stiel and Thodos is recommended
for pure nonpolar compounds, and the method of Chung is recommended for
pure polar compounds.
Recommended Method Stiel-Thodos method.
Reference: Stiel, L. I., and G. Thodos, AIChE J., 10 (1964): 26.
Classification: Empirical extension of theory.
Expected uncertainty: 15 percent.
Applicability: Pure nonpolar gases at low pressure.
Input data: M, Tc, h, and Cu.
Description: The following equations may be used depending upon the
molecular shape:
kM
= 2.5
ηC υ
monatomic
R
0.3523
kM
= 1.30 + 1.7614 −
Tr
ηC υ
Cυ
R
kM
= 1.15 + 2.033
ηC υ
Cυ
linear molecules
nonlinear molecules
(2-103)
(2-104)
(2-105)
where h = viscosity at same conditions as desired for k. Because this method
is only applicable at low pressures, Cu may usually be calculated as C op − R,
where C op is the ideal gas isobaric heat capacity.
Example Estimate the low-pressure thermal conductivity of toluene vapor at
500 K.
Required properties from the DIPPR 801 database:
M = 92.138 g/mol
h(500 K) = 1.1408 × 10−5 Pa ⋅ s
Tc = 591.75 K
Cu = Cpo − R = (170.78 − 8.314) J/(mol ⋅ K) = 162.47 J/(mol ⋅ K)
Auxiliary quantities:
Example Estimate the low-pressure thermal conductivity of naphthalene vapor
at 500 K.
Required properties from the DIPPR 801 database:
M = 128.17 g/mol
Tc = 748.4 K
h(500 K) = 1.0173 × 10−5 Pa ⋅ s
w = 0.30203
Cu = Cpo − R = (219.82 − 8.314) J/(mol ⋅ K) = 211.51 J/(mol ⋅ K)
Auxiliary quantities [Eqs. (2-107) and (2-108)]:
Tr = 500/748.4 = 0.6681
R/Cu = (8.314)/(211.51) = 0.0393
g = 2.0 + (10.5)(0.6681)2 = 6.6866
α = (0.0393)−1 − 1.5 = 23.9388
b = 0.7862 − (0.7109)(0.30203) + (1.3168)(0.30203)2 = 0.6916
0.215 + 0.28288 (23.9388) − 1.061(0.6916) + 0.26665(6.6866)
Ψ = 1 + (23.9388)
0.6366 + 0.6916 (6.6866) + 1.061(23.9388) (0.6916)
= 9.4273
From Eq. (2-106):
J
−5
(1.1408 × 10 Pa ⋅ s) 8.314 mol ⋅ K
mW
k = (3.75) (9.4273)
= 23.33
g
m⋅K
128.17
mol
The estimated value is 1.0 percent above the DIPPR 801 value of 23.09 mW/(m⋅K).
Liquids For hydrocarbons at low to moderate pressures, a modification of the Pachaiyappan method should be used. For nonhydrocarbons, the
Baroncini method provides accurate liquid thermal conductivity estimates
for compounds clearly belonging to one of the chemical families specified
below. Otherwise, the Missenard method is recommended as a general
method for estimating thermal conductivity of pure liquids at ambient
pressure.
Recommended Method Modified Pachaiyappan.
Reference: Pachaiyappan, V., S. H. Ibrahim, and N. R. Kuloor, Chem. Eng.
74(4) (1967): 140; API Technical Databook, 10th ed., chap. 12, 2017.
Classification: Empirical correlation.
Expected uncertainty: 10 percent.
Applicability: Hydrocarbons only; low to moderate pressures.
Input data: M, Tb, and Tc.
Description:
m
M
C
g ⋅ mol −1
k
=
−1 −1
V293
W ⋅m K
cm3 ⋅ mol −1
Tr = 500/591.75 = 0.845 R/Cu = (8.314)/(162.47) = 0.0512
From Eq. (2-105):
J
−5
(1.1408 × 10 Pa ⋅ s) 162.47 mol ⋅ K
mW
k = [1.15 + (2.033) (0.0512)]
= 25.2
g
m⋅K
92.138
mol
3 + 20(1 − Tr )2/3
2/3
3 + 20(1 − Tr ,293 )
where M is molecular weight, V293 is the molar volume at 293.15 K, Tr is the
reduced temperature, Tr,293 = (293.15 K)/(Tc) and the correlation parameters
C and m are obtained from the table below:
Classification
The estimated value is 18 percent below the DIPPR 801 value of 30.76 mW/(m ⋅ K).
Recommended Method Chung-Lee-Starling method.
Reference: Chung, T.-H., L. L. Lee, and K. E. Starling, Ind. Eng. Chem.
Fundam., 23 (1984): 8.
Classification: Corresponding states.
Expected uncertainty: 15 percent.
Applicability: Pure organic gases at low pressure.
Input data: Cv, w, Tc, M, and h.
Description: The following equations apply:
C
m
Unbranched, straight-chain hydrocarbon
0.1811
1.001
All branched, cyclic and aromatic hydrocarbons
0.4407
0.7717
Example Estimate the thermal conductivity of liquid n-butylbenzene at low
pressure and 333.15 K.
Required properties from DIPPR 801 database:
M = 134.218 g/mol
Tc = 660.5 K
(2-106)
V293 = 162.01 cm3/mol
Auxiliary properties:
Tr = (333.15 K)/(660.5 K) = 0.5044
R
kM
= 3.75 Ψ
ηC υ
Cυ
(2-109)
Tr,293 = (293.15 K)/(660.5 K) = 0.4438
Since this is an aromatic hydrocarbon,
C = 0.4407 and m = 0.7717 ( from the above table)
From Eq. (2-109):
0.215 + 0.28288α − 1.061β + 0.26665 γ
Ψ = 1+ α
0.6366 + βγ + 1.061αβ
C
α = υ − 1.5
β = 0.7862 − 0.7109ω + 1.3168ω 2
R
(2-107)
γ = 2.0 + 10.5 Tr2
(2-108)
k
(0.4407) (134.218 )
=
(W ⋅ m -1 K -1 )
162.01
0.7717
3 + 20(1 − 0.5044)2/3
3 + 20(1 − 0.4438)2/3 = 0.112
The estimated value is 5 percent below the experimental value of
0.118 W/(m ∙ K) reported by Rastorguev and Pugach [Rastorguev, Yu. L., and
V. V. Pugach, Izv. Vyssh. Uchebn. Zaved., Neft Gaz, 13 (1970): 69].
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
Recommended Method 1 Baroncini method.
Reference: Baroncini, C., F. DiFilippo, G. Latini, and M. Pacetti, Int. J.
Thermophys., 2 (1981): 21.
Classification: Empirical correlation.
Expected uncertainty: 10 percent.
Applicability: Particularly accurate for the following families: acetates,
aliphatic ethers, halogenated compounds, dicarboxylic acids, ketones, aliphatic alcohols, aliphatic acids, propionates and butyrates, and unsaturated
aliphatic esters.
Input data: M, Tb, and Tc.
Description:
−β
α
−γ
k
T M Tc (1 − Tr )0.38
= A b
W/(m ⋅ K)
K g/mol
K
Tr1/6
(2-110)
Required properties from DIPPR 801 database:
Tb = 475.133 K
Tr = T/Tc = (400 K)/(704.65 K) = 0.5677
From Table 2-176 for alcohols:
α = 1.2
β=
1
2
γ = 0.167
From Eq. (2-110):
k
(1 − 0.5677) 0.38
= (0.00339)(475.13)1.2 (108.1378) − 1/2 (704.65) −0.167
= 0.142
W/(m ⋅ K)
0.56771/6
The estimated value is 7.6 percent higher than the DIPPR 801 value of 0.132 W/(m ⋅ K).
Recommended Method 2 Missenard method.
Reference: Missenard, A., Comptes Rendus, 260 (1965): 5521.
Classification: Corresponding states.
Expected uncertainty: 20 percent.
Applicability: Organic compounds; nonassociating.
Input data: Tc, nA (number of atoms in molecule), r273 (liquid density at
273.15 K), Tb, M, Cp,273 (liquid heat capacity at 273.15 K).
Description:
8.4 T 1/2 ρ
k273
= 1/4 b 273 3
mW/(m ⋅ K) N A K g/m
k=
1/2
M
g/mol
−1/2
nA = 18
Tb = 412.27 K
M = 106.165 kg/kmol
Cp,273 = 200.64 kJ/(kmol ⋅ K)
Auxiliary properties:
Tr = 350/617 = 0.5673
Tr,273 = 273/617 = 0.4425
Tbr = 412.27/617 = 0.6682
From Eq. (2-111):
k273
= (8.4)(412.27)1/2 (0.007681)1/2 (106.165) −1/2 (200.64)(18) −0.25 = 141.3
mW/(m ⋅ K)
The estimated value is 4.5 percent above the DIPPR 801 value of 118.0 mW/(m⋅K).
Auxiliary properties:
A = 0.00339
ρ273 = 7.6812 kmol/m3
Tc = 617 K
141.3 mW [3 + 20(1 − 0.5673)2/3 ]
k273 [3 + 20(1 − Tr )2/3 ]
mW
m⋅K
k=
= 123.3
=
3 + 20(1 − Tr ,273 )2/3
3 + 20(1 − 0.4425)2/3
m⋅K
Example Estimate the thermal conductivity of liquid p-cresol at 400 K.
Tc = 704.65 K
Example Estimate the thermal conductivity of m-xylene at 350 K.
Required properties from DIPPR 801 database:
From Eq. (2-112):
where A, α, β, and γ are obtained from Table 2-176.
M = 108.1378 g/mol
2-357
C p ,273
J/(mol ⋅ K)
(2-111)
k273 [3 + 20(1 − Tr )2/3 ]
3 + 20(1 − Tr ,273 )2/3
(2-112)
where Tr,273 = (273 K)/Tc.
Liquid Mixtures The thermal conductivity of liquid mixtures generally shows a modest negative deviation from a linear mass-fraction average
of the pure-component values. Although more complex methods with some
improved accuracy are available, two simple methods are recommended
here that require very little additional information. The first method
applies only to binary mixtures while the second can be used for multiple
components.
Recommended Method Filippov correlation.
References: Filippov, L. P., Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk,
10 (1955): 67; Filippov, L. P., and N. S. Novoselova, Sugden, Vest. Mosk. Univ.,
Ser. Fiz. Mat. Estestv. Nauk, 10 (1955): 37.
Classification: Empirical correlation.
Expected uncertainty: 4 to 8 percent.
Applicability: Binary liquid mixtures.
Input data: Pure-component thermal conductivities ki at mixture conditions; wi.
Description: The mixture thermal conductivity is calculated from the
pure-component values using
k = w1 k1 + w2 k2 − 0.72w1w2 k2 − k1
(2-113)
where wi is the mass fraction of pure fluid i and ki is the thermal conductivity
of pure component i at the mixture temperature.
Recommended Method Li correlation.
References: Li, C. C., AIChE J., 22 (1976): 927.
Classification: Empirical correlation.
Expected uncertainty: 4 to 8 percent.
Applicability: Liquid mixtures.
Input data: Pure-component thermal conductivities ki at mixture conditions; rL,i
Description: The mixture thermal conductivity is correlated as a function
of the mixture volume fractions fi:
C
C
2 ki k j
j =1
ki + k j
k = ∑ ∑ φi φ j
i =1
(2-114)
TABLE 2-176 Correlation Parameters for Baroncini et al. Method*
for Estimation of Thermal Conductivity
Family
A
a
Saturated hydrocarbons
0.00350
1.2
Olefins
0.0361
1.2
Cycloparaffins
0.0310
1.2
Aromatics
0.0346
1.2
Alcohols
0.00339
1.2
Organic acids
0.00319
1.2
Ketones
0.00383
1.2
Esters
0.0415
1.2
Ethers
0.0385
1.2
Refrigerants
R20, R21, R22, R23
0.562
0
Others
0.494
0
*Baroncini, C., et al., Int. J. Thermophys., 2 (1981): 21.
b
g
0.5
1
1
1
0.5
0.5
0.5
1
1
0.167
0.167
0.167
0.167
0.167
0.167
0.167
0.167
0.167
0.5
0.5
−0.167
−0.167
where φi =
x i ρ−L1,i
C
∑x
j
ρ−L1, j
j =1
Example Estimate the thermal conductivity of a mixture containing 30.2 mol%
diethyl ether(1) and 69.8 mol% methanol(2) at 273.15 K and 0.1 MPa, using the Filippov
and Li correlations.
Auxiliary data: The pure-component thermal conductivities and molar densities at
273.15 K recommended in the DIPPR 801 database are
k1 = 0.1383 W/(m ⋅ K) r1 = 9.9335 kmol/m3 M1 = 74.1216 kg/kmol
k2 = 0.2069 W/(m ⋅ K) r2 = 25.371 kmol/m3 M2 = 32.0419 kg/kmol
The mass fractions corresponding to the mole fractions given above are
w1 = 0.5
w2 = 0.5
2-358
PHYSICAL AnD CHEMICAL DATA
The volume fractions are
Example Estimate the surface tension of ethylacetylene at 237.45 K.
Structure:
-1
φ1 =
(0.302)(9.9335)
= 0.525
(0.302)(9.9335) -1 + (0.698)(25.371) -1
φ2 = 0.475
Calculation using Eq. (2-113):
k = [(0.5)(0.1383) + (0.5)(0.2069) − (0.72)(0.5)(0.5) 0.2069 − 0.1383 ]
W
m⋅K
= 0.160 W/(m ⋅ K)
Group
ni
DPi
ni DPi
≡CH
≡C—
>CH2 (n = 1–11)
CH3
1
1
1
1
43.64
28.64
39.92
55.25
43.64
28.64
39.92
55.25
Total 167.45
Calculation using Eq. (2-114):
(0.525) (0.475) (2) (0.1383) (0.2069)
W
k = (0.525)2 (0.1383) + 2 ⋅
+ (0.475)2 (0.2069)
0.1383 + 0.2069
m⋅K
= 0.167 W/(m ⋅ K)
The Filippov value is 7.5 percent lower than the experimental value of 0.173 W/(m ⋅ K)
[Jamieson, D. T., and B. K. Hastings, Thermal Conductivity, Proceedings of the Eighth
Conference, C. Y. Ho and R. E. Taylor, eds., Plenum Press, New York, 1969]; the Li value is
3.5 percent lower than the experimental value.
SURFACE TEnSIOn
The surface at a vapor-liquid interface is in tension due to the difference
in attractive forces experienced by molecules at the interface between the
dense liquid phase and the low-density gas phase. This causes the liquid to
contract to minimize the surface area. Surface tension is defined as the force
in the surface plane per unit length. Jasper [Jasper, J. J., J. Phys. Chem. Ref.
Data, 1 (1972): 841] has made a critical evaluation of experimental surface
tension data for approximately 2200 pure chemicals and correlated surface
tension s (mN/m = dyn/cm) with temperature as
4
13.2573 mN
N
= 0.02429
σ = (167.45)
1000 m
m
The estimated value is 0.9 percent above the DIPPR 801 recommended value of
0.02407 N/m.
Recommended Method 2 Brock-Bird method.
Reference: Brock, J. R., and R. B. Bird, AIChE J., 1 (1955): 174; Miller, D. G.,
Ind. Eng. Chem. Fundam., 2 (1963): 78.
Classification: Corresponding states.
Expected uncertainty: 5 percent.
Applicability: Nonpolar and moderately polar organic compounds.
Input data: Tc, Pc, and Tb.
Description:
σ
P
= (5.553 × 10 −5 ) c
Pa
mN/m
Jasper’s evaluation also includes values of A and B for most of the tabulated
chemicals. Surface tension decreases with increasing temperature and
increasing pressure.
Pure Liquids An approach suggested by Macleod [Macleod, D. B.,
Trans. Faraday Soc., 19 (1923): 38] and modified by Sugden [Sugden, S. J.,
Chem. Soc., 125 (1924): 32] relates s to the liquid and vapor molar densities
and a temperature-independent parameter called the Parachor P
4
(2-116)
2/3
Tc
K
1/3
F (1 − Tr )11/9
(2-118)
where
(2-115)
s = A − BT
σ
ρL − ρv
= P ⋅
mN/m 10 3 kmol/m3
Required properties: The DIPPR 801 database gives rL = 13.2573 kmol/m3 at 237.45 K.
Calculation using Eq. (2-116):
F=
Tbr [ln(Pc /Pa) − 11.5261]
− 1.3281
1 − Tbr
(2-119)
Example Estimate the surface tension for ethyl mercaptan at 303.15 K.
Required properties from DIPPR 801:
Tc = 499.15 K
Pc = 5.49 × 106 Pa
Tb = 308.15 K
Supporting quantities:
Tr = (303.15 K)/(499.15 K) = 0.6073
Tbr = (308.15 K)/(499.15 K) = 0.6173
F = {0.6173[ln (5.49 × 106) − 11.5261]/(1 − 0.6173)} − 1.3281 = 5.113 [ from Eq. (2-119)]
From Eq. (2-118):
where rL and rV are the saturated molar liquid and vapor densities,
respectively. At low temperatures, where rL >> rV, the vapor density can
be neglected, but at higher temperatures the density of both phases must
be calculated. The surface tension is zero at the critical point where
rL = rV. Quayle [Quayle, O. R., Chem. Rev., 53 (1953): 439] proposed a group
contribution method for estimating P that has been improved in recent
years by Knotts et al. [Knotts, T. A., et. al., J. Chem. Eng. Data, 46 (2001):
1007]. This method using P is recommended when groups are available;
otherwise, the Brock-Bird [Brock, J. R., and R. B. Bird, AIChE J., 1 (1955):
174] corresponding-states method as modified by Miller [Miller, D. G., Ind.
Eng. Chem. Fundam., 2 (1963): 78] may be used to estimate surface tension
for compounds that are not strongly polar or associating.
Recommended Method 1 Parachor method.
References: Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden, S. J.,
Chem. Soc., 125 (1924): 32; Knotts, T. A., W. V. Wilding, J. L. Oscarson, and R.
L. Rowley, J. Chem. Eng. Data, 46 (2001): 1007.
Classification: Group contributions and QSPR.
Expected uncertainty: 4 percent.
Applicability: Organic compounds for which group values are available.
Input data: rL, molecular structure, and Table 2-177.
Description: Equation (2-116) is used with P calculated from
N
P = ∑ ni ∆Pi
i =1
Group values for the Parachor are given in Table 2-177.
(2-117)
s = (5.553 × 10−5) (5.49 × 106)2/3(499.15)1/3(5.113) (1 − 0.6073)11/9 mN/m
= 22.36 mN/m
The estimated value is 1.4 percent lower than the DIPPR 801 value of 22.68 mN/m.
Liquid Mixtures Compositions at the liquid-vapor interface are
not the same as in the bulk liquid, and so simple (bulk) compositionweighted averages of the pure-fluid values do not provide quantitative
estimates of the surface tension at the vapor-liquid interface of a mixture.
The behavior of aqueous mixtures is more difficult to correlate and estimate than that of nonpolar mixtures because small amounts of organic
material can have a pronounced effect upon the surface concentrations
and the resultant surface tension. These effects are usually modeled
with thermodynamic methods that account for the activity coefficients.
For example, a UNIFAC method [Suarez, J. T., C. Torres-Marchal, and
P. Rasmussen, Chem. Eng. Sci., 44 (1989): 782] is recommended and illustrated in [PGL5]. For nonaqueous systems the extension of the Parachor
method, used above for pure fluids, is a simple and reasonably effective
method for estimating s for mixtures.
Recommended Method Parachor correlation.
Reference: Hugill, J. A., and A. J. van Welsenes, Fluid Phase Equilib.,
29 (1986): 383; Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden,
S. J., Chem. Soc., 125 (1924).
Classification: Corresponding states.
Expected uncertainty: 3 to 10 percent.
Applicability: Nonaqueous mixtures.
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
TABLE 2-177
Knotts* Group Contributions for the Parachor in Estimating Surface Tension
Group
Group
DPi
(a) Nonring C
}CH3
55.25
>CH2 (n = 1–11)
39.92
>CH2 (n = 12–20)
40.11
>CH2 (n > 20)
40.51
>CH}
28.90
>C<
15.76
=CH2
49.76
=CH}
34.57
=C<
24.50
=C=
24.76
≡CH
43.64
≡C}
28.64
Branch corrections
Per branch
−6.02
sec-sec adjacency
−2.73
sec-tert adjacency
−3.61
tert-tert adjacency
−6.10
(b) Nonaromatic ring C
}CH2}
39.21
>CH}
23.94
>C<
7.19
=CH}
34.07
=C<
18.85
>CH} ( fused ring)
22.05
Ring corrections
Three-member ring
12.67
Four-member ring
15.76
Five-member ring
7.04
Six-member ring
5.19
Seven-member ring
3.00
(c) Aromatic ring C
>CH
34.36
>C}
16.07
}C} ( fused arom/arom)
19.73
}C} ( fused arom/aliph)
14.41
Arom ring corr
ortho
−0.60
para
3.40
meta
2.24
subst. naphthalene corr
−7.07
(d) Oxygen groups
}OH (alc, primary)
31.42
}OH (alc, sec)
22.68
}OH (alc, tertiary)
20.66
}OH (phenol)
30.32
}O} (nonring)
20.61
}O} (ring)
21.67
}O} (aromatic)
23.54
>C=O (nonring)
47.02
>C=O (ring)
50.04
O=CH} (aldehyde)
66.06
CHOOH ( formic)
94.01
}COOH (acid)
74.57
}OCHO ( formate)
82.29
}COO} (ester)
64.97
}COOCO} (acid anhyd)
115.07
}OC(=O)O} (ring)
84.05
*Knotts, T. A., et al., J. Chem. Eng. Data, 46 (2001): 1007.
Input data: Liquid and vapor r at mixture T; Parachors of pure components; xi.
Description:
ρ
ρ
σm
= PL ,m 3 L ,m 3 − Pv ,m 3 V ,m 3
mN/m
10 kmol/m
10 kmol/m
4
(2-120)
where sm = surface tension of the mixture
PL,m, PV,m = Parachor of liquid and vapor mixtures, respectively
rL,m, rV,m = mixture molar density of liquid and vapor, respectively
PL ,m =
C
1
∑ ∑ x i x j (Pi + Pj )
2 i =1 j=1
C
PV ,m =
44.98
44.63
46.44
46.53
29.04
31.97
33.92
10.77
15.71
23.24
26.49
80.94
65.23
67.54
93.43
73.64
57.05
91.69
77.12
64.32
73.86
75.05
66.89
63.34
65.33
68.30
51.37
51.75
51.47
72.21
93.20
90.13
21.81
26.24
51.16
54.56
66.30
70.39
90.84
92.04
105.11
54.50
44.93
28.64
115.59
48.84
22.65
25.06
106.03
Note that rV is generally very small compared to rL at temperatures substantially lower than Tc and can often be neglected.
Example Estimate the surface tension for a 16.06 mol% n-pentane(1) + 83.94
mol% dichloromethane(2) mixture at 298.15 K.
Required properties from DIPPR 801:
P
C
1
∑ ∑ y i y j (Pi + Pj )
2 i =1 j=1
DPi
(e) Nitrogen groups
R}NH2 (primary R)
R}NH2 (sec R)
R}NH2 (tert R)
A}NH2 (attached to arom ring)
>NH (nonring)
>NH (ring)
>NH (in arom ring)
>N- (nonring)
>N- (ring)
}N= (nonring)
>N (aromatic)
HC≡N (hyd cyanide)
}C≡N
}C≡N (aromatic)
( f) Nitrogen and oxygen groups
}C=ONH2 (amides)
}C=ONH- (amides)
}C=ON< (amides)
}NHCHO
>NCHO
}N=O
}NO2
}NO2 (aromatic)
(g) Sulfur groups
R-SH (primary R)
R-SH (sec R)
R-SH (tert R)
}SH (aromatic)
}S} (nonring)
}S} (ring)
}S} (aromatic)
>S=O (nonring)
>SO2 (nonring)
>SO2 (ring)
(h) Halogen groups
}F
}Cl
}Br
}I
}F (aromatic)
}Cl (aromatic)
}Br (aromatic)
}I (aromatic)
(i) Si groups
SiH4
>SiH}
>Si<
>Si< (ring)
(j) Other inorganic groups
}PO4
>P}
>B}
>Al}
}ClO3
n-Pentane
Dichloromethane
The following definitions are used for the liquid and vapor mixture
Parachors:
C
2-359
(2-121)
8.6173
15.5211
Mixture Parachor from Eq. (2-121) and mixture density:
PL,m = (0.1606)2(231.1) + (0.1606)(0.8394)(231.1 + 146.6) + (0.8394)2(146.6) = 160.17
−1
where xi is the mole fraction of component i in the liquid and yi is the mole
fraction of component i in the vapor.
rL/(kmol ⋅ m−3) at 298.15 K
231.1
146.6
−1
C x
0.1606 0.8394 kmol
kmol
ρL ,m = ∑ i =
= 13.752 3
+
8.6173 15.5211
m3
m
i =1 ρi
2-360
PHYSICAL AnD CHEMICAL DATA
Calculation using Eq. (2-120): Because the temperature is low, the density of the vapor
can be neglected, and
mN
σm
= [(160.17) (0.013752)]4 = 23.54
mN/m
m
The estimated value is 2.9 percent below the experimental value of 24.24 mN/m
reported by De Soria [De Soria, M. L. G., et al., J. Colloid Interface Sci., 103 (1985): 354].
FLAMMABILITY PROPERTIES
Flash Point The flash point is the lowest temperature at which a liquid
gives off sufficient vapor to form an ignitable mixture with air near the surface of the liquid or within the vessel used. ASTM test methods include procedures using a closed-cup apparatus (ASTM D 56, ASTM D 93, and ASTM
D 3828), which is preferred, and an open-cup apparatus (ASTM D 92 and
ASTM D 1310). Closed-cup values are typically lower than open-cup values.
Estimation methods cannot take into account the apparatus and procedural influences on the observed flash point.
Recommended Method Leslie-Geniesse method.
Reference: Leslie, E. H., and J. C. Geniesse, International Critical Tables,
vol. 2, McGraw-Hill, New York, 1927, p. 161.
Classification: GC (element contributions).
Expected uncertainty: ∼4 K or about 1.5 percent.
Applicability: Organic compounds.
Input data: Chemical structure and vapor pressure correlation.
Description: The flash point TFP is obtained from the moles of oxygen
required for stoichiometric combustion β, by back-solving from the vapor
pressure correlation using
P ∗ (TFP ) 1
=
atm
8β
(2-122)
Recommended Method Rowley method.
Reference: Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard.
Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points,
and Their Consanguinity: Critical Analysis, Experimental Exploration, and
Prediction,” Ph.D. Dissertation, Brigham Young University, 2010.
Classification: GC and extended theory.
Expected uncertainty: 10 percent for the lower limit; 25 percent for the
upper limit.
Applicability: Organic compounds.
Input data: Group contributions from Tables 2-178, ∆Hfo, and the thermal
properties (ideal gas heat of formation and average isobaric heat capacity)
of the combustion products. These latter quantities are given in Table 2-179.
A vapor pressure correlation is also required to obtain the corresponding
flammability limit temperature.
Description: A GC method is used to obtain the adiabatic flame temperature (Tad) of a lower-limit fuel-air mixture using the ΔTad, j contributions
shown in Table 2-178:
∑n ⋅∆T
j
o
C p ,i
H i (Tad ) ∆H f ,i
(Tad − 298)K
=
+
kJ/mol kJ/mol (kJ/mol ⋅ K)
NC, NSi, NS, NH, NX, NO = number of carbon, silicon, sulfur, hydrogen, halogen,
and oxygen atoms in the molecule, respectively
Example Estimate the flash point of phenol.
(2-125)
The lower flammability limit in volume percent is then calculated from
where P = vapor pressure at the flash point
(2-123)
(2-124)
N
where N is the total number of groups in the molecule. The ideal gas enthalpies Hi of the combustion products and oxygen at Tad are then calculated
from the ideal gas enthalpies of formation at 298 K and the average isobaric
heat capacities (given in Table 2-179) with Eq. (2-125):
*
N - N X - 2NO
β = N C + N Si + N S + H
4
ad,j
j
Tad =
100%
LFL =
ν=
1+ ν
∆H of ,fuel −
∑
products
ni H i (Tad ) + βH O2 (Tad )
C p ,air (Tad − 298) K
(2-126)
where β is defined in Eq. (2-123).
The upper flammability limit in volume percent is obtained from the UFL
group values given in Table 2-178 and
Structure:
∑n j ⋅ UFL j
UFL
j
= 4.30C st0.72 +
%
N
(2-127)
where Cst is the fuel concentration required for stoichiometric combustion
given by
Atomic contributions:
Atom type
Number
C
H
O
6
6
1
β = 6 + (6 − 2∙1)/4 = 7
From Eq. (2-123),
The DIPPR 801 correlation for the vapor pressure of phenol is
C st =
100
1 + 4.773β
(2-128)
Example Estimate the lower and upper flammability limits of toluene.
Structure:
6
10,113 K
P∗
T
T
= exp 95.444 −
− 10.09 In + 6.7603 × 10 −18
T
Pa
K
K
When this expression is used in Eq. (2-122) and solved for temperature, one obtains
TFP = 350.84 K, which is 0.4 percent below the DIPRR recommended value of 352.15 K.
Flammability Limits The lower flammability limit (LFL) is the
equilibrium-mixture boundary-line volume percent of vapor or gas in air
which if ignited will just propagate a flame away from the ignition source.
Similarly, the upper flammability limit (UFL) is the upper volume percent
boundary at which a flame can propagate in an ignited fuel/air equilibrium
mixture. Each of these limits has a temperature at which the corresponding
volumetric percent is reached. The lower flammability limit temperature
corresponds approximately to the flash point, but since the flash point is
determined with downward flame propagation and nonuniform mixtures
and the lower flammability temperature is determined with upward flame
propagation and uniform vapor mixtures, the measured lower flammability
temperature is generally slightly lower than the flash point.
Group contributions:
Group
CH3—c
c—
c—H
nj
∆Tad
1
1
5
1862.04
1719.69
1731.92
UFLj
−4.49
5.50
−1.25
Auxiliary calculations:
Tad = [1862.04 + 1719.69 + (5)(1731.92)]/7 = 1748.8
β = 7 + 8/4 = 9
PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES
2-361
TABLE 2-178 Group Contributions for Quantities Used to Estimate Flammability Limits by Rowley et al.* Method for Organic Compounds
(special notation: lower case indicates aromatic atom; # = triple bond; R = ring)
Example
DTad,i
UFLi
#C}
vinyl acetate
991.44
−8.65
n
pyridine
2622.13
4.46
#CH
acetylene
1237.85
61.25
n
piperazine
2124.88
13.32
=C<
isobutene
1834.42
−7.15
>NH
n-pentylamine
1566.76
−0.78
=CH
trans-2-butene
1751.82
0.30
>N}(c)
N-ethylaniline
2695.31
−7.25
=CH2
1-hexene
1558.49
3.06
N#C
benzonitrile
939.73
−9.72
=CH}(c)
styrene
−76.72
−11.24
N=C=O
methyl isocyanate
1147.48
4.95
=C}(c)
α-methylstyrene
2091.10
−5.13
}NO2
nitroethane
1777.58
−11.46
>C<
neopentane
1957.78
−0.23
}S}
thiophene
1056.05
23.55
}CH
isopropanol
1558.73
0.62
}SH
ethyl mercaptan
1727.5
}CH2
propane
1705.21
−0.30
S=
carbon disulfide
Group
Group
Example
DTad,i
272.36
UFLi
12.67
53.67
}CH3
butane
1856.30
−1.12
Si
trimethylsilane
−55.66
78.90
CH3}c
toluene
1862.04
−4.49
Si(O3)
tetraethoxysilane
2095.22
120.24
c}
toluene
1719.69
5.50
(Si)}O}
octamethyltrisiloxane
2347.17
−67.75
cH
benzene
1731.92
−1.25
Si-(Cl)
monochlorosilane
1062.27
−13.93
OH}(C)
1-methylcyclohexanol
786.14
4.90
Si}(Cl2)
dichlorosilane
554.54
62.48
OH}(CH)
isopropanol
1508.33
0.12
Si}(Cl3)
methyl trichlorosilane
−34.35
−18.52
−4.95
OH}(CH2)
butanol
1397.73
5.32
F2}(C)
1,1-difluoroethane
2556.15
OH}(c)
phenol
1337.25
9.15
F2}(C=C)
1,1-difluoroethylene
2088.23
3.43
OH}(CC#C)
propargyl alcohol
2209.35
15.57
F3}(C)
3,3,3-trifluoropropene
2451.95
−12.81
O=C
3-pentanone
1532.45
2.50
O=CR
cyclohexanone
954.03
−11.84
F}(C)
methyl fluoride
1841.54
0.80
F}(C=C)
vinyl fluoride
1477.04
15.38
−22.73
O=C}C=C
methacrolein
1761.66
6.00
Cl2}(C)
dichloromethane
2882.45
O=COC
hexyl formate
1492.23
0.47
Cl2}(C=C)
1,1-dichloroethylene
2956.55
−15.50
(C)}O}(C)
diethyl ether
1325.57
13.38
Cl3}(C)
1,1,1-trichloroethane
3046.39
−26.31
}COOH
formic acid
1252.38
−5.12
Cl}(C)
isopropyl chloride
1948.51
−5.20
}OR}
furan
1402.11
26.05
Cl}(C=C)
chloropropene
2294.79
0.16
}O}O}
ethyl peroxide
−728.23
0.76
Cl}(cc}Cl)
o-dichlorobenzene
3257.79
−13.14
triethylamine
1442.71
8.85
Br}
methylbromide
3389.83
>N}
−24.38
*Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard. Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points, and Their Consanguinity: Critical Analysis,
Experimental Exploration, and Prediction,” Ph.D. Dissertation, Brigham Young University, 2010.
Calculation of H(Tad ) from Eq. (2-125) and Table 2-179:
Species
H°(298 K)/(kJ/mol)
Toluene
CO2
H2O
O2
Air
Cp/[kJ/(mol ⋅ K)]
50.17
−393.51
−241.81
0
0
—
0.0372433
0.0335780
0.0293468
0.0289937
LFL =
H(Tad)/(kJ/mol)
—
−339.48
−193.10
42.58
—
From Eq. (2-126) and the stoichiometry of the combustion reaction, C7H8 + 9O2 = 7CO2 +
4H2O:
50.17 − [(7)(−339.48) + (4)(−193.10)] + (9)(42.58)
ν=
= 85.148
(0.0289937)(1749 − 298)
TABLE 2-179 Ideal Gas Enthalpies of Formation and Average
Heat Capacities of Combustion Gases for Use in Eq. (2-125)
Species
Air
O2
N2
CO2
H2O
SO2
SiO2
HF
HCl
HBr
HI
H°/(kJ/mol)
0
0
0
−393.51
−241.81
−296.84
−305.43
−273.30
−92.31
−36.29
−26.50
100%
= 1.16%
1 + 85.148
The UFL is found from Eqs. (2-127) and (2-128):
100
UFL = (4.30)
1 + (4.773)(9)
0.72
+
−4.49 + 5.50 + (5)(−1.25)
= 7.02%
7
These values agree well with the DIPPR 801 recommended values of 1.2 and 7.1 percent,
respectively.
Flammability limit temperatures are found by determining the temperature at
which the vapor pressure equals the partial pressure corresponding to the LFL or UFL.
The vapor pressure correlation for toluene from DIPPR 801 is
2
6729.8 K
P∗
T
T
= exp 76.945 −
− 8.179ln + 5.3017 × 10 −6
T
Pa
K
K
Cp/[J/(mol ⋅ K)]
28.9937
29.3468
29.1260
37.2433
33.5780
39.8980
44.0254
29.1361
29.1436
29.1327
29.1583
Back-solving for T using the partial pressures of 0.0116 atm for LFL and 0.0702 atm
for UFL gives
TLFL = 277 K and TUFL = 311 K
Autoignition Temperature The autoignition temperature (AIT) is
the minimum temperature for a substance to initiate self-combustion in air
in the absence of an ignition source. Methods to estimate AIT are in general
rather approximate. The method illustrated here may provide reasonable
estimates, but significant errors can also result. Estimated values should not
be assumed to be reliable for design and safety purposes.
2-362
PHYSICAL AnD CHEMICAL DATA
TABLE 2-180 Group Contributions for Pintar* Autoignition Temperature Method
for Organic Compounds
Group
bi
Group
bi
Group
bi
}CH3
301.91
}Cl3
1073.47
}SO3}
—
>CH2
−10.86
}F
360.60
}SO4}
−31.71
>CH}
−275.17
}F2
755.54
}CO3}
442.26
>C<
−570.43
}F3
1082.00
}P=
−334.91
}H
391.48
}Br
420.96
}PO}
−549.59
}OH
324.10
}Br2
607.69
}OPO2}
—
}O}
−18.60
}Br3
1260.00
}PO4=
−329.45
†
}O}O}
−397.61
}I
310.53
Si}C
−147.69
=C=O
57.65
}I2
—
Si}O†
−136.99
†
}CHO
195.20
}I3
—
Si}H
−310.52
}COOH
370.75
}NH2
354.11
Si}Cl†
−200.88
}COO}
43.90
>NH
9.88
Si}N†
—
}CO}O}CO}
46.11
}N=
−249.91
Si}Si
—
}C6H5
380.27
}CN
469.67
Al
—
m}C6H4
153.15
=C=N}
−273.70
B
—
o}C6H4
77.48
=N}NH2
378.27
Cr
—
p}C6H4
99.87
>N}NH2
−215.02
Na
534.29
Aromatic ring
−1339.65
}NO2
292.57
cis
−29.19
=
578.72
}SH
273.84
trans
−38.31
≡
1116.50
}S}
−60.75
Nonarom.ring
605.97
}Cl
347.39
}SO}
−91.10
Add’l.ring
565.11
}Cl2
726.03
}SO2}
—
Zn
349.02
*Pintar, A. J., Estimation of Autoignition Temperature, Technical Support Document DIPPR Project 912,
Michigan Technological University, Houghton, 1996.
†
Does not include contribution of atoms attached to silicon.
Recommended Method Pintar method.
Reference: Pintar, A. J., Estimation of Autoignition Temperature, Technical
Support Document DIPPR Project 912, Michigan Technological University,
Houghton, 1996.
Classification: Group contributions.
Expected uncertainty: 25 percent.
Applicability: Organic compounds.
Input data: Group contributions from Table 2-180.
Description: A simple GC method with first-order contributions is given
by
N
AIT = ∑ ni bi
(2-129)
Example Estimate the autoignition temperature of 2,3-dimethylpentane.
Structure and group information:
Group
ni
bi
}CH3
>CH2
>CH}
4
1
2
301.91
−10.86
−275.17
i =1
where ni is the number of groups of type i in the molecule and bi is the contribution of group i to the autoignition temperature. A more accurate but
somewhat more complicated logarithmic GC method was also developed
by Pintar in the same reference cited here.
Calculation using Eq. (2-129):
AIT = 4(301.91) − 10.86 + 2(−275.17) = 646.4 K
The estimated value is 6.3 percent above the DIPPR 801 recommended value of 608.15 K.
Section 3
Mathematics
Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering,
University of Washington; Member, National Academy of Engineering (Section Editor, numerical methods and
all general material)
Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member,
National Academy of Engineering (Optimization)
GEnERAL REFEREnCES
MATHEMATICS
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Miscellaneous Mathematical Constants and Formulas . . . . . . . . . . . . . . . . . . . . . . .
Integral Exponents (Powers and Roots) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algebraic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arithmetic-Geometric Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Carleman’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cauchy-Schwarz Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minkowski’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hölder’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lagrange’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-4
3-5
3-5
3-6
3-6
3-6
3-6
3-6
3-6
3-6
3-6
MEnSURATIOn FORMULAS
Plane Geometric Figures with Straight Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . .
Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parallelogram (opposite sides parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rhombus (equilateral parallelogram). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trapezoid ( four sides, two parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quadrilateral ( four-sided) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Regular Polygon of n Sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plane Geometric Figures with Curved Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . .
Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parabola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Catenary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solid Geometric Figures with Plane Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rectangular Parallelepiped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Frustum of Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volume and Surface Area of Regular Polyhedra with Edge l. . . . . . . . . . . . . . . . .
Solids Bounded by Curved Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Torus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-6
3-6
3-6
3-6
3-6
3-6
3-6
3-6
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-8
Oblate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hemisphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Miscellaneous Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volume of a Solid Revolution
(the solid generated by rotating a plane area about the x axis) . . . . . . . . . . . .
Area of a Surface of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Area Bounded by f (x), the x Axis, and the Lines x = a, x = b . . . . . . . . . . . . . . . . .
Length of Arc of a Plane Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Irregular Areas and Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Irregular Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Irregular Volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-8
3-9
ELEMEnTARY ALGEBRA
Operations on Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operations with Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fractional Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Factoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laws of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Permutations, Combinations, and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Theory of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cubic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quartic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Polynomials of the nth Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-10
3-10
3-10
3-10
3-10
3-10
3-10
3-10
AnALYTIC GEOMETRY
Plane Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Straight Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Asymptotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solid Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lines and Planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-11
3-11
3-11
3-11
3-11
3-12
3-12
3-12
3-12
3-1
3-2
MATHEMATICS
Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-13
3-13
PLAnE TRIGOnOMETRY
Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions of Circular Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plane Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Values of the Trigonometric Functions for Common Angles . . . . . . . . . . . . . . . .
Relations between Functions of a Single Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions of Negative Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relations between Angles and Sides of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solutions of Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Law of Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Right Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hyperbolic Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fundamental Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inverse Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Magnitude of the Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Approximations for Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-14
3-14
3-14
3-15
3-15
3-15
3-15
3-15
3-15
3-15
3-15
3-15
3-15
3-15
3-16
3-16
3-16
3-16
3-16
DIFFEREnTIAL AnD InTEGRAL CALCULUS
Differential Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Indeterminate Forms: L’Hôpital’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Partial Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multivariable Calculus Applied to Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . .
State Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamic State Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Partial Derivatives of Intensive Thermodynamic Functions . . . . . . . . . . . . . . . .
Integral Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Indefinite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-16
3-16
3-16
3-16
3-17
3-17
3-18
3-18
3-18
3-19
3-20
3-20
3-20
3-21
3-21
3-21
3-21
InFInITE SERIES
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operations with Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tests for Convergence and Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Series Summation and Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sums for the First n Numbers to Integer Powers . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arithmetic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geometric Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Harmonic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Binomial Series (See Also Elementary Algebra) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Taylor’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maclaurin’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exponential Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logarithmic Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigonometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Partial Sums of Infinite Series, and How They Grow. . . . . . . . . . . . . . . . . . . . . . . .
3-22
3-22
3-22
3-22
3-22
3-23
3-23
3-23
3-23
3-23
3-23
3-23
3-23
3-23
3-23
3-23
COMPLEX VARIABLES
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Special Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigonometric Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Elementary Complex Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Complex Functions (Analytic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions of a Complex Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Harmonic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conformal Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-23
3-23
3-23
3-23
3-23
3-23
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-24
3-25
3-25
3-25
3-25
DIFFEREnTIAL EQUATIOnS
Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ordinary Differential Equations of the First Order. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equations with Separable Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ordinary Differential Equations of Higher Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear Differential Equations with Constant Coefficients
and Right-Hand Member of Zero (Homogeneous) . . . . . . . . . . . . . . . . . . . . . . . .
Linear Nonhomogeneous Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . .
Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Special Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Euler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bessel’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Legendre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laguerre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hermite’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chebyshev’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Partial Differential Equations of Second and Higher Order . . . . . . . . . . . . . . . . .
Group Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Integral-Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matched-Asymptotic Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-25
3-26
3-26
3-26
3-26
3-27
3-27
3-27
3-27
3-27
3-27
3-27
3-27
3-27
3-27
3-28
3-28
3-29
3-29
3-30
DIFFEREnCE EQUATIOnS
Nonlinear Difference Equations: Riccati Difference Equation . . . . . . . . . . . . . .
3-30
InTEGRAL EQUATIOnS
Classification of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-31
InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS)
Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sufficient Conditions for the Existence of the Laplace Transform . . . . . . . . . .
Properties of the Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Convolution Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Properties of the Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fourier Cosine Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-32
3-32
3-32
3-33
3-33
3-33
3-33
MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS
Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vector and Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LU Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solution of Ax = b by Using LU Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
QR Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Singular-Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-33
3-33
3-34
3-34
3-34
3-34
3-34
3-35
3-35
3-36
nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS
Approximation Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-36
nUMERICAL AnALYSIS AnD APPROXIMATE METHODS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Solution of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Solution of Nonlinear Equations
in One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods for Nonlinear Equations in One Variable . . . . . . . . . . . . . . . . . . . . . . . . .
Methods for Multiple Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Method of Successive Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lagrange Interpolation Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equally Spaced Forward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equally Spaced Backward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Central Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spline Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Use of Interpolation Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Smoothing Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Newton-Cotes Integration Formulas
(Equally Spaced Ordinates) for Functions of One Variable. . . . . . . . . . . . . . . . .
Gaussian Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Romberg’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cubic Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-36
3-37
3-37
3-37
3-37
3-37
3-37
3-37
3-37
3-38
3-38
3-38
3-38
3-38
3-39
3-39
3-39
3-39
3-39
3-39
3-39
3-39
3-40
3-40
3-40
3-40
MATHEMATICS
Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two-Dimensional Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gaussian Quadrature Points and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-40
3-40
3-40
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL
EQUATIOnS AS InITIAL-VALUE PROBLEMS
Implicit Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Differential-Algebraic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability, Bifurcations, and Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Molecular Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ordinary Differential Equations—Boundary-Value Problems . . . . . . . . . . . . . . . . .
Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Finite Difference Methods Solved with Spreadsheets. . . . . . . . . . . . . . . . . . . . . . .
Orthogonal Collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Galerkin Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Adaptive Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Singular Problems and Infinite Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Solution of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Solution of Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . .
Parabolic Equations in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Elliptic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hyperbolic Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Finite Volume Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parabolic Equations in Two or Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . .
Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-42
3-42
3-42
3-42
3-42
3-43
3-43
3-43
3-43
3-44
3-45
3-45
3-45
3-45
3-46
3-46
3-46
3-46
3-47
3-48
3-49
3-49
3-49
3-49
OPTIMIZATIOn
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gradient-Based Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Local Optimality Conditions: A Kinematic Interpretation . . . . . . . . . . . . . . . . . .
Convex Cases of NLP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solving the General NLP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Gradient-Based NLP Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algorithmic Details for NLP Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Optimization Methods without Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Classical Direct Search Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Derivative-Free Optimization (DFO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Global Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixed Integer Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixed Integer Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixed Integer Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Development of Optimization Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-50
3-51
3-51
3-52
3-52
3-53
3-54
3-54
3-54
3-54
3-54
3-55
3-55
3-55
3-55
3-56
3-57
STATISTICS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Type of Data
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-58
3-58
3-58
3-58
3-58
Sample Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Characterization of Chance Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enumeration Data and Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Binomial Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Poisson Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hypergeometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measurement Data and Sampling Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t Distribution of Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t Distribution for the Difference in Two Sample Means
with Equal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t Distribution for the Difference in Two Sample Means
with Unequal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chi-Square Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Interval for a Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Interval for the Difference in Two
Population Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Interval for a Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tests of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Nature of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for a Mean Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two-Population Test of Hypothesis for Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for Paired Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for Matched Pairs: Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for a Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for a Proportion: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for Two Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test of Hypothesis for Two Proportions: Procedure . . . . . . . . . . . . . . . . . . . . . . . .
Goodness-of-Fit Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Goodness-of-Fit Test: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two-Way Test for Independence for Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two-Way Test for Independence for Count Data: Procedure. . . . . . . . . . . . . . . .
Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Polynomial Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiple Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nonlinear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Error Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of Variance (ANOVA) and Factorial Design of Experiments . . . . . . . . . .
ANOVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of Variance: Estimating the Variance of Four Treatments . . . . . . . . . .
Factorial Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two-Level Factorial Design with Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . .
3-3
3-59
3-59
3-59
3-59
3-59
3-59
3-60
3-60
3-60
3-61
3-61
3-62
3-62
3-62
3-63
3-63
3-63
3-63
3-64
3-64
3-64
3-64
3-65
3-65
3-66
3-66
3-67
3-67
3-67
3-68
3-68
3-69
3-69
3-69
3-70
3-70
3-70
3-70
3-70
3-71
3-71
3-71
3-72
3-72
DIMEnSIOnAL AnALYSIS
PROCESS SIMULATIOn
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Process Modules or Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Process Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Commercial Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-73
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GEnERAL REFEREnCES
Courant, R., and D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience, New York, 1953; Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980; Finlayson, B. A., L. T. Biegler, and I. E.
Grossmann, Mathematics in Chemical Engineering, Ullmann’s Encyclopedia
of Industrial Chemistry, Published Online: 15 DEC 2006, DOI:
10.1002/14356007.b01_01.pub2, Wiley, New York, 2006; Jeffrey, A., Mathematics
for Engineers and Scientists, 6th ed., Chapman & Hall/CRC, New York, 2004;
Kaplan, W., Advanced Calculus, 5th ed., Addison-Wesley, Redwood City, Calif.,
2003; Lipschultz, S., M. Spiegel, and J. Liu, Schaum’s Outline of Mathematical
Handbook of Formulas and Tables, 4th ed., McGraw-Hill Education, New York,
2012; Logan, J. D., and W. R. Wolesensky, Mathematical Methods in Biology,
Wiley, New York, 2009; Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W.
Clark, eds., NIST Handbook of Mathematical Functions, Cambridge University
Press, London, 2010; see also http://dlmf.nist.gov; Press, W. H., S. A. Teukolsky,
W. T. Vetterling, and B. P. Plannery, Numerical Recipes, 3d ed., Cambridge
University Press, London, 2007; Rice, R. G., and D. D. Do, Applied Mathematics
and Modeling for Chemical Engineers, 2d ed., Wiley, New York, 2012;
Stroud, K. A., and D. J. Booth, Engineering Mathematics, 7th ed., Industrial
Press, South Norwick, Conn., 2013; Thompson, W. J., Atlas for Computing
Mathematical Functions, Wiley, New York, 1997; Varma, A., and M. Morbidelli,
Mathematical Methods in Chemical Engineering, Oxford Press, New York,
1997; Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 3d ed., CRC
Press, New York, 2009; Wrede, R. C., and M. R. Spiegel, Schaum’s Outline of
Theory and Problems of Advanced Calculus, 3d ed., McGraw-Hill, New York,
2010.
MATHEMATICS
GEnERAL
The basic problems of the sciences and engineering fall broadly into three
categories:
1. Steady-state problems. In such problems the configuration of the system
is to be determined. This solution does not change with time but continues
indefinitely in the same pattern, hence the name steady state. Typical chemical
engineering examples include steady temperature distributions in heat conduction, equilibrium in chemical reactions, and steady diffusion problems.
2. Eigenvalue problems. These are extensions of equilibrium problems
in which critical values of certain parameters are to be determined in addition to the corresponding steady-state configurations. The determination of
eigenvalues may also arise in propagation problems and stability problems.
Typical chemical engineering problems include those in heat transfer and
resonance in which certain boundary conditions are prescribed.
3. Propagation problems. These problems are concerned with predicting the subsequent behavior of a system from a knowledge of the initial
state. For this reason they are often called the transient (time-varying) or
unsteady-state phenomena. Chemical engineering examples include the
transient state of chemical reactions (kinetics), the propagation of pressure
waves in a fluid, transient behavior of an adsorption column, and the rate of
approach to equilibrium of a packed distillation column.
The mathematical treatment of engineering problems involves four basic
steps:
1. Formulation. This involves the expression of the problem in mathematical language. That translation is based on the appropriate physical laws
governing the process.
2. Solution. Appropriate mathematical and numerical operations are
carried out so that logical deductions may be drawn from the mathematical
model.
3. Interpretation. This process develops relations between the mathematical results and their meaning in the physical world.
4. Refinement. The procedure is recycled to obtain better predictions,
as indicated by experimental checks.
Steps 1 and 2 are of primary interest here. The actual details are left to the
various subsections, and only general approaches will be discussed.
The formulation step may result in algebraic equations, difference equations, differential equations, integral equations, or combinations of these. In
any event these mathematical models usually arise from statements of
physical laws such as the laws of mass and energy conservation in the form
Input of x - output of x + production of x = accumulation of x
Many general laws of the physical universe are expressible by differential equations. Specific phenomena are then singled out from the infinity
of solutions of these equations by assigning the individual initial or boundary conditions which characterize the given problem. For steady-state or
boundary-value problems (Fig. 3-1), the solution must satisfy the differential
equation inside the region and the prescribed conditions on the boundary.
FIG. 3-1 Boundary conditions.
In mathematical language, the propagation problem is known as an initialvalue problem (Fig. 3-2). Schematically, the problem is characterized by a
differential equation plus an open region in which the equation holds. The
solution of the differential equation must satisfy the initial conditions plus
any “side” boundary conditions.
FIG. 3-2 Propagation problem.
The description of phenomena in a continuous medium such as a gas or a
fluid often leads to partial differential equations. In particular, phenomena
of “wave” propagation are described by a class of partial differential equations called hyperbolic, and these are essentially different in their properties
from other classes such as those that describe equilibrium (elliptic) or diffusion and heat transfer (parabolic). Prototypes are as follows:
1. Elliptic. Laplace’s equation
∂2 u ∂2 u
+
=0
∂x 2 ∂ y 2
or
Rate of input of x - rate of output of x + rate of production of
x = rate of accumulation of x
where x = mass, energy, etc. These statements may be abbreviated by the
statement
Input - output + production = accumulation
3-4
Poisson’s equation
∂2 u ∂2 u
+
= g (x , y )
∂x 2 ∂ y 2
These do not contain the variable t (time) explicitly; accordingly, their solutions represent equilibrium configurations. Laplace’s equation corresponds
to a “natural” equilibrium, while Poisson’s equation corresponds to an
MATHEMATICS
equilibrium under the influence of g(x, y). Steady heat-transfer and masstransfer problems are elliptic.
2. Parabolic. The heat equation
∂u ∂2 u ∂2 u
=
+
∂t ∂ x 2 ∂ y 2
describes unsteady or propagation states of diffusion as well as heat transfer.
3. Hyperbolic. The wave equation
∂2 u ∂2 u ∂2 u
=
+
∂t 2 ∂ x 2 ∂ y 2
describes wave propagation of all types when the assumption is made that
the wave amplitude is small and that interactions are linear.
The solution phase has been characterized in the past by a concentration
on methods to obtain analytic solutions to the mathematical equations.
These efforts have been most fruitful in the area of linear equations such as
those just given. However, many natural phenomena are nonlinear. While
there are a few nonlinear problems that can be solved analytically, most
cannot. In those cases, numerical methods are used. Due to the widespread
availability of software for computers, the engineer has quite good tools
available. Numerical methods almost never fail to provide an answer to any
particular situation, but they can never furnish a general solution of any
problem. The mathematical details outlined here include both analytic and
numeric techniques useful in obtaining solutions to problems.
Our discussion to this point has been confined to those areas in which the
governing laws are well known. However, in many areas, information on the
governing laws is lacking and statistical methods are used. Broadly speaking,
statistical methods may be of use whenever conclusions are to be drawn or
decisions made on the basis of experimental evidence. Since statistics could
be defined as the technology of the scientific method, it is primarily concerned with the first two aspects of the method, namely, the performance of
experiments and the drawing of conclusions from experiments. Traditionally
the field is divided into two areas:
1. Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are
most useful when experimental data are subject to errors. First, the design
of experiments may be carried out in such a fashion as to avoid some of the
sources of experimental error and make the necessary allowances for that
portion which is unavoidable. Second, the results can be presented in terms
of probability statements which express the reliability of the results. Third,
a statistical approach frequently forces a more thorough evaluation of the
experimental aims and leads to a more definitive experiment than would
otherwise have been performed.
2. Statistical inference. The broad problem of statistical inference is
to provide measures of the uncertainty of conclusions drawn from experimental data. This area uses the theory of probability, enabling scientists to
assess the reliability of their conclusions in terms of probability statements.
Both of these areas, the mathematical and the statistical, are intimately
intertwined when applied to any given situation. The methods of one are
often combined with those of the other. And both, in order to be successfully used, must result in the numerical answer to a problem, that is, they
constitute the means to an end. Increasingly the numerical answer is being
obtained from the mathematics with the aid of computers. The mathematical notation is given in Table 3-1.
MISCELLAnEOUS MATHEMATICAL COnSTAnTS
AnD FORMULAS
Numerical values of the constants that follow are approximate to the number of significant digits given.
π = 3.1415926536
e = 2.7182818285
γ = 0.5772156649
Radian = 57.2957795131°
Pi
Napierian (natural) logarithm base
Euler’s constant
Integral Exponents (Powers and Roots) If m and n are positive integers and a and b are numbers or functions, then the following properties hold:
a −n = 1/a n
a≠0
(ab)n = a n b n
a n a m = a n+m
(a n )m = a nm
n
a = a 1/n
if
a 0 = 1 (a ≠ 0)
0 a = 0 (a ≠ 0)
a>0
3-5
TABLE 3-1 Mathematical Signs, Symbols, and Abbreviations
∓ (±)
plus or minus (minus or plus)
∶
divided by, ratio sign
∷
proportional sign
<
less than
≮
not less than
>
greater than
≯
not greater than
≅
approximately equals, congruent to
∼
similar to
≎
≠
equivalent to
≐
not equal to
approaches, is approximately equal to
∝
varies as
∞
infinity
∴
therefore
∩
intersection
square root
cube root
3
n
nth root
∠
angle
⊥
perpendicular to
∙
x
log (or log10)
ln (or loge)
e
a°
a′
a″
sin
cos
tan
cot (or ctn)
sec
csc
sin–1
sinh
cosh
tanh
sinh–1
f (x) or f(x)
Δx
Σ
dx
dy/dx or y ′
d 2y/dx 2 or y″
d ny/dx n
∂y/∂x
∂ny/∂xn
∂n z
∂x ∂ y
parallel to
∫
∫
numerical value of x
common logarithm or Briggsian logarithm
natural logarithm or hyperbolic logarithm or Napierian logarithm
base (2.718) of natural system of logarithms
an angle a degrees
a prime, an angle a minutes
a double prime, an angle a seconds, a second
sine
cosine
tangent
cotangent
secant
cosecant
inverse sin, anti-sine, or angle whose sine is
hyperbolic sine
hyperbolic cosine
hyperbolic tangent
anti-hyperbolic sine or angle whose hyperbolic sine is
function of x
increment of x, delta x
summation of
differential of x
derivative of y with respect to x
second derivative of y with respect to x
nth derivative of y with respect to x
partial derivative of y with respect to x
nth partial derivative of y with respect to x
nth partial derivative with respect to x and y
integral of
b
a
.
y
ÿ
Δ or ∇2
d
∮
integral between the limits a and b
first derivative of y with respect to time
second derivative of y with respect to time
∂2
∂2
∂2
laplacian 2 + 2 + 2
∂x ∂ y ∂z
sign of a variation
sign for integration around a closed path
3-6
MATHEMATICS
The equality holds if, and only if, the sequences |a1|p, |a2|p, …, |an|p and |b1|q,
|b2|q, …, |bn|q are proportional and the argument (angle) of the complex
numbers ak bk is independent of k. This last condition is of course automatically satisfied if a1, …, an and b1, …, bn are positive numbers.
Lagrange’s Inequality Let a1, a2, …, an and b1, b2, …, bn be real numbers. Then
Logarithms
log ab = log a + log b , a > 0, b > 0
log a n = n log a
log (a /b) = log a − log b
2
log n a = (1/n ) log a
The common logarithm (base 10) is denoted log a (or log10 a in some texts).
The natural logarithm (base e) is denoted ln a (or in some texts loge a). If
the text is ambiguous (perhaps using log x for ln x), test the formula by
evaluating it.
ALGEBRAIC InEQUALITIES
Arithmetic-Geometric Inequality Let An and Gn denote, respectively, the arithmetic and the geometric means of a set of positive numbers
a1, a2, …, an. Then An ≥ Gn, that is,
n n
n
∑ ak bk = ∑ a k2 ∑ bk2 − ∑
(a k b j − a j bk )2
k =1 k =1 1 ≤ k ≤ j ≤ n
k =1
Example Two chemical engineers, Mary and John, purchase stock in
the same company at times t1, t2, …, tn, when the price per share is, respectively, p1, p2, …, pn. Their methods of investment are different, however: John
purchases x shares each time, whereas Mary invests P dollars each time
( fractional shares can be purchased). Who is doing better?
While one can argue intuitively that the average cost per share for Mary
does not exceed that for John, we illustrate a mathematical proof using
inequalities. The average cost per share for John is equal to
n
a1 + a2 + + an
≥ (a1a2 an )1/n
n
x ∑ pi
The equality holds only if all the numbers ai are equal.
Carleman’s Inequality The arithmetic and geometric means just
defined satisfy the inequality
Total money invested
i =1
=
Number of shares purchased
nx
1 2
nP
n
= n
1
P
∑p ∑p
i =1 i
i =1 i
ar )1/r ≤ neAn
n
r =1
where e is the best possible constant in this inequality.
Cauchy-Schwarz Inequality Let a = (a1, a2, …, an) and b = (b1, b2, …, bn),
where the ai and bi are real or complex numbers. Then
2
n
∑ (a b )
k k
k =1
n
n
≤ ∑| a k |2 ∑| bk |2
k =1
k =1
The equality holds if, and only if, the vectors a and b are linearly dependent
(i.e., one vector is a scalar times the other vector).
Minkowski’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets
of complex numbers. Then for any real number p > 1,
n
∑| ak + bk | p
k =1
1/p
n
≤ ∑| a k | p
k =1
1/p
n
+ ∑| bk | p
k =1
n
∑ akbk ≤ ∑| ak | p
k =1
k =1
1/ p
n
∑| bk |q
k =1
Thus the average cost per share for John is the arithmetic mean of p1,
p2, …, pn, whereas that for Mary is the harmonic mean of these n numbers.
Since the harmonic mean is less than or equal to the arithmetic mean for
any set of positive numbers and the two means are equal only if p1 = p2 = … =
pn, we conclude that the average cost per share for Mary is less than that for
John if two of the prices pi are distinct. One can also give a proof based on the
Cauchy-Schwarz inequality. To this end, define the vectors
a = ( p1−1/2 , p2−1/2 , , pn−1/2 ) b = ( p11/2 , p21/2 , , pn1/2 )
Then a · b = 1 + … + 1 = n, and so by the Cauchy-Schwarz inequality
1/p
Hölder’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets
of complex numbers, and let p and q be positive numbers with 1/p + 1/q = 1.
Then
n
1 n
∑ pi
n i =1
The average cost per share for Mary is
n
∑(a a
=
n
n
1
pi
(a ⋅ b ) 2 = n 2 ≤ ∑
i =1
∑p
j
j =1
with the equality holding only if p1 = p2 = … = pn. Therefore
n
∑p
i
n
1/q
n
∑
i =1
1
pi
≤
i =1
n
MEnSURATIOn FORMULAS
Reference: http://mathworld.wolfram.com/SphericalSector.html, etc.
PLAnE GEOMETRIC FIGURES WITH STRAIGHT BOUnDARIES
Let A denote area and V volume in the following.
Triangles (see also “Plane Trigonometry”) A = ½bh where b = base,
h = altitude.
Rectangle A = ab where a and b are the lengths of the sides.
Parallelogram (opposite sides parallel) A = ah = ab sin α where a and
b are the lengths of the sides, h is the height, and α is the angle between the
sides. See Fig. 3-3.
Rhombus (equilateral parallelogram) A = ½ab where a and b are the
lengths of the diagonals.
Trapezoid (four sides, two parallel) A = ½(a + b)h where the lengths of
the parallel sides are a and b and h = height.
Quadrilateral (four-sided) A = ½ab sin q where a and b are the lengths
of the diagonals and the acute angle between them is q.
Regular Polygon of n Sides
See Fig. 3-4.
1
180°
A = nl 2 cot
where l = length of each side
4
n
FIG. 3-3 Parallelogram.
FIG. 3-4 Regular polygon.
MEnSURATIOn FORMULAS
l
180°
R = csc
2
n
where R is the radius of the circumscribed circle
l
180°
r = cot
2
n
where r is the radius of the inscribed circle
3-7
Radius r of Circle Inscribed in Triangle with Sides a, b, c
r=
( s − a )( s − b)( s − c )
where s = 1 2 (a + b + c )
s
FIG. 3-7 Parabola .
FIG. 3-6 Ellipse .
Radius R of Circumscribed Circle
R=
abc
4 s ( s − a )( s − b)( s − c )
Ellipse (Fig. 3-6)
Let the semiaxes of the ellipse be a and b.
A = πab
Area of Regular Polygon of n Sides Inscribed in a Circle of Radius r
A = (nr /2) sin (360°/n)
2
C = 4aE(e)
where e2 = 1 - b2/a2 and E(e) is the complete elliptic integral of the second
kind
Perimeter of Inscribed Regular Polygon
2
π 1
E (e ) = 1 − e 2 +
2 2
P = 2nr sin (180°/n)
Area of Regular Polygon Circumscribed about a Circle of Radius r
A = nr2 tan (180°/n)
Perimeter of Circumscribed Regular Polygon
P = 2nr tan
180°
n
PLAnE GEOMETRIC FIGURES WITH CURVED BOUnDARIES
Circle (see Fig. 3-5). Let
C = circumference
r = radius
D = diameter
A = area
S = arc length subtended by q
l = chord length subtended by q
H = maximum rise of arc above chord, r - H = d
q = central angle (rad) subtended by arc S
C = 2πr = πD
(π = 3.14159 …)
S = rq = ½ Dq
l = 2 r 2 − d 2 = 2 r sin (θ/2) = 2 d tan (θ/2)
1
1
θ
4 r 2 − l 2 = l cot
2
2
2
S
d
l
θ = = 2 cos−1 = 2 sin −1
r
r
D
d=
A (circle) = πr2 = ¼πD2
A (sector) = ½rS = ½r2q
A (segment) = A (sector) - A (triangle) = ½r2(q - sin q)
Ring (area between two circles of radii r1 and r 2) The circles need not
be concentric, but one of the circles must enclose the other.
A = π(r1 + r2)(r1 - r2)
FIG. 3-5 Circle .
r1 > r2
[an approximation for the circumference C = 2 π (a 2 + b 2 )/ 2)].
Parabola
(Fig. 3-7)
Length of arc EFG =
4x2 + y 2 +
Area of section EFG =
4
xy
3
y 2 2x + 4x 2 + y 2
ln
2x
y
Catenary (the curve formed by a cord of uniform weight suspended
freely between two points A and B; Fig. 3-8)
y = a cosh (x/a)
The length of arc between points A and B is equal to 2a sinh (L/a). The sag of
the cord is D = a cosh (L/a) - a.
SOLID GEOMETRIC FIGURES WITH PLAnE BOUnDARIES
Cube Volume = a3; total surface area = 6a2; diagonal = a 3 , where a =
length of one side of the cube.
Rectangular Parallelepiped Volume = abc; surface area = 2(ab + ac + bc);
diagonal = a 2 + b 2 + c 2 , where a, b, and c are the lengths of the sides.
Prism Volume = (area of base) × (altitude); lateral surface area =
(perimeter of right section) × (lateral edge).
Pyramid Volume = ⅓ (area of base) × (altitude); lateral area of regular pyramid = ½ (perimeter of base) × (slant height) = ½ (number of sides)
(length of one side) (slant height) .
Frustum of Pyramid It is formed from the pyramid by cutting off the
top with a plane
V = 1 3 ( A1 + A2 + A1 ⋅ A2 )h
where h = altitude and A1 and A2 are the areas of the base; lateral area of a
regular figure = ½ (sum of the perimeters of base) × (slant height) .
FIG. 3-8 Catenary .
3-8
MATHEMATICS
Volume and Surface Area of Regular Polyhedra with Edge l
Type of surface
4 equilateral triangles
6 squares
8 equilateral triangles
12 pentagons
20 equilateral triangles
Name
Tetrahedron
Hexahedron (cube)
Octahedron
Dodecahedron
Icosahedron
Volume
0.1179l3
1.0000l3
0.4714l3
7.6631l3
2.1817l3
Surface area
1.7321l2
6.0000l2
3.4641l2
20.6458l2
8.6603l2
SOLIDS BOUnDED BY CURVED SURFACES
Cylinders (Fig. 3-9) V = (area of base) × (altitude); lateral surface area =
(perimeter of right section) × (lateral edge).
Right Circular Cylinder V = π (radius)2 × (altitude); lateral surface area =
2π (radius) × (altitude).
Truncated Right Circular Cylinder
V = πr2h
lateral area = 2πrh
h = ½ (h1 + h2)
Hollow Cylinders Volume = πh(R2 - r2), where r and R are the internal
and external radii, respectively, and h is the height of the cylinder.
Sphere See Fig. 3-10.
V (sphere) = 4∕3πR3 = 1∕6πD3
V (spherical sector) = ⅔πR2h1
V (spherical segment of one base) = 1∕6πh1(3 r 22 + h 21)
V (spherical segment of two bases) = 1∕6πh2(3 r 21+ 3 r 22 + h 22 )
A (sphere) = 4πR2 = πD2
A (zone) = 2πRh = πDh
A (lune on surface included between two great circles, with inclination of
q radians) = 2R2q .
Cone V = ⅓ (area of base) × (altitude) .
Right Circular Cone V = (π/3)r2h, where h is the altitude and r is the
radius of the base; curved surface area = πr r 2 + h 2 , curved surface of
the frustum of a right cone = π(r1 + r2 ) h 2 + (r1 − r2 )2 , where r1 and r2 are the
radii of the base and top, respectively, and h is the altitude; volume of the
the frustum of a right cone = π(h/3) (r 21 + r1r2 + r 22) = h/3 ( A1 + A2 + A1 A2 ),
where A1 = area of base and A2 = area of top .
Ellipsoid V = (4∕3)πabc, where a, b, and c are the lengths of the semiaxes .
Torus (obtained by rotating a circle of radius r about a line whose distance is R > r from the center of the circle)
V = 2π2Rr2
Surface area = 4π2Rr
Prolate Spheroid ( formed by rotating an ellipse about its major axis 2a)
Surface area = 2πb2 + 2π(ab/e) sin-1 e
b2 1 + e
ln
1−e
e
Hemisphere V =
V = 4∕3πa2b
π 3
D
12
π
A = D2
2
For a hemisphere (concave up) partially filled to a depth h1, use the formulas
for spherical segment with one base, which simplify to
V = πh 21(R - h1/3) = πh 21 (D/2 - h1/3)
A = 2πRh1 = πDh1
For a hemisphere (concave down) partially filled from the bottom, use
the formulas for a spherical segment of two bases, one of which is a plane
through the center, where h = distance from the center plane to the surface
of the partially filled hemisphere .
V = πh(R2 - h2/3) = πh(D2/4 - h2/3)
A = 2πRh = πDh
Cone For a cone partially filled, use the same formulas as for right circular cones, but use r and h for the region filled .
Ellipsoid If the base of a vessel is one-half of an oblate spheroid (the
cross section fitting to a cylinder is a circle with radius of D/2 and the minor
axis is smaller), then use the formulas for one-half of an oblate spheroid .
V = 0 .1745D3
V = 0 .1309D3
S = 1 .236D2
S = 1 .084D2
minor axis = D/3
minor axis = D/4
MISCELLAnEOUS FORMULAS
See also “Differential and Integral Calculus .”
Volume of a Solid Revolution (the solid generated by rotating a plane
area about the x axis)
V = π ∫ [ f ( x )]2 dx
b
a
where y = f (x) is the equation of the plane curve and a ≤ x ≤ b.
Area of a Surface of Revolution
S = 2 π ∫ y ds
b
a
where ds = 1 + (dy /dx )2 dx and y = f ( x ) is the equation of the plane curve
rotated about the x axis to generate the surface .
Area Bounded by f (x), the x Axis, and the Lines x = a, x = b
A=
∫
b
a
f ( x ) dx
[ f ( x ) ≥ 0]
Length of Arc of a Plane Curve
If y = f (x),
Length of arc s =
V = 4∕3πab2
where a and b are the major and minor axes and e = eccentricity (e < 1) .
Oblate Spheroid ( formed by the rotation of an ellipse about its minor
axis 2b)
Surface area = 2 πa 2 + π
For process vessels, the formulas reduce to the following:
∫
b
a
2
dy
1 + dx
dx
If x = f (t), y = g(t),
Length of arc s =
∫
t1
t0
2
2
dx dy
+ dt
dt dt
In general, (ds)2 = (dx)2 + (dy)2 .
IRREGULAR AREAS AnD VOLUMES
Irregular Areas Let y0, y1, …, yn be the lengths of a series of equally
spaced parallel chords and h be their distance apart (Fig . 3-11) . The area of
the figure is given approximately by any of the following:
FIG. 3-9 Cylinder .
FIG. 3-10 Sphere .
FIG. 3-11 Irregular area .
ELEMEnTARY ALGEBRA
AT = (h/2)[(y0 + yn) + 2(y1 + y2 + + yn-1)]
As = (h/3)[(y0 + yn) + 4(y1 + y3 + y5 + + yn-1)
+ 2(y2 + y4 + + yn-2)]
(trapezoidal rule)
(n even, Simpson’s rule)
3-9
The greater the value of n, the greater the accuracy of the approximation.
Irregular Volumes To find the volume, replace the y’s by cross-sectional
areas Aj and use the results in the preceding equations.
ELEMEnTARY ALGEBRA
References: Stillwell, J., Elements of Algebra, Springer-Verlag, New York, 2010; Rich, B.,
and P. Schmidt, Schaum’s Outline of Elementary Algebra, 3d ed., McGraw-Hill Education,
New York, 2009.
OPERATIOnS On ALGEBRAIC EXPRESSIOnS
An algebraic expression will be denoted here as a combination of letters and
numbers such as
3ax - 3xy + 7x2 + 7x3/2 - 2.8xy
Addition and Subtraction Only like terms can be added or subtracted
in two algebraic expressions.
Example (3x + 4xy - x2) + (3x2 + 2x - 8xy) = 5x - 4xy + 2x2.
Multiplication Multiplication of algebraic expressions is term by term,
and corresponding terms are combined.
Example (2x + 3y - 2xy)(3 + 3y) = 6x + 9y + 9y2 - 6xy2.
Division This operation is analogous to that in arithmetic.
Example Divide 3e2x + ex + 1 by ex + 1.
Divisor e x + 1
Dividend
| 3e 2x + e x + 1
n
n!
where =
= number of combination of n things taken j at a time
j j !(n − j )!
and n! = 1 ⋅ 2 ⋅ 3 ⋅ 4 … n, 0! = 1.
Example ( x + y ) 4 = x 4 + 4 x 3 y + 6 x 2 y 2 + 4 xy 3 + y 4.
If n is not a positive integer, the sum formula no longer applies and an
infinite series results for (a + b)n.
Example (1 + x)1/2 = 1 + ½x - ½ ⋅ ¼x2 + ½ ⋅ ¼ ⋅ 3∕6 x3 … (convergent for
x2 < 1) . Additional discussion can be found under “Infinite Series .”
PROGRESSIOnS
An arithmetic progression is a succession of terms such that each term,
except the first, is derivable from the preceding by the addition of a quantity d,
called the common difference . All arithmetic progressions have the form a,
a + d, a + 2d, a + 3d, … . With a = first term, l = last term, d = common
difference, n = number of terms, and s = sum of the terms, the following
relations hold:
s n −1
l = a + (n − 1)d = +
d
n
2
n
n
n
s = [2 a + (n − 1)d ] = (a + l ) = [2 l − (n − 1)d ]
2
2
2
s (n − 1)d 2 s
= −l
a = l − (n − 1)d = −
2
n
n
l − a 2( s − an ) 2(nl − s )
=
=
d=
n − 1 n (n − 1) n (n − 1)
l −a
2s
+1=
n=
d
l +a
3e x − 2 quotient
3e 2x + 3e x
− 2e x + 1
−2 e x − 2
+ 3 (remainder)
Therefore, 3e2x + ex + 1 = (ex + 1)(3ex - 2) + 3.
Operations with Zero All numerical computations (except division)
can be done with zero. Both a/0 and 0/0 have no meaning.
Fractional Operations
−x x −x
x
x −x
x ax
if a ≠ 0
− = − =
=
=
=
y
y −y
y ay
−y −y y
x z xz
x z x±z
x /y x t xt
± =
= =
=
y y
y
y
t
yt
z /t y z yz
Factoring It is that process of analysis consisting of reducing a given
expression to the product of two or more simpler expressions, called factors.
Some of the more common expressions are factored here:
(1) x2 - y2 = (x - y)(x + y)
(2) x2 + 2xy + y2 = (x + y)2
(3) x3 - y3 = (x - y)(x2 + xy + y2)
(4) x3 + y3 = (x + y)(x2 - xy + y2)
(5) x4 - y4 = (x - y)(x + y)(x2 + y2)
(6) x5 + y5 = (x + y)(x4 - x3y + x2y2 - xy3 + y4)
(7) xn - yn = (x - y)(xn -1 + xn -2y + xn -3y2 + … + yn -1)
Laws of Exponents
(a n )m = a nm ; a n + m = a n ⋅ a m ; a n/m = (a n )1/m ; a n − m = a n /a m ; a 1/m = m a ;
a 1/2 = a ; x 2 = | x | (absolute value of x ). For x > 0, y > 0, xy = x y ;
The arithmetic mean or average of two numbers a and b is (a + b)/2 and of
n numbers a1, …, an is (a1 + a2 + … + an)/n.
A geometric progression is a succession of terms such that each term,
except the first, is derivable from the preceding by the multiplication of a
quantity r called the common ratio . All such progressions have the form a, ar,
ar2, …, ar n-1 . With a = first term, l = last term, r = ratio, n = number of terms,
and s = sum of the terms, the following relations hold:
l = ar n −1 =
s=
a (r n − 1) a (1 − r n ) rl − a lr n − l
=
=
=
r −1
r − 1 r n − r n −1
1− r
a=
s−a
(r − 1) s
log l − log a
l
=
,r =
, log r =
n −1
rn−l rn −1
s−l
n=
log[ a + (r − 1) s ] − log a
log l − log a
+1 =
log r
log r
The geometric mean of two nonnegative numbers a and b is ab ; of n
numbers is (a1a2 … an)1/n . The geometric mean of a set of positive numbers
is less than or equal to the arithmetic mean .
Example Find the sum of 1 + ½ + ¼ + … + 1∕64 . Here a = 1, r = ½, n = 7 . Thus
for x > 0 n x m = x m/n ; n 1/x = 1/ n x
s=
BInOMIAL THEOREM
+
1
2
( 1 64 ) − 1
= 127/64
1 −1
2
s = a + ar + ar 2 + + ar n −1 =
If n is a positive integer, then
(a + b)n = a n + na n−1b +
a + (r − 1) s (r − 1) sr n − 1
=
r
rn −1
n (n − 1) n−2 2
a b
2!
n
n n− j j
n (n − 1) (n − 2) n−3 3
a b
a b + + b n = ∑
j
3!
j = 0
If | r | < 1,
then
lim s =
n →∞
a
ar n
−
1− r 1− r
a
1−r
which is called the sum of the infinite geometric progression .
3-10
MATHEMATICS
Example The present worth (PW) of a series of cash flows Ck at the end
of year k is
n
PW = ∑
k =1
Ck
(1 + i ) k
where i is an assumed interest rate. (Thus the present worth always requires
specification of an interest rate.) If all the payments are the same, Ck = R,
then the present worth is
n
PW = R ∑
k =1
1
(1 + i ) k
This can be rewritten as
PW =
R
1+ i
n
1
∑ (1 + i )
k =1
k -1
=
R
1+ i
n -1
1
∑ (1 + i )
j =0
j
This is a geometric series with r = 1/(1 + i) and a = R/(1 + i). The formulas
above give
PW (= s ) =
R (1 + i )n − 1
i (1 + i )n
The same formula applies to the value of an annuity (PW) now, to provide
for equal payments R at the end of each of n years, with interest rate i.
A progression of the form a, (a + d)r, (a + 2d)r2, (a + 3d)r3, etc., is a combined arithmetic and geometric progression. The sum of n such terms is
s=
a − [ a + (n − 1)d ]r n rd (1 − r n − 1 )
+
2
1− r
(1 − r )
a
+ rd /(1 − r )2 .
1− r
The nonzero numbers a, b, c, etc., form a harmonic progression if their
reciprocals 1/a, 1/b, 1/c, etc., form an arithmetic progression.
Example The progression 1, ⅓, 1∕5, 1∕7, …, 1∕31 is harmonic since 1, 3, 5,
7, …, 31 form an arithmetic progression .
The harmonic mean of two numbers a and b is 2ab/(a + b) .
Quadratic Equations Every quadratic equation in one variable is
expressible in the form ax2 + bx + c = 0, a ≠ 0 . This equation has two solutions, say, x1 and x2, given by
x 1 −b ± b 2 − 4 ac
=
x 2
2a
If a, b, and c are real, the discriminant b2 - 4ac gives the character of the
roots . If b2 - 4ac > 0, the roots are real and unequal . If b2 - 4ac < 0, the roots
are complex conjugates . If b2 - 4ac = 0, the roots are real and equal. Two quadratic equations in two variables in general can be solved only by numerical
methods (see Numerical Analysis and Approximate Methods) .
Cubic Equations A cubic equation in one variable has the form x3 +
bx2 + cx + d = 0 . Every cubic equation having complex coefficients has three
complex roots . If the coefficients are real numbers, then at least one of the
roots must be real . The cubic equation x3 + bx2 + cx + d = 0 may be reduced
by the substitution x = y - b/3 to the form y3 + py + q = 0, where p = ⅓(3c - b2)
and q = 1∕27(27d - 9bc + 2b3) .
This reduced equation has the solutions
y 1 = A + B , y 2 = − 1 2 ( A + B ) + (i 3/2) ( A − B ),
y 3 = − 1 2 ( A + B ) − (i 3/2) ( A − B ), where i 2 = − 1, A = 3 − q /2 + R ,
B = 3 − q /2 − R , and R = ( p /3)3 + (q /2)2 .
If b, c, and d are all real and if R > 0, there are one real root and two conjugate
complex roots; if R = 0, there are three real roots, of which at least two are
equal; if R < 0, there are three real unequal roots . If R < 0, which requires
p < 0, these formulas are impractical . In this case, the roots are given by
y k = 2 − p /3 cos[(ϕ/3) + 120 k ], k = 0, 1, 2 , where
If | r | < 1, lim s =
n →∞
PERMUTATIOnS, COMBInATIOnS, AnD PROBABILITY
Each separate arrangement of all or a part of a set of things is called a permutation .
The number of permutations of n things taken r at a time is written
P (n , r ) =
n!
= n (n − 1) (n − 2) (n − r + 1)
(n − r )!
Each separate selection of objects that is possible irrespective of the order
in which they are arranged is called a combination . The number of combinations of n things taken r at a time is written C(n, r) = n!/[r!(n - r)!] .
An important relation is r!C(n, r) = P(n, r) .
If an event can occur in p ways and can fail to occur in q ways, with all
ways being equally likely, the probability of its occurrence is p/(p + q), and
that of its failure is q/(p + q) .
Example Two dice may be thrown in 36 separate ways . What is the
probability of throwing such that their sum is 7? The number 7 may arise in
6 ways: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1 . The probability of
shooting a 7 is 1⁄6 .
THEORY OF EQUATIOnS
Linear Equations A linear equation is one of the first degree (i .e ., only
the first powers of the variables are involved), and the process of obtaining
definite values for the unknown is called solving the equation . Every linear
equation in one variable is written Ax + B = 0 or x = -B/A. Linear equations
in n variables have the form
a11x1 + a12x2 + + a1nxn = b1
a21x1 + a22x2 + + a2nxn = b2
am1x1 + am2x2 + + amnxn = bm
The solution of the system may then be found by elimination or matrix
methods if a solution exists (see Matrix Algebra and Matrix Computations) .
φ = cos−1
q 2 /4
− p 3 /27
and the negative sign applies if q > 0, and the positive sign applies if q < 0 .
Example Many equations of state involve solving cubic equations for
the compressibility factor Z . For example, the Soave-Redlich-Kwong equation of state requires solving
Z3 - Z2 + cZ + d = 0
d<0
where c and d depend on critical constants of the chemical species and temperature and pressure . In this case, only positive solutions, Z > 0, are desired .
Quartic Equations See Olver et al . (2010) in General References .
General Polynomials of the nth Degree If n > 4, there is no formula
that gives the roots of the general equation . The roots can be found numerically (see “Numerical Analysis and Approximate Methods”) .
Fundamental Theorem of Algebra Every polynomial of degree n has
exactly n real or complex roots, counting multiplicities .
Determinants Consider the system of two linear equations
a11x1 + a12x2 = b1
a21x1 + a22x2 = b2
If the first equation is multiplied by a22 and the second by -a12 and the
results are added, we obtain
(a11a22 - a21a12)x1 = b1a22 - b2a12
The expression a11a22 - a21a12 may be represented by the symbol
a11
a21
a12
= a11a22 − a21a12
a22
This symbol is called a determinant of second order . The value of the square
array of n2 quantities aij, where i = 1, …, n, is the row index, j = 1, …, n. The
column index, written in the form
a11
a12
a13 ⋯ a1n
a
| A | = 21
⋮
an 1
a22
⋯⋯a2 n
an 2
an 3 ⋯ ann
AnALYTIC GEOMETRY
is called a determinant. The n2 quantities aij are called the elements of the
determinant. In the determinant |A|, let the ith row and jth column be
deleted and a new determinant be formed having n - 1 rows and columns.
This new determinant is called the minor of aij, denoted Mij.
Example
a11
a21
a31
a12
a22
a32
a13
a11
a23 The minor of a23 is M 23 =
a31
a33
The cofactor Aij of the element aij is the signed minor of aij determined
by the rule Aij = (-1)i+ jMij. The value of |A| is obtained by forming any of the
n
n
equivalent expressions ∑ j = 1 aij Aij, ∑ i = 1 aijAij, where the elements aij must be
taken from a single row or a single column of A.
Example
a11
a21
a31
a12
a22
a32
a13
a23 = a31 A31 + a32 A32 + a33 A33
a33
= a31
a12
a22
a13
a11
− a32
a23
a21
In general, Aij will be determinants of order n - 1, but they may in turn be
expanded by the rule. Also,
n
∑a
j =1
a12
a32
a13
a11
+ a33
a23
a21
a12
a22
3-11
ji
| A | i = k
n
A jk = ∑ aij A jk =
0 i ≠ k
j =1
Fundamental Properties of Determinants
1. The value of a determinant |A| is not changed if the rows and columns
are interchanged.
2. If the elements of one row (or one column) of a determinant are all
zero, the value of |A| is zero.
3. If the elements of one row (or column) of a determinant are multiplied
by the same constant factor, the value of the determinant is multiplied by
this factor.
4. If one determinant is obtained from another by interchanging any two
rows (or columns), the value of either is the negative of the value of the other.
5. If two rows (or columns) of a determinant are identical, the value of the
determinant is zero.
6. If two determinants are identical except for one row (or column), the
sum of their values is given by a single determinant obtained by adding corresponding elements of dissimilar rows (or columns) and leaving unchanged
the remaining elements.
7. The value of a determinant is not changed if one row (or column) is
multiplied by a constant and added to another row (or column).
AnALYTIC GEOMETRY
References: Gersting, J. L., Technical Calculus with Analytic Geometry, Dover,
Mineola, N.Y., 2010.
Analytic geometry uses algebraic equations and methods to study geometric problems. It also permits one to visualize algebraic equations in terms of
geometric curves, which frequently clarifies abstract concepts.
PLAnE AnALYTIC GEOMETRY
Coordinate Systems The basic concept of analytic geometry is the
establishment of a one-to-one correspondence between the points of the
plane and number pairs (x, y). This correspondence may be done in a number of ways. The rectangular or cartesian coordinate system consists of two
straight lines intersecting at right angles (Fig. 3-12). A point is designated by
(x, y). Another common coordinate system is the polar coordinate system
(Fig. 3-13). In this system the position of a point is designated by the pair
(r, q), with r = x 2 + y 2 being the distance to the origin O(0, 0) and q being
the angle the line r makes with the positive x axis (polar axis). To change
from polar to rectangular coordinates, use x = r cos q and y = r sin q. To
change from rectangular to polar coordinates, use r = x 2 + y 2 and q = tan-1
(y/x) if x ≠ 0; q = π/2 if x = 0. The distance between two points (x1, y1) and
(x2, y2) is defined by d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 in rectangular coordinates or
by d = r 21 + r 22 − 2 r1r2 cos (θ1 − θ2 ) in polar coordinates. Other coordinate systems are sometimes used. For example, on the surface of a sphere, latitude
and longitude prove useful.
Straight Line See Fig. 3-14. The slope m of a straight line is the tangent
of the inclination angle q made with the positive x axis. If (x1, y1) and (x2, y2)
are any two points on the line, then slope = m = (y2 - y1)/(x2 - x1). The slope
of a line parallel to the x axis is zero; the slope of a line parallel to the y axis
is undefined. Two lines are parallel if and only if they have the same slope.
Two lines are perpendicular if and only if the product of their slopes is -1
(the exception being that case when the lines are parallel to the coordinate
axes). Every equation of the type Ax + By + C = 0 represents a straight line,
and every straight line has an equation of this form. A straight line is determined by a variety of conditions:
FIG. 3-14 Straight line.
Given conditions
Equation of line
1. Parallel to x axis
2. Parallel to y axis
3. Point (x1, y1) and slope m
4. Intercept on y axis (0, b), m
5. Intercept on x axis (a, 0), m
6. Two points (x1, y1), (x2, y2)
7. Two intercepts (a, 0), (0, b)
y = constant
x = constant
y - y1 = m(x - x1)
y = mx + b
y = m(x - a)
y −y
y − y 1 = 2 1 ( x − x1 )
x 2 − x1
x/a + y/b = 1
The angle b that a line with slope m1 makes with a line having slope m2 is
given by tan b = (m2 - m1)/(m1m2 + 1). The distance from a point (x1, y1) to a
line with equation Ax + By + C = 0 is
d=
| Ax 1 + By 1 + C |
A2 + B 2
Occasionally some nonlinear algebraic equations can be reduced to linear
equations under suitable substitutions or changes of variables.
Example Consider y = bxn and B = log b. Taking logarithms gives log y =
n log x + log b. Let Y = log y, X = log x, and B = log b. The equation then has
the form Y = nX + B, which is a linear equation. Consider k = k0 exp (-E/RT);
taking logarithms gives ln k = ln k0 - E/(RT). Let
Y = ln k, B = ln k0, m = -E/R, and X = 1/T, and the result is Y = mX + B.
II
I
III
IV
FIG. 3-12
Rectangular coordinates.
FIG. 3-13 Polar coordinates.
Asymptotes The limiting position of the tangent to a curve, as the
point of contact tends to an infinite distance from the origin, is called an
asymptote.
Conic Sections The curves included in this group are obtained from
plane sections of the cone. They include the circle, ellipse, parabola, hyperbola, and degeneratively the point and straight line. A conic is the locus of
a point whose distance from a fixed point called the focus is in a constant
3-12
MATHEMATICS
ratio to its distance from a fixed line, called the directrix. This ratio is the
eccentricity e. If e = 0, the conic is a circle; if 0 < e < 1, the conic is an ellipse;
if e = 1, the conic is a parabola; if e > 1, the conic is a hyperbola. Every conic
section is representable by an equation of second degree. Conversely, every
equation of second degree in two variables represents a conic. The general
equation of the second degree is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Let Δ be
defined as the determinant
2A B
∆ = B 2C
D
E
Δ≠0
Δ=0
AΔ < 0, A ≠ C, an ellipse
AΔ < 0, A = C, a circle
AΔ > 0, no locus
4
3
4 −4 −2
3
−2
= −596 ≠ 0, B 2 − 4 AC = 40 > 0
14
Polar equation
B2 - 4AC = 0
B2 - 4AC > 0
Parabola
Hyperbola
Two parallel lines if
Q = D2 + E2 - 4(A + C)F > 0
One straight line if Q = 0
no locus if Q < 0
Point
6
∆=
The curve is therefore a hyperbola.
D
E
2F
The table characterizes the curve represented by the equation.
B2 - 4AC < 0
Example 3x2 + 4xy - 2y2 + 3x - 2y + 7 = 0.
Two intersecting
straight lines
Type of curve
(1) r = a
(2) r = 2a cos q
(3) r = 2a sin q
(4) r2 - 2br cos (q - b) + b2 - a2 = 0
(5) r =
ke
1 − e cos θ
Circle, Fig. 3-20
Circle, Fig. 3-21
Circle, Fig. 3-22
Circle at (b, b), radius a
e = 1 parabola, Fig. 3-17
0 < e <1 ellipse, Fig. 3-16
e > 1 hyperbola, Fig. 3-18
Parametric Equations It is frequently useful to write the equations of
a curve in terms of a parameter. For example, a circle of radius a, center at (0, 0),
can be written in the equivalent form x = a cos f, y = a sin f, where f is the
parameter. Similarly, x = a cos f and y = b sin f are the parametric equations
of the ellipse x2/a2 + y2/b2 = 1 with parameter f.
SOLID AnALYTIC GEOMETRY
(1) ( x − h)2 + ( y − k )2 − a 2
x = h + acos θ
y = k + asin θ
(2)
( x − h)2 ( y − k )2
+
=1
a2
b2
x = h + a cos φ
y = k + a sin φ
−at
x = 2
t +1
y = a
t 2 +1
(3) x 2 + y 2 = a 2
Circle (Fig. 3-15) parameter
is angle q
Ellipse (Fig. 3-16) parameter
is angle q
dy
=
dx
slope of tangent at (x, y)
Circle parameter is t =
(4) x 2 = y + k
Parabola (Fig. 3-17)
x2 y2
(5) 2 − 2 = 1
a b
x
(6) y = a cosh
a
Hyperbola with the origin
at the center (Fig. 3-18)
s
x = a sinh−1
a
2
2
2
y =a +s
x = a (φ − sin φ)
y = a (1 − cos φ)
(7) Cycloid
FIG. 3-15
Catenary (such as hanging
cable under gravity)
Parameter s = arc length
from (0, a) to (x, y)
(Fig. 3-19)
FIG. 3-16 Ellipse, 0 < e < 1.
Circle.
FIG. 3-19 Cycloid.
Coordinate Systems There are three commonly used coordinate systems.
Others may be used in specific problems (see Morse, P. M., and H. Feshbach,
Methods of Theoretical Physics, vols. 1 and I2, McGraw-Hill, New York, 1953).
The rectangular (cartesian) system (Fig. 3-23) consists of mutually orthogonal axes x, y, and z. A triple of numbers (x, y, z) is used to represent each
point. The cylindrical coordinate system (r, q, z; Fig. 3-24) is frequently used
to locate a point in space. These are essentially the polar coordinates (r, q)
coupled with the z coordinate. As before, x = r cos q, y = r sin q, z = z and
r2 = x2 + y2, y/x = tan q. If r is held constant and q and z are allowed to vary,
the locus of (r, q, z) is a right circular cylinder of radius r along the z axis. The
locus of r = C is a circle, and q = constant is a plane containing the z axis and
making an angle q with the xz plane. Cylindrical coordinates are convenient
to use when the problem has an axis of symmetry.
The spherical coordinate system is convenient if there is a point of symmetry in the system. This point is taken as the origin and the coordinates
(r, f, q) are illustrated in Fig. 3-25. The relations are x = r sin f cos q,
y = r sin f sin q, z = r cos f, and r = r sin f. Also q = constant is a plane
containing the z axis and making an angle q with the xz plane; f = constant
is a cone with vertex at 0; r = constant is the surface of a sphere of radius r,
center at the origin 0. Every point in the space may be given spherical
coordinates restricted to the ranges 0 ≤ f ≤ π, r ≥ 0, 0 ≤ q < 2π.
Lines and Planes The distance between two points ( x 1 , y 1 , z1 ),
(x2, y2, z2) is d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 + ( z1 − z 2 )2 . There is nothing in the
geometry of three dimensions quite analogous to the slope of a line in
FIG. 3-17
Parabola, e = 1.
FIG. 3-20 Circle center (0, 0), r = a.
FIG. 3-18 Hyperbola, e > 1.
FIG. 3-21 Circle center (a, 0), r = 2a cos q.
AnALYTIC GEOMETRY
FIG. 3-22
Circle center (0, a), r = 2a sin θ.
3-13
Space Curves Space curves are usually specified as the set of points
whose coordinates are given parametrically by a system of equations x = f (t),
y = g(t), z = h(t) in the parameter t.
Example The equation of a straight line in space is (x - x1)/a = (y - y1)/b =
(z - z1)/c. Since all these quantities must be equal (say, to t), we may write
x = x1 + at, y = y1 + bt, and z = z1 + ct, which represent the parametric equations of the line.
Example The equations z = a cos βt, y = a sin βt, and z = bt, with a, β, and
b positive constants, represent a circular helix.
Surfaces The locus of points (x, y, z) satisfying f (x, y, z) = 0, broadly
speaking, may be interpreted as a surface. The simplest surface is the plane.
The next simplest is a cylinder.
Example The parabolic cylinder y = x2 (Fig. 3-26) is generated by a
straight line parallel to the z axis passing through y = x2 in the plane z = 0.
A surface whose equation is a quadratic in the variables x, y, and z is called a
quadric surface. Some of the more common such surfaces are tabulated and
pictured in Figs. 3-26 to 3-34.
FIG. 3-23 Cartesian coordinates.
FIG. 3-27 Ellipsoid.
FIG. 3-24 Cylindrical coordinates.
FIG. 3-25
FIG. 3-26
Parabolic cylinder.
FIG. 3-28
Hyperboloid of one sheet.
x 2 y 2 z2
+
+ = 1 (sphere if a = b = c )
a 2 b2 c 2
Spherical coordinates.
the plane. Instead of specifying the direction of a line by a trigonometric
function evaluated for one angle, a trigonometric function evaluated for
three angles is used. The angles α, β, and γ that a line segment makes with
the positive x, y, and z axes, respectively, are called the direction angles of the
line, and cos α, cos β, and cos γ are called the direction cosines. Let (x1, y1, z1)
and (x2, y2, z2) be on the line. Then cos α = (x2 - x1)/d, cos β = (y2 - y1)/d, and
cos γ = (z2 - z1)/d, where d = the distance between the two points. Clearly
cos2 α + cos2 β + cos2 γ = 1. If two lines are specified by the direction cosines
(cos α1, cos β1, cos γ1) and (cos α2, cos β2, cos γ2), then the angle θ between the
lines is cos θ = cos α1 cos α2 + cos β1 cos β2 + cos γ1 cos γ2. Thus the lines are
perpendicular if and only if θ = 90° or cos α1 cos α2 + cos β1 cos β2 + cos γ1
cos γ2 = 0. The equation of a line with direction cosines (cos α, cos β, cos γ)
passing through (x1, y1, z1) is (x - x1)/cos α = (y - y1)/cos β = (z - z1)/cos γ.
The equation of every plane is of the form Ax + By + Cz + D = 0. The
numbers
A
B
C
,
,
A2 + B 2 + C 2
A2 + B 2 + C 2
A2 + B 2 +C 2
x 2 y 2 z2
+ − =1
a2 b2 c 2
FIG. 3-29
Hyperboloid of two sheets.
x 2 y 2 z2
+ − = −1
a 2 b2 c 2
are direction cosines of the normal lines to the plane. The plane through the
point (x1, y1, z1) whose normals have these as direction cosines is A(x - x1) +
B(y - y1) + C(z - z1) = 0.
Example Find the equation of the plane through (1, 5, -2) perpendicular to the line (x + 9)/7 = (y - 3)/(-1) = z/8. The numbers (7, -1, 8) are
called direction numbers. They are a constant multiple of the direction
cosines cos α = 7/114, cos β = -1/114, and cos γ = 8/114. The plane has the
equation 7(x - 1) - 1(y - 5) + 8(z + 2) = 0 or 7x - y + 8z + 14 = 0.
The distance from the point (x1, y1, z1) to the plane Ax + By + Cz + D = 0 is
d=
| Ax 1 + By 1 + Cz1 + D |
A2 + B 2 + C 2
FIG. 3-31 Elliptic paraboloid.
x 2 y 2 z2
FIG. 3-30 Cone. 2 + 2 + 2 = 0
a b c
x2 y2
+ + cz = 0
a2 b2
3-14
MATHEMATICS
FIG. 3-32 Hyperbolic paraboloid .
x2 y2
− + cz = 0
a 2 b2
FIG. 3-33
Elliptic cylinder .
x2 y2
+ =1
a 2 b2
PLAnE TRIGOnOMETRY
References: Gelfand, I. M., and M. Saul, Trigonometry, Birkhäuser, Boston, 2001;
Heineman, E. Richard, and J. Dalton Tarwater, Plane Trigonometry, 7th ed., McGraw-Hill,
New York, 1993.
AnGLES
An angle is generated by the rotation of a line about a fixed center from
some initial position to some terminal position. If the rotation is clockwise,
the angle is negative; if it is counterclockwise, the angle is positive. Angle
size is unlimited. If α and b are two angles such that α + b = 90°, they are
complementary; they are supplementary if α + b = 180°. Angles are most
commonly measured in the sexagesimal system or by radian measure. In the
first system there are 360° in 1 complete revolution (1 r); 1° = 1∕90 of a right
angle . The degree is subdivided into 60 minutes; the minute is subdivided
into 60 seconds . In the radian system, 1 radian (1 rad) is the angle at the
center of a circle subtended by an arc whose length is equal to the radius of
the circle . Thus 2π rad = 360°; 1 rad = 57 .29578°; 1° = 0 .01745 rad; 1 min =
0 .00029089 rad . The advantage of radian measure is that it is dimensionless.
The quadrants are conventionally labeled, as Fig . 3-35 shows .
FIG. 3-36 Triangles .
FUnCTIOnS OF CIRCULAR TRIGOnOMETRY
The trigonometric functions of angles are the ratios between the various
sides of the reference triangles shown in Fig . 3-36 for the various quadrants .
Clearly r = x 2 + y 2 ≥ 0. The fundamental functions (see Figs . 3-37, 3-38, 3-39)
are as follows:
Plane Trigonometry
Sine of q = sin q = y/r
Cosine of q = cos q = x/r
Tangent of q = tan q = y/x
FIG. 3-37 Graph of y = sin x.
Secant of q = sec q = r/x
Cosecant of q = csc q = r/y
Cotangent of q = cot q = x/y
FIG. 3-38 Graph of y = cos x.
II
I
III
IV
FIG. 3-35 Quadrants .
FIG. 3-39 Graph of y = tan x.
FIG. 3-34
Hyperbolic cylinder .
x2 y2
− =1
a 2 b2
PLAnE TRIGOnOMETRY
Values of the Trigonometric Functions for Common Angles
1− x2
x
= cot −1
2
x
1− x
sin −1 x = cos−1 1 − x 2 = tan −1
q°
q, rad
sin q
0
30
0
π/6
45
π/4
2/2
60
π/3
3/2
90
π/2
0
1/2
1
cos q
tan q
1
0
3/2
= sec−1
3/3
0
Given a > 0
Required angles are
sin q0 = a
cos q0 = a
tan q0 = a
sin q0 = a
cos q0 = a
tan q0 = a
q0 and 180° - q0
q0 and 360° - q0
q0 and 180° + q0
180° + q0 and 360° - q0
180° - q0 and 180° + q0
180° - q0 and 360° - q0
x
= cot −1
x
1
= sec−1
x
1− x2
= csc−1
π
1
= − sin −1 x
1− x 2 2
tan −1 x = sin −1
= cot −1
Find an acute
angle q0 such that
1− x2
cos−1 x = sin −1 1 − x 2 = tan −1
3
+∞
If 90° ≤ q ≤ 180°, sin q = sin (180° - q); cos q = -cos (180° - q); tan q =
-tan (180° - q). If 180° ≤ q ≤ 270°, sin q = -sin (270° - q); cos q = -cos (270° - q);
tan q = tan (270° - q). If 270° ≤ q ≤ 360°, sin q = -sin (360° - q); cos q =
cos (360° - q); tan q = -tan (360° - q). The reciprocal properties may be used
to find the values of the other functions.
If it is desired to find the angle when a function of it is given, the procedure is as follows: There will in general be two angles between 0° and 360°
corresponding to the given value of the function.
sin q = +a
cos q = +a
tan q = +a
sin q = -a
cos q = -a
tan q = -a
1 π
1
= csc−1 = − cos−1 x
x 2
1− x2
1
2/2
1/2
3-15
x
1
= cos−1
1+ x 2
1− x2
1+ x 2
1
= sec−1 1 + x 2 = csc−1
x
x
RELATIOnS BETWEEn AnGLES
AnD SIDES OF TRIAnGLES
Relations between Functions of a Single Angle sec q = 1/cos q;
csc q = 1/sin q, tan q = sin q/cos q = sec q/csc q = 1/cot q; sin2 q + cos2 q = 1;
1 + tan2 q = sec2 q; 1 + cot2 q = csc2 q. For 0 ≤ q ≤ 90° the following results hold:
Solutions of Triangles (Fig. 3-40) Let a, b, and c denote the sides and
α, b, and γ the angles opposite the sides in the triangle. Let 2s = a + b + c,
A = area, r = radius of the inscribed circle, R = radius of the circumscribed
circle, and h = altitude. In any triangle α + b + γ = 180°.
Law of Sines sin α/a = sin b/b = sin γ/c = 1/(2R).
Law of Tangents
θ
θ
sin θ = 2 sin cos
2
2
a + b tan 1 2 (α + β) b + c tan 1 2 (β + γ) a + c tan 1 2 (α + γ)
=
=
=
;
;
a − b tan 1 2 (α − β) b − c tan 1 2 (β − γ) a − c tan 1 2 (α − γ)
and
θ
θ
cos θ = cos 2 − sin 2
2
2
The cofunction property is very important. cos q = sin (90° - q), sin q = cos
(90° - q), tan q = cot (90° - q), cot q = tan (90° - q), etc.
Functions of Negative Angles sin (-q) = -sin q, cos (-q) = cos q,
tan (-q) = -tan q, sec (-q) = sec q, csc (-q) = -csc q, cot (-q) = -cot q.
Identities
Sum and Difference Formulas Let x, y be two angles. sin (x ± y) = sin x
cos y ± cos x sin y; cos (x ± y) = cos x cos y ∓ sin x sin y ; tan (x ± y) = (tan x ±
tan y)/(1 ∓ tan x tan y); sin x ± sin y = 2 sin ½(x ± y) cos ½(x ∓ y); cos x +
cos y = 2 cos ½(x + y) cos ½(x - y); cos x - cos y = -2 sin ½(x + y) sin ½(x - y);
tan x ± tan y = [sin (x ± y)]/(cos x cos y); sin2 x - sin2 y = cos2 y - cos2 x =
sin (x + y) sin (x - y); cos2 x - sin2 y = cos2 y - sin2 x = cos (x + y) × cos (x - y);
sin (45° + x) = cos (45° - x); sin (45° - x) = cos (45° + x); tan (45° ± x) = cot (45° ∓ x).
Multiple and Half-Angle Identities Let x = angle, sin 2x = 2 sin x cos x;
sin x = 2 sin ½x × cos ½x; cos 2x = cos2 x - sin2x = 1 - 2 sin2 x = 2 cos2 x - 1.
tan 2x = (2 tan x)/(1 - tan2 x); sin 3x = 3 sin x - 4 sin3x; cos 3x = 4 cos3 x - 3 cos x.
tan 3x = (3 tan x - tan3 x)/(1 - 3 tan2 x); sin 4x = 4 sin x cos x - 8 sin3 x cos x;
cos 4x = 8 cos4 x - 8 cos2 x + 1.
x
sin =
2
x
cos =
2
1
2
1
2
(1 − cos x )
(1 + cos x )
1 − cos x
sin x
1 − cos x
x
tan =
=
=
2
1 + cos x 1 + cos x
sin x
Law of Cosines a2 = b2 + c2 - 2bc cos α; b2 = a2 + c2 - 2ac cos b; c2 =
a2 + b2 - 2ab cos γ.
More formulas can be generated by replacing a by b, b by c, c by a, α by b,
b by γ, and γ by α.
1
1
A = bh = ab sin γ = s ( s − a ) ( s − b) ( s − c ) = rs
2
2
where
r=
( s − a ) ( s − b) ( s − c )
s
R = a/(2 sin α) = abc/4A
h = c sin α = a sin γ = 2rs/b
Right Triangle (Fig. 3-41) Given one side and any acute angle α or
any two sides, the remaining parts can be obtained from the following
formulas:
a = (c + b) (c − b) = c sin α = b tan α
b = (c + a ) (c − a ) = c cos α = a cot α
c = a 2 + b2
sin α =
a
c
cos α =
b
c
tan α =
a
b
β = 90° − α
b 2 tan α c 2 sin 2α
1
a2
=
=
A = ab =
2
2 tan α
2
4
InVERSE TRIGOnOMETRIC FUnCTIOnS
Note that y = sin -1 x = arcsin x is the angle y whose sine is x.
Example y = sin-1 (½), y is 30°.
The complete solution of the equation x = sin y is y = (-1)n sin-1 x +
n(180°), -π/2 ≤ sin-1 x ≤ π/2 where sin-1 x is the principal value of the angle
whose sine is x. The range of principal values of cos-1 x is 0 ≤ cos-1 x ≤ π and
-π/2 ≤ tan-1 x ≤ π/2. If these restrictions are allowed to hold, the following
formulas result:
FIG. 3-40 Triangle.
FIG. 3-41 Right triangle.
3-16
MATHEMATICS
HYPERBOLIC TRIGOnOMETRY
The hyperbolic functions are certain combinations of exponentials ex
and e-x.
Inverse Hyperbolic Functions If x = sinh y, then y is the inverse hyperbolic sine of x, written as y = sinh-1 x or arcsinh x. sinh-1 x = ln e ( x + x 2 + 1)
cosh x =
e x + e−x
e x − e−x
sinh x e x − e − x
=
; sinh x =
; tanh x =
cosh x e x + e − x
2
2
1+ x
1
cosh −1 x = ln e ( x + x 2 − 1); tanh −1 x = ln e
;
2
1− x
coth x =
cosh x
ex + ex
1
1
2
=
=
=
; sech x =
;
cosh x e x + e − x
e x − e − x tanh x sinh x
1+ 1− x2
x +1
1
coth −1 x = ln e
; sech −1 x = ln e
;
x
x −1
2
csch x =
1
2
=
sinh x e x − e − x
Fundamental Relationships sinh x + cosh x = ex; cosh x - sinh x = e-x;
cosh2 x - sinh2 x = 1; sech2 x + tanh2 x = 1; coth2 x - csch2 x = 1; sinh 2x = 2 sinh x
cosh x; cosh 2x = cosh2 x + sinh2 x = 1 + 2 sinh2 x = 2 cosh2 x - 1. tanh 2x =
(2 tanh x)/(1 + tanh2 x); sinh (x ± y) = sinh x cosh y ± cosh x sinh y ; cosh (x ± y) =
cosh x cosh y ± sinh x sinh y; 2 sinh2 x/2 = cosh x - 1; 2 cosh2 x/2 = cosh x + 1;
sinh (-x) = -sinh x; cosh (-x) = cosh x; tanh (-x) = -tanh x.
When u = a cosh x and u = a sinh x, then u2 - u2 = a2, which is the equation
for a hyperbola. In other words, the hyperbolic functions in the parametric
equations u = a cosh x and u = a sinh x have the same relation to the hyperbola u2 - u2 = a2 that the equations u = a cos q and u = a sin q have to the
circle u2 + u2 = a2.
1+ 1+ x2
csch −1 = ln e
x
Magnitude of the Hyperbolic Functions cosh x ≥ 1 with equality only
for x = 0; -∞ < sinh x < ∞; -1 < tanh x < 1. cosh x ~ ex/2 as x → ∞; sinh x → ex/2
as x → ∞.
APPROXIMATIOnS FOR TRIGOnOMETRIC FUnCTIOnS
For small values of q (q measured in radians) sin q ≈ q, tan q ≈ q; cos q ≈
1 - q2/2.
DIFFEREnTIAL AnD InTEGRAL CALCULUS
References: Larson, R., and B. H. Edwards, Calculus, 10th ed., Brooks/Cole,
Pacific Grove, Calif., 2013.
exists. This implies continuity at x = a. However, a function may be continuous but not have a derivative. The derivative function is
DIFFEREnTIAL CALCULUS
f ′( x ) =
Limits The limit of function f (x) as x approaches a (a is finite or else x
is said to increase without bound) is the number N.
Differentiation Define Δy = f (x + Δx) - f (x). Then dividing by Δx gives
∆y f ( x + ∆x ) − f ( x )
=
∆x
∆x
lim f ( x ) = N
x →a
This states that f (x) can be calculated as close to N as desirable by making x
sufficiently close to a. This does not put any restriction on f (x) when x = a.
Alternatively, for any given positive number e, a number d can be found such
that 0 < |a - x| < d implies that |N - f (x)| < e.
The following operations with limits (when they exist) are valid:
lim bf ( x ) = b lim f ( x )
x →a
x →a
lim[ f ( x ) + g ( x )] = lim f ( x ) + lim g ( x )
x →a
x →a
x →a
lim[ f ( x ) g ( x )] = lim f ( x ) ⋅ lim g ( x )
x →a
x →a
x →a
f (x )
f ( x ) lim
if lim g ( x ) ≠ 0
lim
= x →a
x →a
x →a g ( x )
lim g ( x )
x →a
See “Indeterminant Forms” below when g(a) = 0.
Continuity A function f (x) is continuous at the point x = a if
lim [ f (a + h) − f (a )] = 0
h→0
Rigorously, it is stated that f (x) is continuous at x = a if for any positive e
there exists a d > 0 such that | f (a + h) - f (a)| < e for all x with |x - a| < d. For
example, the function (sin x)/x is not continuous at x = 0 and therefore is
said to be discontinuous. Discontinuities are classified into three types:
1. Removable
y = (sin x)/x
at x = 0
2. Infinite
y = 1/x
at x = 0
1/x
3. Jump
y = 10/(1 + e )
at x = 0+ y = 0+
x=0y=0
x = 0- y = 10
Derivative The function f (x) has a derivative at x = a, denoted as f ′(a), if
lim
h→0
f (a + h ) − f (a )
h
f ( x + h) − f ( x )
df
= lim
dx h → 0
h
Call
Then
lim
∆x → 0
∆y dy
=
∆ x dx
f ( x + ∆x ) − f ( x )
dy
= lim
dx ∆x → 0
∆x
Differential Operations The following differential operations are valid:
f, g, … are differentiable functions of x; c and n are constants; e is the base of
the natural logarithms.
dc
=0
dx
(3-1)
dx
=1
dx
(3-2)
df dg
d
( f + g) =
+
dx dx
dx
(3-3)
df
dg
d
( f × g) = f
+g
dx
dx
dx
(3-4)
dy
1
=
dx dx /dy
if
dx
≠0
dy
(3-5)
d n
df
f = nf n−1
dx
dx
(3-6)
d f g (df /dx ) − f (dg /dx )
=
dx g
g2
(3-7)
df df d υ
=
×
(chain rule)
dx d υ dx
(3-8)
DIFFEREnTIAL AnD InTEGRAL CALCULUS
df g
=gf
dx
g −1
df
dg
+ f g ln f
dx
dx
(3-10)
d
d
d 2 d 3 d
A
xy +
x+
y =
x +
dx
dx
dx
dx
dx
dy
dy
2x + 3 y 2
=1+ y + x
+0
dx
dx
u = sin x
y = tan x
Then,
d tan x dy dy dx
=
=
d sin x d υ dx d υ
by the rules in Eqs. (3-6), (3-6), (3-2), (3-4), and (3-1), respectively.
Thus
dy 2 x − 1 − y
=
dx
x − 3y2
d tan x
1
dx d sin x
dx
= sec2 x /cos x
dex = ex dx
(3-11)
d(a ) = a lna dx
(3-12)
d ln x = (1/x) dx
(3-13)
x
d log x = (log e/x) dx
(3-14)
d sin x = cos x dx
(3-15)
d cos x = -sin x dx
(3-16)
d tan x = sec x dx
(3-17)
d cot x = -csc2 x dx
(3-18)
d sec x = tan x sec x dx
(3-19)
d csc x = -cot x csc x dx
(3-20)
2
d sin x = (1 - x )
2 –1/2
-1
(3-21)
dx
d cos-1 x = -(1 - x2)–1/2 dx
(3-22)
d tan-1 x = (1 + x2)–1 dx
(3-23)
d cot-1 x = -(1 + x2)–1 dx
(3-24)
d sec-1 x = x–1(x2 - 1)–1/2 dx
(3-25)
d csc x = -x (x - 1)
(3-26)
–1
-1
2
–1/2
dx
d sinh x = cosh x dx
(3-27)
d cosh x = sinh x dx
(3-28)
d tanh x = sech x dx
(3-29)
d coth x = -csch2 x dx
(3-30)
d sech x = -sech x tanh x dx
(3-31)
d csch x = -csch x coth x dx
(3-32)
2
d sinh-1 x = (x2 + 1)–1/2 dx
d cosh = (x - 1)
-1
2
–1/2
(3-33)
d coth x = -(x - 1) dx
2
-1
d sech x = -(1/x)(1 - x )
2 –1/2
-1
d csch x = -x (x + 1)
-1
–1
(3-8)
2
–1/2
dx
If f ′( x ) > 0 on (a, b), then f is increasing on (a, b). If f ′( x ) < 0 on (a, b), then
f is decreasing on (a, b). The graph of a function y = f (x) is concave up if f ′ is
increasing on (a, b); it is concave down if f ′ is decreasing on (a, b). If f ′′( x )
exists on (a, b) and if f ′′( x ) > 0, then f is concave up on (a, b). If f ′′( x ) < 0,
then f is concave down on (a, b).
An inflection point is a point at which a function changes the direction of
its concavity.
Indeterminate Forms: L’Hôpital’s Theorem Forms of the type 0/0,
∞/∞, 0 × ∞, etc., are called indeterminates. To find the limiting values that
the corresponding functions approach, L’Hôpital’s theorem is useful: If two
functions f (x) and g(x) both become zero at x = a, then the limit of their
quotient is equal to the limit of the quotient of their separate derivatives, if
the limit exists, or is +∞ or -∞.
Example Find lim
n→0
lim
Here
x →0
Example Find dy/dx for y = x cos (1 − x ) .
dy
d
d
cos (1 − x 2 ) + cos (1 − x 2 )
= x
dx
dx
dx
d
d
cos (1 − x 2 ) = − sin (1 − x 2 )
(1 − x 2 )
dx
dx
x →∞
Example Find lim (1 − x )1/ x .
x →0
= − sin (1 − x 2 ) (0 − 2 x )
y = (1 − x )1/ x
(3-36)
Then
(3-37)
lim (ln y ) = lim
(3-16)
(3-1), (3-6)
x3
6
= lim x = 0
x →∞ ex
x →∞ e
lim x 3e − x = lim
Let
(3-4)
d sin x
cos x
sin x
dx
/lim = lim
= lim
=1
x →0
x → 0 dx
x →0
x
dx
1
x →∞
x →0
x →0
Using
x
sin x
.
x
Example Find lim x 3e − x .
=
2
(3-17), (3-15)
d 3 f (x )
d n f (x )
d 2 f (x )
df ( x )
= 0 for n ≥ 4
= 9 x 2 + 2,
= 18 x ,
= 18,
2
3
dx
dx n
dx
dx
(3-35)
(3-38)
dx
(3-5)
If the functions and derivatives are known only numerically at some point,
the same formulas may be used.
Higher Differentials The first derivative of f (x) with respect to x is
denoted by f ′ or df/dx. The derivative of the first derivative is called the second derivative of f (x) with respect to x and is denoted by f ′′, f (2), or d 2f/dx2;
and similarly for the higher-order derivatives.
Example Given f (x) = 3x3 + 2x + 1, calculate all derivative values.
(3-34)
dx
d tanh-1 x = (1 - x2)–1 dx
-1
Using
=
Differentials
x
(3-6)
Example Find the derivative of tan x with respect to sin x.
Let
Example Derive dy/dx for x2 + y3 = x + xy + A.
Here
d x 1 −1/2
= x
dx
2
dy
1
= 2 x 3/2 sin (1 − x 2 ) + x −1/2 cos (1 − x 2 )
dx
2
(3-9)
da x
= (ln a ) a x
dx
3-17
Therefore,
ln y = (1/x) ln (1 - x)
ln (1 − x ) lim x →0 ln (1 − x )
=
lim x →0 x
x
d [ln(1 − x )]/dx
dx /dx x =0
x =0
=
1
(−1)
1− x
= −1
x =0
lim y = e −1
x →0
Partial Derivative The abbreviation z = f (x, y) means that z is a
function of the two variables x and y. The derivative of z with respect to x,
treating y as a constant, is called the partial derivative with respect to x and
is usually denoted as ∂z/∂x or ∂f (x, y)/∂x or simply fx . Partial differentiation,
3-18
MATHEMATICS
like full differentiation, is quite simple to apply. Conversely, the solution
of partial differential equations is appreciably more difficult than that of
differential equations.
2
Example Find ∂z/∂x and ∂z/∂y for z = ye x + xe y .
2
2
∂x
∂e x
∂z
+ ey
=y
= 2 xye x + e y
∂x
∂x
∂x
2 ∂y
2
∂e y
∂z
= e x + xe y
+x
= ex
∂y
∂y
∂y
Order of Differentiation It is generally true that the order of differentiation is immaterial for any number of differentiations or variables, provided
the function and the appropriate derivatives are continuous . For z = f (x, y)
it follows that
∂3 f
∂3 f
∂3 f
=
=
2
∂ y ∂x ∂ y ∂x ∂ y ∂x ∂ y 2
MULTIVARIABLE CALCULUS APPLIED TO THERMODYnAMICS
Many of the functional relationships needed in thermodynamics are direct
applications of the rules of multivariable calculus . This section reviews
those rules in the context of the needs of thermodynamics . These ideas
were expounded in one of the classic books on chemical engineering
thermodynamics (see Hougen, O . A ., et al ., Part II, “Thermodynamics,” in
Chemical Process Principles, 2d ed ., Wiley, New York, 1959) .
State Functions State functions depend only on the state of the system,
not on history or how one got there . If z is a function of two variables x and
y, then z(x, y) is a state function, since z is known once x and y are specified .
The differential of z is
dz = M dx + N dy
The line integral
∫ ( M dx + N dy )
c
is independent of the path in xy space if and only if
General Form for Partial Differentiation
1 . Given f (x, y) = 0 and x = g(t), y = h(t) .
Then
∂M ∂N
=
∂ y ∂x
df ∂ f dx ∂ f dy
=
+
dt ∂x dt ∂y dt
and dz is called an exact differential . The total differential can be written as
2
∂z
∂z
dz = dx + dy
∂x y
∂y x
2
∂ 2 f dx dy ∂ 2 f dy ∂ f d 2 x ∂ f d 2 y
d 2 f ∂2 f dx
+
+
=
+
+2
∂ x dt 2 ∂ y dt 2
∂ x ∂ y dt dt ∂ y 2 dt
dt 2 ∂ x 2 dt
Example Find df/dt for f = xy, x = r sin t, and y = r cos t.
∂ ∂z
∂ ∂z
=
∂ y ∂ x y ∂ x ∂ y x
= y (r cos t) + x(-r sin t)
or
= r2 cos2 t - r2 sin2 t
2 . Given f (x, y) = 0 and x = g(t, s), y = h(t, s) .
Rearrangement gives the triple product rule
(∂ y / ∂ x ) z
∂ y ∂z
∂z
∂z ∂x ∂ y
or = − 1 (3-42)
= − = −
∂x y ∂ y z ∂z x
∂x z ∂ y x
(∂ y / ∂ z ) x
∂x y
Differentiation of Composite Function
∂ f /∂x
dy
=−
dx
∂ f /∂y
Rule 2.
Given f (u) = 0 where u = g(x), then
∂ f
≠ 0 .
y
∂
du
df
= f ′(u )
dx
dx
2
d 2u
du
d2 f
= f ′′ (u ) + f ′(u ) 2
dx
dx
dx 2
Rule 3.
Given f (u) = 0 where u = g(x, y), then
2
∂2 f
∂2 u
∂u
= f ′′ + f ′ 2
2
∂x
∂x
∂x
2
(3-41)
∂z
∂z
0 = dx + dy
∂ y x z
∂ x y
∂ f ∂ f ∂x ∂ f ∂y
=
+
∂s ∂x ∂s ∂y ∂s
Given f (x, y) = 0, then
∂2 z
∂2 z
=
∂ y ∂x ∂x ∂ y
Example Suppose z is constant and apply Eq . (3-40) .
∂ f ∂ f ∂x ∂ f ∂y
=
+
∂t ∂x ∂t ∂y ∂t
Rule 1.
(3-40)
and thus the following application of Eq . (3-39) guarantees path
independence .
df ∂( xy ) d ρ sin t ∂( xy ) d ρ cos t
=
+
∂ y dt
∂ x dt
dt
Then
(3-39)
2
∂ f
∂ u ∂u
∂ u
= f ′′
+ f′
∂x ∂ y
∂x ∂ y
∂x ∂ y
Alternatively, divide Eq . (3-40) by dy when holding some other variable w
constant to obtain
∂z ∂z ∂x ∂z
∂ y = ∂ x ∂ y + ∂ y
y
w
w
x
(3-43)
Also divide both numerator and denominator of a partial derivative by dw
while holding a variable y constant to get the chain rule .
(∂ z / ∂w ) y ∂ z ∂w
∂z
=
=
∂ x y (∂ x / ∂w ) y ∂w y ∂ x y
(3-44)
Thermodynamic State Functions In thermodynamics, the state
functions include the internal energy U, enthalpy H, and Helmholtz and
Gibbs free energies A and G, respectively, defined as follows:
H = U + PV
A = U - TS
G = H - TS = U + PV - TS = A + PV
2
∂u
∂2 f
∂2 u
= f ′′ + f ′ 2
2
∂y
∂y
∂y
where S is the entropy, T the absolute temperature, P the pressure, and V
the volume . These are also state functions, in that the entropy is specified
DIFFEREnTIAL AnD InTEGRAL CALCULUS
once two variables (such as T and P) are specified, for example. Likewise, V is
specified once T and P are specified; it is therefore a state function.
In an open system, extensive properties, such as the total internal
energy, are functions of two thermodynamic variables plus the mass or
moles of each component. The mathematical derivations below are for a
single-component system of constant mass. They are applicable when
the mass stays constant, i.e., in an intensive system (or else an additional
variable for moles N must be added). However, the relations between the
thermodynamic variables can be regarded as internal energy per moles in a
closed system, or at a point in an open system. The formulas illustrate the
use of calculus in thermodynamics.
If a process is reversible and only P-V work is done, the first law and differentials can be expressed as follows:
dU = T dS - P dV
(3-45)
dH = T dS + V dP
(3-46)
dA = -S dT - P dV
(3-47)
dG = -S dT + V dP
(3-48)
Alternatively, if the internal energy is considered a function of S and V, then
the differential is
∂U
∂U
dV
dS +
dU =
∂V S
∂S V
This is the equivalent of Eq. (3-43) and gives the following definitions:
∂U
∂U
, P = −
T =
∂V S
∂S V
Since the internal energy is a state function, Eq. (3-44) must be satisfied.
2
2
∂U
∂U
=
∂V ∂S ∂S ∂V
∂P
∂T
= −
∂S V
∂V S
This is
This is one of the Maxwell relations, and the other Maxwell relations can
be derived in a similar fashion by applying Eq. (3-41). See Sec. 4, Thermodynamics, “Constant-Composition Systems.”
Partial Derivatives of Intensive Thermodynamic Functions The
various partial derivatives of the thermodynamic functions can be classified into six groups. In the general formulas below, the variables U, H, A, G,
and S are denoted by Greek letters (these can be extensive properties), while
the variables V, T, and P are denoted by Latin letters (T and P can only be
intensive properties).
Type I (3 possibilities plus reciprocals)
∂a
General:
∂b c
∂P
specific:
∂T V
Equation (3-42) gives
3-19
First evaluate the derivative, using Eq. (3-45).
(∂S / ∂T )V
∂S ∂V
∂V
=−
= −
∂T V ∂S T
(∂S / ∂V )T
∂T S
Then evaluate the numerator and denominator as type II derivatives. Use
Eq. (3-45) and Eq. (3-41) to get (∂S / ∂T )V = C v /T . Use Eqs. (3-47) and (3-41) to
get the Maxwell relation (∂ P / ∂T )V = (∂S / ∂V )T . Finally use Eq. (3-42).
∂V
Cv
Cv ∂ P T
∂V
T
=
= −
∂
∂
∂
V
P
V
∂T S
T
−
∂T P ∂V T
∂T P
These derivatives are of importance for reversible, adiabatic processes (such
as in an ideal turbine or compressor), since then the entropy is constant. An
example is the Joule-Thomson coefficient for constant H.
1
∂V
∂T
−V + T
=
∂T P
∂ P H C p
Type IV (30 possibilities plus reciprocals)
∂α
General:
∂β c
∂G
specific:
∂A p
Use Eq. (3-47) to introduce a new variable T.
(∂G / ∂T ) P
∂G ∂G ∂T
=
=
∂ A P ∂T P ∂ A P (∂ A / ∂T ) P
This operation has created two type II derivatives; using the differential
Eqs. (3-47) and (3-48), we obtain
S
∂G
=
∂ A P S + P (∂V / ∂T ) P
Type V (60 possibilities plus reciprocals)
∂α
General:
∂b β
∂G
specific:
∂P A
Start from the differential for dG. Then we get
∂T
∂G
+V
= − S
∂P A
∂P A
The derivative is type III and can be evaluated by using Eq. (3-42).
(∂ A / ∂ P )T
∂G
+V
=S
∂ P A
(∂ A / ∂T ) P
The two type II derivatives are then evaluated using the differential Eq. (3-47).
(∂V / ∂T ) P
∂V ∂ P
∂P
=−
= −
∂T P ∂V T
(∂V / ∂ P )T
∂T V
Type II (30 possibilities plus reciprocals)
∂α
General:
∂b c
∂G
specific:
∂T V
The differential for G is from Eq. (3-48) or Eq. (3-43) with x → P :
∂P
∂G
= − S + V
∂T V
∂T V
Using the other equations for U, H, A, or S gives the other possibilities.
Type III (15 possibilities plus reciprocals)
∂a
General:
∂b α
∂V
specific:
∂T S
SP (∂V / ∂ P )T
∂G
+V
=
∂ P A S + P (∂V / ∂T ) P
These derivatives are also of interest for free expansions or isentropic
changes.
Type VI (30 possibilities plus reciprocals)
∂α
General:
∂β γ
∂G
specific:
∂A H
We use Eq. (3-44) to obtain two type V derivatives.
(∂G / ∂T ) H
∂G
=
∂ A H (∂ A / ∂T ) H
These can then be evaluated using the procedures for type V derivatives.
3-20
MATHEMATICS
InTEGRAL CALCULUS
2
2
2
⌠ 4 − 9x
dx . Let x = sin θ; then dx = cos θ d θ.
Example Find
2
3
3
x
⌡
Indefinite Integral If f ′( x ) is the derivative of f (x), an antiderivative
of f ′( x ) is f (x). Symbolically, the indefinite integral of f ′(x) is
2
2
⌠ 2/3 1 − sin 2 θ 2
⌠ (2/3) − x
dx = 3
3
cos θ d θ
2
2
2
x
⌡
⌡ (2/3) sin θ 3
∫ f ′( x ) dx = f ( x ) + c
where c is an arbitrary constant to be determined by the problem. By
virtue of the known formulas for differentiation, the following relationships
hold (a is a constant):
∫ (du + d υ + dw ) = ∫ du + ∫ d υ + ∫ dw
(3-49)
= −3 cot θ − 3θ + c by trigonometric transform
∫a dυ = a ∫dυ
(3-50)
=−
∫υ
n
d υ=
∫
υ n +1
+c
n +1
(n ≠ − 1)
dυ
= ln | υ | + c
υ
∫a
υ
∫e
dυ =
υ
aυ
+c
ln a
υ
dυ = e + c
(3-51)
∫ cos υ d υ = sin υ + c
(3-56)
2
+ e x − 10) dx = 3 ∫ x 2 dx + ∫ e x dx − 10 ∫ dx = x 3 + e x − 10 x + c
Example: Constant of Integration By definition the derivative of x3 is
3x2, and x3 is therefore the integral of 3x2. However, if f = x3 + 10, it follows
that f ′ = 3x2, and x3 + 10 is therefore also the integral of 3x2. For this reason
the constant c in ∫3x2 dx = x3 + c must be determined by the problem conditions, i.e., the value of f for a specified x.
Methods of Integration In practice it is rare when generally encountered functions can be directly integrated. For example, the integrand in
∫ sin x dx which appears quite simple has no elementary function whose
derivative is sin x . In general, there is no explicit way of determining
whether a particular function can be integrated into an elementary form.
When they do not exist or cannot be found either from tabled integration
formulas or directly, the only recourse is series expansion, as illustrated
later. Indefinite integrals cannot be solved numerically unless they are redefined as definite integrals (see “Definite Integral”), that is, F (x) = ∫ f (x) dx is
x
indefinite, whereas F ( x ) = ∫ f (t ) dt is definite.
Partial Fractions Rational functions are of the type f (x)/g(x) where f (x)
and g(x) are polynomial expressions of degrees m and n, respectively. If the
degree of f is higher than the degree of g, perform the algebraic division—
the remainder will then be at least one degree less than the denominator.
Consider the following types:
Example Reducible denominator to linear unequal factors.
1
1
=
x 3 − x 2 − 4 x + 4 ( x + 2) ( x − 2) ( x − 1)
A = 1 12
3 x 3 +10 dx = ∫ (3 x 3 + 10)1/2 ( x 2 dx )
Trigonometric Substitution This technique is particularly well adapted
to integrands in the form of radicals. For these the function is transformed
to a trigonometric form. In the latter form they may be more easily recognizable relative to the identity formulas. These functions and their transformations are as follows:
x 2 − a 2 Let x = a sec θ
x 2 + a 2 Let x = a tan θ
2
a −x
2
Let x = a sin θ
=
A ( x − 2) ( x − 1) + B ( x + 2) ( x − 1) + C ( x + 2) ( x − 2)
( x + 2) ( x − 2) ( x − 1)
=
x 2 ( A + B + C ) + x (−3 A + B ) + (2 A − 2 B − 4C )
( x + 2) ( x − 2) ( x − 1)
-3A + B = 0
2A - 2B - 4C = 1
C = −13
1
1
1
1
=
+
−
x 2 − x 2 − 4 x + 4 12( x + 2) 4( x − 2) 3( x − 1)
Example Find ∫ x 2 3 x 3 +10 dx . Let υ = 3x3 + 10 for which dυ = 9x2 dx.
Thus
1
1
= ∫ (3 x 3 + 10)1/2 (9 x 2 dx ) = ∫ υ1/2 d υ
9
9
1 υ3/2
[by
Eq.
(3
-51)]
=
+
c
9 32
2
= (3 x 3 +10)3/2 + c
27
A
B
C
+
+
x + 2 x − 2 x −1
A+B+C=0
a
2
=
Equate coefficients and solve for A, B, and C.
Direct Formula Many integrals can be solved by transformation in the
integrand to one of the forms given previously.
∫x
3
− 3 sin −1 x + c in terms of x
2
y4 −3 3
⌠
y dy 1
⌠ x dx
= 4
= ∫ y 2 ( y 4 − 3) dy
1/4
4
y
⌡ (3 + 4 x )
⌡
7
3
1
1 y
3 y
1
=
−
+ c = (3 + 4 x )7/4 − (3 + 4 x )3/4 + c
4
4 7 4 3
28
(3-54)
(3-55)
x
x dx
4
3
Example Find ⌠
. Let 3 + 4x = y ; then 4 dx = 4y dy and
1/4
⌡ (3 + 4 x )
(3-53)
∫ sin υ d υ = − cos υ + c
4 − 9x 2
Algebraic Substitution Functions containing elements of the type
(a + bx)1/n are best handled by the algebraic transformation y n = a + bx.
(3-52)
Other integrals can be found at en.wikipedia.org/wiki/Lists_of_integrals.
Example Find ∫ (3 x 2 + e x − 10) dx using Eq. (3-49).
∫ (3 x
cos 2 θ
2
= 3⌠
2 d θ = 3 ∫ cot θ d θ
⌡ sin θ
B = 14
Hence
dx
⌠ dx + ⌠ dx - ⌠ dx
⌠
=
3
⌡ x − x 2 − 4 x + 4 ⌡ 12( x + 2) ⌡ 4( x - 2) ⌡ 3( x - 1)
Integration by Parts An extremely useful formula for integration is the
relation d(uυ) = u dυ + υ du
and
uυ = ∫u dυ + ∫υ du
or
∫u dυ = uυ - ∫u du
It is particularly useful for trigonometric and exponential functions.
Example Find ∫xex dx. Let
u = x and dv = ex dx
du = dx
υ = ex
DIFFEREnTIAL AnD InTEGRAL CALCULUS
∫xex dx = xex - ∫ex dx = xex - ex + c
Therefore
∂
∂b
∂
∂b
Example Find ∫e sin x dx. Let
x
u = ex
du = ex dx
du = sin x dx
u = -cos x
u = ex
du = ex dx
du = cos x dx
u = sin x
∫
Series Expansion When an explicit function cannot be found, the integration can sometimes be carried out by a series expansion.
2
Example Find ∫e-x dx. Since
∫e
−x2
dx
d
∫
c
∫
When F ( x ) =
2
Example Find ∫
f ( x ) dx = − f (a )
b( x )
a(x )
if
∫
d
c
dα
a and b are constant
∫
b
a
f ( x , y ) dy
(3-57)
f ( x , α ) dx
the Leibniz rule gives
∫
b( x )
a(x )
∂f
dy
∂x
the incorrect value
2
x3
x5
x7
+
−
+ for all x
3 5(2!) 7(3!)
Definite Integral The value of a definite integral depends on the limits
a and b and any selected variable coefficients in the function but not on the
dummy variable of integration x. Symbolically
indefinite integral where dF/dx = f (x)
2
1
⌠ dx
= −
= −2
⌡0 ( x − 1)2 x − 1 0
Note that f (x) = 1/(x - 1)2 becomes unbounded as x → 1 and by rule 2 the
integral diverges and hence is said not to exist.
Methods of Integration All the methods of integration available for
the indefinite integral can be used for definite integrals. In addition, several
others are available for the latter integrals and are indicated below.
Change of Variable This substitution is basically the same as previously indicated for indefinite integrals. However, for definite integrals, the
limits of integration must also be changed: i.e., for x = f (t),
∫
b
F (a , b) = ∫ f ( x ) dx
b
dx
. Direct application of the formula would yield
( x − 1)2
x4
x6
dx = ∫ dx − ∫ x dx + ∫ dx − ∫ dx +
2!
3!
F (x) = ∫ f (x) dx
a
f ( x ) dx = f (b)
dF db
da
f [ x , b( x )] −
f [ x , a ( x )] +
=
dx dx
dx
2
=x−
∫
b
f ( x , α) d α =
0
6
x
x
−
+
2! 3!
2
e− x = 1 − x 2 +
b
a
∫ex sin x dx = -ex cos x + ex sin x - ∫ex sin x dx + c
c
= (e x /2) (sin x − cos x ) +
2
4
a
b ∂ f ( x , α)
dF (α )
=∫
dx
a
∂α
dα
∫ex sin x dx = -ex cos x + ∫ex cos x dx
Again
∫
3-21
definite integral
b
a
t1
f ( x ) dx = ∫ f [φ(t )] ϕ′ (t ) dt
t0
a
t = t0 when x = a
t = t1 when x = b
where
b
F (α ) = ∫ f ( x , α ) dxF
a
There are certain restrictions of the integration definition: The function
f (x) must be continuous in the finite interval (a, b) with at most a finite
number of finite discontinuities. Relaxing two of these restrictions gives
rise to so-called improper integrals and requires special handling. These
occur when
∞
1. The limits of integration are not both finite, i.e., ∫ e − x dx .
4
Example Find ∫
16 − x 2 dx . Let
0
x = 4 sin q
(x = 0, q = 0)
dx = 4 cos q dq
(x = 4, q = π/2)
0
2. The function becomes infinite within the interval of integration, i.e.,
∫
1
0
1
dx
x
Techniques for determining when integration is valid under these conditions are available in the references.
Properties The fundamental theorem of calculus states
∫
b
f ( x ) dx = F (b) − F (a )
a
dF ( x )/dx = f ( x )
where
Then
∫
4
0
16 − x 2 dx = 16 ∫
π/2
cos 2 θ d θ = 16[ 1 2 θ + 1 4 sin 2θ]0π/2 = 4 π
0
Integration It is sometimes useful to generate a double integral to
solve a problem. By this approach, the fundamental theorem indicated in
Eq. (3-57) can be used.
1
xb − xa
dx .
Example Find ⌠
⌡0 ln x
∫
Consider
1
0
Other properties of the definite integral are as follows:
x α dx =
1
(α > − 1)
α +1
Multiply both sides by dα and integrate between a and b.
∫
b
a
b
c[ f ( x ) dx ] = c ∫ f ( x ) dx
a
b
∫ [ f ( x ) + f ( x )] dx = ∫
a
∫
b
∫
b
∫
b
a
a
a
1
2
b
a
f1 ( x ) dx +
∫
b
a
f 2 ( x ) dx
∫
∫
f ( x ) dx = − ∫ f ( x ) dx
b
f ( x ) dx =
∫
a
b
b
a
d α ∫ x α dx =
1
0
∫
1
0
c
for some ξ in (a , b)
1
Therefore
1
⌠ xb − xa
b
dx ∫ x α d α =
dx
a
⌡0 ln x
b
f ( x ) dx + ∫ f ( x ) dx
f ( x ) dx = (b − a ) f (ξ)
1
⌠ dα
b +1
d α ∫ x α dx =
= ln
0
⌡a α + 1
a +1
But also
a
c
b
a
b +1
⌠ xb − xa
ln x dx = ln a + 1
⌡0
3-22
MATHEMATICS
InFInITE SERIES
References: de Brujin, N. G., Asymptotic Methods in Analysis, Dover,
New York, 2010; Zwillinger, D., Table of Integrals, Series, and Products, 8th ed.,
Academic, New York, 2014.
where B1 = 1/b1
B2 = − b2 /b 31
B3 = (1/b 51 ) (2b 22 − b1b3 )
DEFInITIOnS
B4 = (1/b 71) (5b1b2b3 − b 21b4 − 5b 32)
A succession of numbers or terms formed according to some definite rule
is called a sequence. The indicated sum of the terms of a sequence is called
a series. A series of the form a0 + a1(x - c) + a2(x - c)2 + … + an(x - c)n + … is
called a power series.
Consider the sum of a finite number of terms in the geometric series
(a special case of a power series).
Sn = a + ar + ar2 + ar3 + … + ar n -1
(3-58)
For any number of terms n, the sum equals
∫
1− r
1− r
n
Sn = a
S = a + ar + ar2 + … + arn + …
(3-59)
However, the defined sum of the terms [Eq. (3-59)]
1 − rn
1− r
x2
x1
x2
f ( x ) dx = ∫ a0 dx +
x1
∫
x2
x1
x2
a1 x dx + ∫ a2 x 2 dx +
x1
6. A power series may be differentiated term by term and represents the
function df (x)/dx within the same region of convergence as f (x).
In this form, the geometric series is assumed finite.
In the form of Eq. (3-58), it can further be defined that the terms in the
series be nonending and therefore an infinite series.
Sn = a
Additional coefficients are available in the references.
3. Two series may be added or subtracted term by term provided each is
a convergent series. The joint sum is equal to the sum (or difference) of the
individuals.
4. The sum of two divergent series can be convergent. Similarly, the sum
of a convergent series and a divergent series must be divergent.
5. A power series may be integrated term by term to represent the
integral of the function within an interval of the region of convergence. If
f (x) = a0 + a1x + a2x2 + …, then
r ≠1
while valid for any finite value of r and n, now takes on a different interpretation. In this sense it is necessary to consider the limit of Sn as n increases
indefinitely:
S = lim Sn
n→∞
1 − rn
n→∞ 1 − r
= a lim
The infinite series converges if the limit of Sn approaches a fixed finite value
as n approaches infinity. Otherwise, the series is divergent. If r is less than 1
but greater than -1, the infinite series is convergent. For values outside of
the range -1 < r < 1, the series is divergent because the sum is not defined.
The range -1 < r < 1 is called the region of convergence. (We assume a ≠ 0.)
There are also two types of convergent series. Consider the new series
TESTS FOR COnVERGEnCE AnD DIVERGEnCE
In general, the problem of determining whether a given series will converge
can require a great deal of ingenuity and resourcefulness. It is necessary to
apply one or more of the developed theorems in an attempt to ascertain the
convergence or divergence of the series under study. The following defined
tests are given in relative order of effectiveness. For examples, see references
on advanced calculus.
1. Comparison test. A series will converge if the absolute value of each
term (with or without a finite number of terms) is less than the corresponding term of a known convergent series. Similarly, a positive series is divergent if it is termwise larger than a known divergent series of positive terms.
2. nth-Term test. A series is divergent if the nth term of the series does not
approach zero as n becomes increasingly large.
3. Ratio test. If the absolute ratio of the n + 1 term divided by the nth term
as n becomes unbounded approaches
a. A number less than 1, the series is absolutely convergent.
b. A number greater than 1, the series is divergent.
c. A number equal to 1, the test is inconclusive.
Example For the power series
a0 + a1 ( x − x 0 ) + a2 ( x − x 0 )2 +
the absolute ratio gives
ε = lim
n −>∞
1
1 1 1
S = 1 − + − + + (−1)n + 1 +
2 3 4
n
1
an+1
x − x0 = x − x0
an
R
In this case series (3-60) is defined as a conditionally convergent series. If the
replacement series of absolute values also converges, the series is defined to
converge absolutely. Series (3-60) is further defined as an alternating series,
while series (3-61) is referred to as a positive series.
where R is the inverse of the limit. For convergence e < 1; therefore the series
converges for x − x 0 < R .
4. Alternating-series Leibniz test. If the terms of a series are alternately
positive and negative and never increase in value, the absolute series will
converge, provided that the terms tend to zero as a limit.
5. Cauchy’s root test. If the nth root of the absolute value of the nth term,
as n becomes unbounded, approaches
a. A number less than 1, the series is absolutely convergent.
b. A number greater than 1, the series is divergent.
c. A number equal to 1, the test is inconclusive.
6. Maclaurin’s integral test. Suppose ∑an is a series of positive terms and
f is a continuous decreasing function such that f (x) ≥ 0 for 1 ≤ x < ∞ and
∞
f (n) = an. Then the series and the improper integral ∫ f ( x ) dx either both
1
converge or both diverge.
OPERATIOnS WITH InFInITE SERIES
SERIES SUMMATIOn AnD IDEnTITIES
(3-60)
It can be shown that series (3-60) does converge to the value S = ln 2.
However, if each term is replaced by its absolute value, the series becomes
unbounded and therefore divergent (unbounded divergent):
1 1 1 1
S = 1 + + + + +
2 3 4 5
(3-61)
1. The convergence or divergence of an infinite series is unaffected by the
removal of a finite number of finite terms. This is a trivial theorem but useful
to remember, especially when using the comparison test to be described in
the subsection “Tests for Convergence and Divergence.”
2. A power series can be inverted, provided the first-degree term is not
zero. Given
y = b1x + b2x + b3x + b4x + b5x + b6x + b7x + …
2
then
3
4
5
6
7
x = B1y + B2y2 + B3y3 + B4y4 + B5y5 + B6y6 + B7y7 + …
Sums for the First n Numbers to Integer Powers
n
∑j=
j =1
n
∑j
n (n + 1)
= 1 + 2 + 3 + 4 ++ n
2
2
=
n (n + 1)(2n +1) 2
= 1 + 22 + 32 + 4 2 + + n2
6
3
=
n 2 (n + 1)2 3
= 1 + 23 + 33 + + n3
4
j =1
n
∑j
j =1
COMPLEX VARIABLES
This is simply a special case of Taylor’s series when h is set to zero.
Exponential Series
Arithmetic Progression
n
∑[a + (k − 1) d ] = a + (a + d ) + (a + 2d )
ex =1+ x +
k =1
+ (a + 3 d ) + + [ a + (n − 1)]d
2
ln x =
Geometric Progression
∑ar
j -1
= a + ar + ar 2 + ar 3 + + ar n - 1 = a
j =1
1- r
1- r
1
1
1
r ≠1
1
1
1
x3 x5 x7
+ − + −∞ < x < ∞
3! 5! 7!
2
x
x4 x6
cos x = 1 − + − + −∞ < x < ∞
2! 4! 6!
x3 1 3 x5 1 3 5 x7
−1
sin x = x + + ⋅ ⋅ + ⋅ ⋅ ⋅ + ( x 2 < 1)
6 2 4 5 2 4 6 7
1
1
1
tan −1 x = x − x 3 + x 5 − x 7 + ( x 2 < 1)
3
5
7
sin x = x −
1
k=0
The reciprocals of the terms of the arithmetic progression series are called
a harmonic progression. No general summation formulas are available for
this series.
Binomial Series (See Also Elementary Algebra)
n (n − 1) 2 n (n − 1)(n − 2) 3
x ±
x +
2!
3!
( x 2 < 1)
Taylor’s Series
2
or
x
x
f (h + x ) = f (h) + xf ′(h) +
f ′′(h) +
f ′′′(h) +
2!
3!
f ′′′( x 0 )
f ′′′( x 0 )
( x - x 0 )2
( x − x 0 )3 +
f ( x ) = f ( x 0 ) + f ′( x 0 ) ( x − x 0 ) +
3!
2!
f ′( x ) = (1 + x )−1 , f ′′( x ) = − (1 + x )−2 , f ′′′( x ) = 2(1 + x )−3 , etc.
f (0) = 0, f ′(0) = 1, f ′′(0) = −1, f ′′′(1) = 2, etc.
ln ( x + 1) = x −
x2 x3 x4
xn
+
−
+ + (−1)n + 1 +
2
3
4
n
which converges for -1 < x ≤ 1.
Maclaurin’s Series
f ( x ) = f (0) + xf ′(0) +
Taylor Series The Taylor series for a function of two variables,
expanded about the point (x0, y0), is
f (x , y ) = f (x0 , y 0 ) +
3
Example Find a series expansion for f (x) = ln (1 + x) about x0 = 0.
Thus
3
x − 1 1 x − 1 1 x − 1
+
+ ( x > 1 2)
+
x
2 x 3 x
Trigonometric Series*
∑ a + kd = a + a + d + a + 2d + a + 3d + a + 4 d + + a + nd
(1 ± x )n = 1 ± nx +
−∞ < x < ∞
x − 1 1 x − 1 3
ln x = 2
+ ( x > 0)
+
x + 1 3 x + 1
n
Harmonic Progression
n
x2 x3
xn
+ ++ +
2! 3!
n!
Logarithmic Series
1
= na + n (n − 1)d
2
n
3-23
+
1 ∂2 f
2! ∂ x 2
∂f
∂x
x0 , y0
( x − x 0 )2 + 2
x0 , y0
(x − x0 )+
∂2 f
∂x ∂ y
∂f
∂y
( y - y0 )
x0 , y0
( x - x 0 )( y - y 0 ) +
x0 , y0
∂2 f
∂y 2
( y - y 0 )2 +
x0 , y0
Partial Sums of Infinite Series, and How They Grow Calculus textbooks devote much space to tests for convergence and divergence of series
that are of little practical value, since a convergent series either converges
rapidly, in which case almost any test (among those presented in the preceding subsections) will do, or it converges slowly, in which case it is not
going to be of much use unless there is some way to get at its sum without
adding an unreasonable number of terms. To find out, as accurately as possible, how fast a convergent series converges and how fast a divergent series
diverges, see Boas, R. P., Jr., Am. Math. Mon. 84: 237–258 (1977).
*The tan x series has awkward coefficients and should be computed as
(sign) sin x
1 − sin 2 x
x2
x3
f ′′(0) +
f ′′′(0) +
2!
3!
COMPLEX VARIABLES
References: Ablowitz, M. J., and A. S. Fokas, Complex Variables: Introduction and Applications, 2d ed., Cambridge University Press, New York, 2012;
Asmar, N., and G. C. Jones, Applied Complex Analysis with Partial Differential
Equations, Prentice-Hall, Upper Saddle River, N.J., 2002; Brown, J. W., and
R. V. Churchill, Complex Variables and Applications, 9th ed., McGraw-Hill,
New York, 2013; Kwok, Y. K., Applied Complex Variables for Scientists and
Engineers, 2d ed., Cambridge University Press, New York, 2010.
Numbers of the form z = x + iy, where x and y are real, i2 = -1, are called
complex numbers. The numbers z = x + iy are representable in the plane, as
shown in Fig. 3-42. The following definitions and terminology are used:
1. Distance OP = r = modulus of z written | z |. | z | = x 2 + y 2
2. x is the real part of z.
3. y is the imaginary part of z.
4. The angle θ, 0 ≤ θ < 2π, measured counterclockwise from the positive x
axis to OP, is the argument of z. θ = arctan y/x = arcsin y/r = arccos x/r if
x ≠ 0, θ = π/2 if x = 0 and y > 0.
5. The numbers r, θ are the polar coordinates of z.
6. z = x - iy is the complex conjugate of z.
ALGEBRA
Let z1 = x1 + iy1 and z2 = x2 + iy2.
Equality z1 = z2 if and only if x1 = x2 and y1 = y2.
Addition z1 + z2 = (x1 + x2) + i(y1 + y2).
Subtraction z1 - z2 = (x1 - x2) + i(y1 - y2).
Multiplication z1z2 = (x1x2 - y1y2) + i(x1y2 + x2y1).
Division
FIG. 3-42
Complex plane.
z1 /z 2 =
x1 x 2 + y 1 y 2
x y − x1 y 2
, z 2 ≠ 0.
+ i 2 21
x 22 + y 22
x 2 + y 22
3-24
MATHEMATICS
SPECIAL OPERATIOnS
2
2
2
zz = x + y = | z | ; z1 ± z 2 = z1 ± z 2 ; z1 = z1 ; z1 z 2 = z1 z 2 ;| z1 ⋅ z 2 | = | z1 | ⋅ | z 2 |; arg
(z1 ⋅ z2) = arg z1 + arg z2; arg (z1/z2) = arg z1 - arg z2; i4n = 1 for n any integer;
i2n = -1 where n is any odd integer; z + z = 2x; z - z = 2iy.
Every complex quantity can be expressed in the form x + iy.
General powers of z are defined by zα = eα log z. Since log z is infinitely many
valued, so too is zα unless α is a rational number.
DeMoivre’s formula can be derived from properties of ez.
zn = rn (cos q + i sin q)n = rn (cos nq + i sin nq)
TRIGOnOMETRIC REPRESEnTATIOn
Thus
By referring to Fig. 3-42, there results x = r cos θ and y = r sin θ so that
z = x + iy = r (cos q + i sin q), which is called the polar form of the complex
number. cos q + i sin q = eiq. Hence z = x + iy = reiq. z = x - iy = re-iq. Two
important results from this are cos q = (eiq + e-iq)/2 and sin q = (eiq - e-iq)/2i.
Let z1 = r1eiq1 and z2 = r2eiq2. This form is convenient for multiplication for
z1 z 2 = r1 r2e i ( θ1 +θ2 ) and for division for z1 /z 2 = (r1 /r2 )e i ( θ1 −θ2 ) , z 2 ≠ 0.
COMPLEX FUnCTIOnS (AnALYTIC)
POWERS AnD ROOTS
If n is a positive integer, zn = (reiq)n = rneinq = rn(cos nq + i sin nq).
If n is a positive integer,
θ + 2 kπ
θ + 2 kπ
+ i sin
z 1/n = r 1/n e i [( θ+ 2 kπ )/n ] = r 1/n cos
n
n
and selecting values of k = 0, 1, 2, 3, …, n - 1 gives the n distinct values of z1/n.
The n roots of a complex quantity are uniformly spaced around a circle with
radius r1/n in the complex plane in a symmetric fashion.
Example Find the three cube roots of -8. Here r = 8, q = π. The roots
are z0 = 2(cos π/3 + i sin π/3) = 1 + i 3 , z1 = 2(cos π + i sin π) = -2, and
z2 = 2(cos 5π/3 + i sin 5π/3) = 1 - i 3 .
(cos q + i sin q)n = cos nq + i sin nq
In the real-number system a greater than b (a > b) and b less than
c (b < c) define an order relation. These relations have no meaning for
complex numbers. The absolute value is used for ordering. Some important relations follow: |z| ≥ x; |z| ≥ y ; |z1 ± z2| ≤ |z1| + |z2|; |z1 - z2| ≥ ||z1| - |z2||;
|z| ≥ (|x| + |y|)/ 2 . Parts of the complex plane, commonly called regions or
domains, are described by using inequalities.
Example |z - 3| ≤ 5. This is equivalent to ( x − 3)2 + y 2 ≤ 5, which is the
set of all points within and on the circle, centered at x = 3, y = 0 of radius 5.
Example |z - 1| ≤ x represents the set of all points inside and on the
parabola 2x = y2 + 1 or, equivalently, 2x ≥ y2 + 1.
Functions of a Complex Variable If z = x + iy, w = u + iu and if for each
value of z in some region of the complex plane one or more values of w are
defined, then w is said to be a function of z, w = f (z). Some of these functions
have already been discussed, such as sin z and log z. All functions are reducible to the form w = u(x, y) + iu(x, y), where u and u are real functions of the
real variables x and y.
Example z3 = (x + iy)3 = x3 + 3x2(iy) + 3x(iy)2 + (iy)3 = (x3 - 3xy2) +
i(3x2y - y3).
Differentiation The derivative of w = f (z) is
ELEMEnTARY COMPLEX FUnCTIOnS
Polynomials A polynomial in z, anzn + an -1zn -1 + … + a0, where n is a
positive integer, is simply a sum of complex numbers times integral powers
of z which have already been defined. Every polynomial of degree n has
precisely n complex roots provided each multiple root of multiplicity m
is counted m times.
Exponential Functions The exponential function ez is defined
by the equation ez = ex + iy = ex ⋅ eiy = ex(cos y + i sin y). Properties: e0 = 1;
e z1 e z2 = e z1 + z2 ; e z1 / z2 = e z1 − z2 ; e z +2 kπi = e z , k an integer.
Trigonometric Functions sin z = (eiz - e-iz)/2i; cos z = (eiz + e-iz)/2;
tan z = sin z/cos z; cot z = cos z/sin z; sec z = 1/cos z; csc z = 1/sin z.
Fundamental identities for these functions are the same as their real
counterparts. Thus cos2 z + sin2 z = 1, cos (z1 ± z2) = cos z1 cos z2 sin z1
sin z2, sin (z1 ± z2) = sin z1 cos z2 ± cos z1 sin z2. The sine and cosine of z
are periodic functions of period 2π; thus sin (z + 2π) = sin z. For computation purposes sin z = sin (x + iy) = sin x cosh y + i cos x sinh y, where
sin x, cosh y, etc., are the real trigonometric and hyperbolic functions.
Similarly, cos z = cos x cosh y - i sin x sinh y. If x = 0 in the results given,
cos iy = cosh y and sin iy = i sinh y.
Example Find all solutions of sin z = 3. From previous data sin z =
sin x cosh y + i cos x sinh y = 3. Equating real and imaginary parts gives
sin x cosh y = 3 and cos x sinh y = 0. The second equation can hold for
y = 0 or for x = π/2, 3π/2, … . If y = 0, cosh 0 = 1 and sin x = 3 is impossible for real x. Therefore, x = ±π/2, ±3π/2, …, ±(2n + 1)π/2, n = 0, ±1, ±2, … .
However, sin 3π/2 = -1 and cosh y ≥ 1. Hence x = π/2, 5π/2, … . The solution
is z = [(4n + 1)π]/2 + i cosh-13, n = 0, 1, 2, 3, … .
Example Find all solutions of ez = -i. ez = ex(cos y + i sin y) = -i. Equating
real and imaginary parts gives ex cos y = 0, ex sin y = -1 from the first y = ±π/2,
±3π/2, … . But ex > 0. Therefore, y = 3π/2, 7π/2, -π/2, … . Then x = 0. The solution is z = i[(4n + 3)π]/2.
Two important facets of these functions should be recognized. First, sin z
is unbounded; second, ez takes all complex values except 0.
Hyperbolic Functions sinh z = (ez - e-z)/2; cosh z = (ez + e-z)/2;
tanh z = sinh z/cosh z; coth z = cosh z/sinh z; csch z = 1/sinh z; sech z =
1/cosh z. Identities are cosh2 z - sinh2 z = 1; sinh (z1 + z2) = sinh z1 cosh z2 +
cosh z1 sinh z2; cosh (z1 + z2) = cosh z1 cosh z2 + sinh z1 sinh z2; cosh z +
sinh z = ez; cosh z - sinh z = e-z. The hyperbolic sine and hyperbolic
cosine are periodic functions with the imaginary period 2πi. That is,
sinh (z + 2πi) = sinh z.
Logarithms The logarithm of z, log z = log |z| + i(q + 2nπ), where log |z|
is taken to the base e and q is the principal argument of z, that is, the particular argument lying in the interval 0 ≤ q < 2π. The logarithm of z is infinitely many valued. If n = 0, the resulting logarithm is called the principal
value. The familiar laws log z1z2 = log z1 + log z2, log z1/z2 = log z1 - log z2, and
log zn = n log z hold for the principal value.
dw
f ( z + ∆z ) − f ( z )
= lim
dz ∆z → 0
∆z
and for the derivative to exist, the limit must be the same no matter how Δz
approaches zero. If w1 and w2 are differentiable functions of z, the following
rules apply:
d (w1 ± w2 ) dw1 dw2
dw2
dw
d (w1w2 )
=
±
= w2 1 + w1
dz
dz
dz
dz
dz
dz
d (w1 /w2 ) w2 (dw1 /dz ) - w1 (dw2 /dz )
=
dz
w22
and
dw
dw1n
= nw1n - 1 1
dz
dz
For w = f (z) to be differentiable, it is necessary that ∂u/∂x = ∂u/∂y and
∂u/∂x = -∂u/∂y. The last two equations are called the Cauchy-Riemann
equations . The derivative
∂u
∂v ∂υ
dw ∂u
−i
=
+i
=
∂y
∂x ∂ y
dz ∂ x
If f (z) possesses a derivative at z0 and at every point in some neighborhood
of z0, then f (z) is said to be analytic or homomorphic at z0 . If the CauchyRiemann equations are satisfied and
u , υ,
∂u ∂u ∂υ ∂υ
,
,
,
∂x ∂ y ∂x ∂ y
are continuous in a region of the complex plane, then f (z) is analytic in that
region .
Example w = z z = x2 + y2 . Here u = x2 + y2, u = 0 . ∂u/∂x = 2x, ∂u/∂y = 2y,
∂u/∂x = ∂u/∂y = 0 . These are continuous everywhere, but the CauchyRiemann equations hold only at the origin . Therefore, w is nowhere analytic,
but it is differentiable at z = 0 only .
Example w = ez = ex cos y + iex sin y. u = ex cos y and u = ex sin y. ∂u/∂x =
ex cos y, ∂u/∂y = -ex sin y, ∂u/∂x = ex sin y, ∂u/∂y = ex cos y. The continuity
and Cauchy-Riemann requirements are satisfied for all finite z. Hence ez is
analytic (except at ∞) and dw/dz = ∂u/∂x + i(∂u/∂x) = ez.
Example w =
y
1 x − iy
x
=
−i
=
z x2 + y2 x2 + y2 x2 + y2
It is easy to see that dw/dz exists except at z = 0 . Thus 1/z is analytic except
at z = 0 .
DIFFEREnTIAL EQUATIOnS
Singular Points If f (z) is analytic in a region except at certain points,
those points are called singular points.
Example 1/z has a singular point at zero.
Example tan z has singular points at z = ±(2n + 1)(π/2), n = 0, 1, 2, ….
The derivatives of the common functions, given earlier, are the same as their
real counterparts.
Example (d/dz)(ln z) = 1/z, (d/dz)(sin z) = cos z.
Harmonic Functions Both the real and the imaginary parts of any
analytic function f = u + iu satisfy Laplace’s equation ∂2f/∂x2 + ∂2f/∂y2 = 0 .
A function which possesses continuous second partial derivatives and satisfies Laplace’s equation is called a harmonic function.
Example ez = ex cos y + iex sin y. u = ex cos y, ∂u/∂x = ex cos y, ∂2u/∂x2 =
ex cos y, ∂u/∂y = -ex sin y, ∂2u/∂y2 = -ex cos y. Clearly ∂2u/∂x2 + ∂2u/∂y2 = 0 .
Similarly, u = ex sin y is also harmonic .
If w = u + iu is analytic, the curves u(x, y) = c and u(x, y) = k intersect at
right angles, if w′(z) ≠ 0 .
Integration In much of the work with complex variables a simple
extension of integration called line or curvilinear integration is of fundamental importance . Since any complex line integral can be expressed in terms of
real line integrals, we define only real line integrals . Let F (x, y) be a real,
continuous function of x and y, and let c be any continuous curve of finite
length joining points A and B (Fig . 3-43) . F(x, y) is not related to the curve c .
Divide c into n segments, Δsi, whose projection on the x axis is Δxi and on
the y axis is Δyi . Let (ei, hi) be the coordinates of an arbitrary point on Δsi .
The limits of the sums
3-25
are known as line integrals . Much of the initial strangeness of these integrals
b
will vanish if it is observed that the ordinary definite integral ∫ f ( x ) dx is
a
just a line integral in which the curve c is a line segment on the x axis and
F(x, y) is a function of x alone . The evaluation of line integrals can be reduced
to evaluation of ordinary integrals .
Example ∫c y (1 + x) dy, where c: y = 1 - x2 from (-1, 0) to (1, 0) . Clearly
y = 1 - x2, dy = -2x dx. Thus ∫c y (1 + x) dy = -2 ∫1-1 (1 - x2)(1 + x)x dx = -8⁄15 .
Let f (z) be any function of z, analytic or not, and c any curve as above . The
complex integral is calculated as ∫c f (z) dz = ∫c (u dx - u dy) + i ∫c (u dx + u dy),
where f (z) = u(x, y) + i u(x, y) . Properties of line integrals are the same as for
ordinary integrals . That is, ∫c [ f (z) ± g(z)] dz = ∫c f (z) dz ± ∫c g(z) dz; ∫c kf (z)
dz = k ∫c f (z) dz for any constant k, etc .
Example ∫ c (x2 + iy) dz along c: y = x, 0 to 1 + i. This becomes
∫ (x
c
2
+ iy ) dz = ∫ ( x 2 dx - y dy )
c
1
1
1
0
0
0
+ i ∫ ( y dx + x dy ) = ∫ x 2 dx − ∫ x dx + i ∫ x dx + i
2
c
∫
1
0
x 2 dx = − 1 6 + 5i /6
lim ∑ F (ε i , ηi ) ∆y i = ∫ F ( x , y ) dy
Conformal Mapping Every function of a complex variable w = f (z) =
u(x, y) + iu(x, y) transforms the x, y plane into the u, u plane in some manner .
A conformal transformation is one in which angles between curves are
preserved in magnitude and sense . Every analytic function, except at those
points where f ′(z) = 0, is a conformal transformation . See Fig . 3-44 .
Example w = z2 . u + iu = (x2 - y2) + 2ixy or u = x2 - y2, u = 2xy. These are
the transformation equations between the (x, y) and (u, u) planes . Lines
parallel to the x axis, y = c1 map into curves in the u, u plane with parametric equations u = x2 - c12, u = 2c1x. Eliminating x, u = (u2/4c12) - c12,
which represents a family of parabolas with the origin of the w plane as
focus, the line u = 0 as axis and opening to the right . Similar arguments
apply to x = c2 .
The principles of complex variables are useful in the solution of a variety
of applied problems, including Laplace transforms (see Integral Transforms)
and process control (Sec . 8) .
FIG. 3-43 Line integral .
FIG. 3-44 Conformal transformation .
n
lim ∑ F (εi , ηi ) ∆si = ∫ F ( x , y ) ds
∆si → 0
i =1
c
n
lim ∑ F (ε i , ηi ) ∆x i = ∫ F ( x , y ) dx
∆si → 0
i =1
c
n
∆si → 0
i =1
c
DIFFEREnTIAL EQUATIOnS
References: Ames, W . F ., Nonlinear Partial Differential Equations in
Engineering, Academic Press, New York, 1965; Aris, R ., and N . R . Amundson,
Mathematical Methods in Chemical Engineering, vol . 2, First-Order Partial
Differential Equations with Applications, Prentice-Hall, Englewood Cliffs,
N .J ., 1973; Asmar, N . H ., Partial Differential Equations with Fourier Series
and Boundary Value Problems, 3rd ed ., Pearson, New York, 2016 . Asmar, N .,
Applied Complex Analysis with Partial Differential Equations, Prentice-Hall,
Upper Saddle River, N .J ., 2002; Bronson, R ., and G . Costa, Schaum’s Outline
of Differential Equations, 4th ed ., McGraw-Hill, New York, 2014; Brown,
J . W ., and R . V . Churchill, Fourier Series and Boundary Value Problems,
8th ed ., McGraw-Hill Education, New York, 2011; Duffy, D ., Green’s Functions with Applications, 2d ed ., Chapman and Hall/CRC, New York, 2015;
Kreyszig, E ., Advanced Engineering Mathematics, 10th ed ., Wiley, New York,
2011; Ramkrishna, D ., and N . R . Amundson, Linear Operator Methods in
Chemical Engineering with Applications to Transport and Chemical Reaction
Systems, Prentice-Hall, Englewood Cliffs, N .J ., 1985 .
The natural laws in any scientific or technological field are not regarded
as precise and definitive until they have been expressed in mathematical
form . Such a form, often an equation, is a relation between the quantity of
interest, say, product yield, and independent variables such as time and
temperature upon which yield depends . When it happens that this equation
involves, besides the function itself, one or more of its derivatives it is called
a differential equation .
Example The rate of the homogeneous bimolecular reaction
A + B k→ C is characterized by the differential equation dx/dt = k(a - x)
(b - x), where a = initial concentration of A, b = initial concentration of B,
and x = x(t) = concentration of C as a function of time t.
Example The differential equation of heat conduction in a moving fluid
with velocity components ux, uy is
∂T
∂T
k ∂2 T ∂2 T
∂T
=
+
+υy
+ υx
∂ y ρc p ∂ x 2 ∂ y 2
∂x
∂t
where T = T(x, y, t) = temperature, k = thermal conductivity, r = density, and
cp = specific heat at constant pressure .
ORDInARY DIFFEREnTIAL EQUATIOnS
When the function involved in the equation depends upon only one variable, its derivatives are ordinary derivatives and the differential equation
is called an ordinary differential equation . When the function depends
upon several independent variables, then the equation is called a partial
differential equation . The theories of ordinary and partial differential
equations are quite different . In almost every respect the latter is more
difficult .
3-26
MATHEMATICS
Whichever the type, a differential equation is said to be of nth order if
it involves derivatives of order n but no higher. The equation in the first
example is of first order and that in the second example of second order.
The degree of a differential equation is the power to which the derivative of
the highest order is raised after the equation has been cleared of fractions
and radicals in the dependent variable and its derivatives.
A relation between the variables, involving no derivatives, is called a
solution of the differential equation if this relation, when substituted in the
equation, satisfies the equation. A solution of an ordinary differential equation which includes the maximum possible number of “arbitrary” constants
is called the general solution. The maximum number of “arbitrary” constants
is exactly equal to the order of the differential equation. If any set of specific
values of the constants is chosen, the result is called a particular solution.
Example The general solution of (d2x/dt2) + k2x = 0 is x = A cos kt +
B sin kt, where A and B are arbitrary constants. A particular solution is
x = ½ cos kt + 3 sin kt.
In the case of some equations still other solutions exist called singular
solutions. A singular solution is any solution of the differential equation
which is not included in the general solution.
Example y = x(dy/dx) - ¼(dy/dx)2 has the general solution y = cx - ¼c2,
where c is an arbitrary constant; y = x2 is a singular solution, as is easily
verified.
ORDInARY DIFFEREnTIAL EQUATIOnS OF THE FIRST ORDER
Equations with Separable Variables Every differential equation of
the first order and of the first degree can be written in the form M(x, y) dx +
N(x, y)dy = 0. If the equation can be transformed so that M does not involve
y and N does not involve x, then the variables are said to be separated.
The solution can then be obtained by quadrature, which means that
y = ∫ f (x)dx + c, which may or may not be expressible in simpler form.
Exact Equations The equation M(x, y) dx + N(x, y) dy = 0 is exact if and
only if ∂M/∂y = ∂N/∂x. In this case there exists a function w = f (x, y) such that
∂f/∂x = M, ∂f/∂y = N, and f (x, y) = C is the required solution . f (x, y) is found
as follows: treat y as though it were constant and evaluate ∫M(x, y) dx. Then
treat x as though it were constant and evaluate ∫N(x, y) dy. The sum of all
unlike terms in these two integrals (including no repetitions) is f (x, y) .
Example (2xy - cos x) dx + (x2 - 1) dy = 0 is exact for ∂M/∂y =
2x, ∂N/∂x = 2x. ∫M dx = ∫(2xy - cos x) dx = x2y - sin x, ∫N dy = ∫(x2 - 1) dy =
x2y - y. The solution is x2y - sin x - y = C, as may easily be verified .
Linear Equations A differential equation is said to be linear when it
is of first degree in the dependent variable and its derivatives . The general
linear first-order differential equation has the form dy/dx + P(x)y = Q(x) .
Its general solution is
− P dx
P dx
y = e ∫ ∫ Qe ∫ dx + C
Example A tank initially holds 200 gal of a salt solution in which
100 lb is dissolved . Six gallons of brine containing 4 lb of salt run into the
tank per minute . If mixing is perfect and the output rate is 4 gal/min, what
is the amount A of salt in the tank at time t ? The differential equation of
A is dA/dt = 4 - 2A/[100 + t] . Its general solution is A = (4/3)(100 + t) +
C/(100 + t)2 . At t = 0, A = 100; so the particular solution is A = (4/3)(100 + t) (1/3) ×106/(100 + t)2 .
ORDInARY DIFFEREnTIAL EQUATIOnS OF HIGHER ORDER
The higher-order differential equations, especially those of order 2, are of
great importance because of physical situations describable by them .
Equation y(n) = f (x). The superscript (n) means n derivatives . Such a differential equation can be solved by n integrations . The solution will contain
n arbitrary constants .
Linear Differential Equations with Constant Coefficients and
Right-Hand Member of Zero (Homogeneous) The solution of
y ′′ + ay ′ + by = 0 depends upon the nature of the roots of the characteristic
equation m2 + am + b = 0 obtained by substituting the trial solution y = emx
in the equation .
Distinct Real Roots If the roots of the characteristic equation are
distinct real roots, r1 and r2, say, the solution is y = Ae r1 x + Be r2 x , where A and B
are arbitrary constants .
Example y ′′ + 4 y ′ + 3 = 0 . The characteristic equation is m2 + 4m + 3 = 0 .
The roots are -3 and -1, and the general solution is y = Ae–3x + Be–x.
Multiple Real Roots If r1 = r2, the solution of the differential equation
is y = e r1 x ( A + Bx ) .
Example y ′′ + 4 y + 4 = 0 . The characteristic equation is m2 + 4m + 4 = 0
with roots -2 and -2 . The solution is y = e-2x(A + Bx) .
Complex Roots If the characteristic roots are p ± iq, then the solution is
y = e px × (A cos qx + B sin qx) .
Example The differential equation My ′′ + Ay ′ + ky = 0 represents the
vibration of a linear system of mass M, spring constant k, and damping
constant A. If A < 2 kM , the roots of the characteristic equation
Mm 2 + Am + k = 0 are complex: −
A
±i
2M
k A
−
M 2M
2
and the solution is
k A 2
k A 2
t + ic2 sin
y = e − ( At /2 M ) c1 cos
−
−
t
M 2 M
M 2M
This solution is oscillatory, representing undercritical damping .
All these results generalize to homogeneous linear differential equations with constant coefficients of order higher than 2 . These equations
(especially of order 2) have been much used because of the ease of solution .
Oscillations, electric circuits, diffusion processes, and heat flow problems
are a few examples for which such equations are useful .
Second-Order Equations: Dependent Variable Missing Such an equation
is of the form
dy d 2 y
F x, , 2 = 0
dx dx
It can be reduced to a first-order equation by substituting p = dy/dx and
dp/dx = d2y/dx2 .
Second-Order Equations: Independent Variable Missing Such an
equation is of the form
dy d 2 y
F y, , 2 = 0
dx dx
dp
d2y
du
= p,
=p
dy
dx 2
dx
Set
The result is a first-order equation in p
dp
F y , p, p = 0
dy
Example The capillary curve for one vertical plate is given by
d2y 4y
=
dx 2 c 2
dy 2
1 +
dx
3/2
Its solution by this technique is
c
c
c
x + c 2 − y 2 − c 2 − h02 = cosh −1 − cosh −1
2
y
h0
where c and h0 are physical constants .
Example The equation governing chemical reaction in a porous catalyst in plane geometry of thickness L is
D
dc
d 2c
(0) = 0, c ( L) = cυ
= k f (c ),
dx
dx 2
where D is a diffusion coefficient, k is a reaction rate parameter, c is the concentration, kf (c) is the rate of reaction, and c0 is the concentration at the
dc
gives (Finlayson, 1980, p . 92)
boundary . Making the substitution p =
ds
p
Integrating gives
dp k
= f (c )
dc D
p2 k
=
2 D
∫
c
c (0)
f (c ) dc
DIFFEREnTIAL EQUATIOnS
If the reaction is very fast, c(0) ≈ 0 and the average reaction rate is related to
p(L). This variable is given by
2k
p ( L) =
D
∫
c (0)
0
1/2
f (c ) dc
c0′ (0) + ac1′ (0) + a 2c2′ (0) + = 0
Form of Particular Integral
Then P(x) is
a (constant)
A (constant)
axn
Anxn + An-1 xn -1 + … + A1x + A0
aerx
Berx
c cos kx
d sin kx
A cos kx + B sin kx
g x n e rx cos kx
h x n e rx sin kx
(Anx + … + A0)e cos kx + (Bnx + … + B0)e sin kx
n
rx
The goal is to find equations governing the functions {ci(x)} and solve them .
Substitution into the equations gives the following equations:
c0′′ ( x ) + ac1′′( x ) + a 2c2′′ ( x ) + = a[c0 ( x ) + ac1 ( x ) + a 2c2 ( x ) + ]2
Thus, the average reaction rate can be calculated without solving the complete problem.
Linear Nonhomogeneous Differential Equations
Linear Differential Equations Right-Hand Member f (x) ≠ 0 Again the
specific remarks for y ′′ + ay ′ + by = f ( x ) apply to differential equations of
similar type but higher order. We shall discuss two general methods.
Method of Undetermined Coefficients Use of this method is limited to
equations exhibiting both constant coefficients and particular forms of the
function f (x). In most cases f (x) will be a sum or product of functions of the
type constant, xn (n a positive integer), emx, cos kx, sin kx. When this is the
case, the solution of the equation is y = H(x) + P(x), where H(x) is a solution
of the homogeneous equations found by the method of the preceding subsection and P(x) is a particular integral found by using the following table
subject to these conditions: (1) When f (x) consists of the sum of several
terms, the appropriate form of P(x) is the sum of the particular integrals corresponding to these terms individually. (2) When a term in any of the trial
integrals listed is already a part of the homogeneous solution, the indicated
form of the particular integral is multiplied by x.
If f (x) is
3-27
n
rx
c0 (1) + ac1 (1) + a 2c2 (1) + = 1
Like terms in powers of a are collected to form the individual problems .
c0′′= 0, c0′ (0) = 0, c0 (1) = 1
c1′′= c02 , c1′(0) = 0, c1 (1) = 0
c2′′= 2c0 c1 , c2′ (0) = 0, c 2 (1) = 0
The solution proceeds in turn .
c0 ( x ) = 1, c1 ( x ) =
( x 2 − 1)
5 − 6x 2 + x 4
, c2 ( x ) =
2
12
SPECIAL DIFFEREnTIAL EQUATIOnS
See Olver et al . (2010) in General References .
Euler’s Equation The linear equation xny(n) + a1xn -1y n-1 + … + an-1xy′ +
any = R(x) can be reduced to a linear equation with constant coefficients by
the change of variable x = et . To solve the homogeneous equation substitute
y = xr into it, cancel the powers of x, which are the same for all terms, and
solve the resulting polynomial for r . In case of multiple or complex roots
there results the form y = xr(log x)r and y = xα[cos (b log x) + i sin (b log x)] .
Bessel’s Equation The linear equation x2(d2y/dx2) + x(dy/dx) + (x2 - p2)
y = 0 is the Bessel equation of integer order . By series methods, not to be
discussed here, this equation can be shown to have the solution
x
J p ( x ) =
2
p
∞
(−1) k ( x /2)2 k
k = 0 k !( p + k )!
∑
(Bessel function of the first kind of order p) and
Since the form of the particular integral is known, the constants may be
evaluated by substitution in the differential equation.
Example y ′′ + 2 y ′ + y = 3e2x - cos x + x3. The characteristic equation is
(m + 1)2 = 0 so that the homogeneous solution is y = (c1 + c2x)e-x. To find
a particular solution we use the trial solution from the table, y = a1e2x +
a2 cos x + a3 sin x + a4x3 + a5x2 + a6x + a7. By substituting this in the differential
equation and collecting and equating like terms, there results a1 = ⅓, a2 = 0,
a3 = -½, a4 = 1, a5 = -6, a6 = 18, and a7 = -24 . The solution is y = (c1 + c2x)e-x +
⅓e2x - ½ sin x + x3 - 6x2 + 18x - 24 .
Method of Variation of Parameters This method is applicable
to any linear equation . The technique is developed for a second-order
equation but immediately extends to higher order . Let the equation be
y ′′ + a ( x ) y ′ + b( x ) y = R ( x ), and let the solution of the homogeneous equation, found by some method, be y = c1f1(x) + c2f2(x) . It is now assumed that a
particular integral of the differential equation is of the form P(x) = uf1 + vf2,
where u and v are functions of x to be determined by two equations . One
equation results from the requirement that uf1 + vf2 satisfy the differential
equation, and the other is a degree of freedom open to the analyst . The best
choice proves to be
u ′f1 + v ′f 2 = 0 and u ′f1′+ vf 2′ = 0
Then
u′ =
du
f2
=−
R(x )
dx
f1 f 2′− f 2 f1′
v′ =
dv
f1
R(x )
=
dx f1 f 2′ − f 2 f1′
and since f1, f2, and R are known, u, v may be found by direct integration .
Perturbation Methods If the ordinary differential equation has a
parameter that is small and is not multiplying the highest derivative, perturbation methods can give solutions for small values of the parameter .
Example Consider the differential equation for reaction and diffusion
in a catalyst; the reaction is second-order: c″ = ac2, c′(0) = 0, c(1) = 1 . The
solution is expanded in the following Taylor series in a.
c(x, a) = c0(x) + ac1(x) + a c2(x) + …
2
Y p (x ) =
J p ( x ) cos ( pπ) − J − p ( x )
sin ( pπ)
(Bessel function of the second kind) (replace right-hand side by limiting
value if p is an integer or zero) .
The series converges for all x. Much of the importance of Bessel’s equation
and Bessel functions lies in the fact that the solutions of numerous linear
differential equations can be expressed in terms of them .
Legendre’s Equation The Legendre equation (1 - x2)y″ - 2xy′ + n(n + 1)
y = 0, n ≥ 0, has the solution Pn for n an integer .
The polynomials Pn are the so-called Legendre polynomials, P0(x) = 1,
P1(x) = x, P2(x) = ½(3x2 - 1), P3(x) = ½(5x3 - 3x), … For n positive and not an
integer, see Olver et al . (2010) in General References .
Laguerre’s Equation The Laguerre equation x(d2y/dx2) + (c - x)
(dy/dx) - ay = 0 is satisfied by the confluent hypergeometric function . See
Olver et al . (2010) in General References .
Hermite’s Equation The Hermite equation y ′′ − 2 xy ′ + 2ny = 0 is satisfied by the Hermite polynomial of degree n, y = AHn(x), if n is a positive
integer or zero . H0(x) = 1, H1(x) = 2x, H2(x) = 4x2 - 2, H3(x) = 8x3 - 12x, H4(x) =
16x4 - 48x2 + 12, Hr+1(x) = 2xHr(x) - 2rHr-1(x) .
Chebyshev’s Equation The equation (1 − x 2 ) y ′′ − xy ′ + n 2 y = 0 for
n a positive integer or zero is satisfied by the nth Chebyshev polynomial
y = ATn(x) . T0(x) = 1, T1(x) = x, T2(x) = 2x2 - 1, T3(x) = 4x3 - 3x, T4(x) = 8x4 8x2 + 1; Tr+1(x) = 2xTr(x) - Tr -1(x) .
PARTIAL DIFFEREnTIAL EQUATIOnS
The analysis of situations involving two or more independent variables
frequently results in a partial differential equation .
Example The equation ∂T/∂t = k(∂2T/∂x2) represents the unsteady onedimensional conduction of heat .
Example The equation for the unsteady transverse motion of a uniform
beam clamped at the ends is
∂ 4 y ρ ∂2 y
=0
+
∂ x 4 EI ∂t 2
3-28
MATHEMATICS
Example The expansion of a gas behind a piston is characterized by the
simultaneous equations
The equations for flow and adsorption in a packed bed or chromatography
column give a quasilinear equation .
∂u
∂u
∂ρ
∂u c 2 ∂ρ
∂u
+ρ = 0
+u
= 0 and
+u +
∂x
∂x
∂t
∂x ρ ∂x
∂t
The partial differential equation ∂2f/(∂x ∂y) = 0 can be solved by two integrations yielding the solution f = g(x) + h(y), where g(x) and h(y) are arbitrary differentiable functions . This result is an example of the fact that the general solution
of partial differential equations involves arbitrary functions in contrast to the
solution of ordinary differential equations, which involve only arbitrary constants . A number of methods are available for finding the general solution of a
partial differential equation . In most applications of partial differential equations, the general solution is of limited use . In such applications the solution of a
partial differential equation must satisfy both the equation and certain auxiliary
conditions called initial and/or boundary conditions, which are dictated by the
problem . Examples of these include those in which the wall temperature is a
fixed constant T(x0) = T0, there is no diffusion across a nonpermeable wall, and
the like . In ordinary differential equations, these auxiliary conditions allow
definite numbers to be assigned to the constants of integration .
Partial Differential Equations of Second and Higher Order Many
of the applications to scientific problems fall naturally into partial differential equations of second order, although there are important exceptions
in elasticity, vibration theory, and elsewhere . A second-order differential
equation can be written as
a
∂2 u
∂2 u
∂2 u
+c 2 = f
+b
2
∂y
∂x ∂ y
∂x
where a, b, c, and f depend upon x, y, u, ∂u/∂x, and ∂u/∂y. This equation is
hyperbolic, parabolic, or elliptic, depending on whether the discriminant
b2 - 4ac > 0, = 0, or < 0, respectively . Since a, b, c, and f depend on the solution, the type of equation can be different at different x and y locations . If the
equation is hyperbolic, discontinuities can be propagated . See Courant and
Hilbert (1953, 1962) and LeVeque, R . J ., Numerical Methods for Conservation
Laws, Birkhäuser, Basel, Switzerland, 1992 .
Phenomena of propagation such as vibrations are characterized by equations of “hyperbolic” type which are essentially different in their properties
from other classes such as those which describe equilibrium (elliptic) or
unsteady diffusion and heat transfer (parabolic) . Prototypes are as follows:
Elliptic Laplace’s equation ∂2u/∂x2 + ∂2u/∂y2 = 0 and Poisson’s equation
∂2u/∂x2 + ∂2u/∂y2 = g(x, y) do not contain the variable time explicitly and consequently represent equilibrium configurations . Laplace’s equation is satisfied
by static electric or magnetic potential at points free from electric charges or
magnetic poles . Other important functions satisfying Laplace’s equation are
the velocity potential of the irrotational motion of an incompressible fluid,
used in hydrodynamics; the steady temperature at points in a homogeneous
solid; and the steady state of diffusion through a homogeneous body .
Parabolic The heat equation ∂T/∂t = ∂2T/∂x2 + ∂2T/∂y2 represents nonequilibrium or unsteady states of heat conduction and diffusion .
Hyperbolic The wave equation ∂2u/∂t2 = c2(∂2u/∂x2 + ∂2u/∂y2) represents
wave propagation of many varied types .
Quasilinear first-order differential equations are like
a
∂u
∂u
= f
+b
∂y
∂x
φ
df ∂c
∂c
∂c
=0
+ (1 − φ)
+ φu
dc ∂t
∂x
∂t
Here n = f (c) is the relation between concentration on the adsorbent and
fluid concentration .
The solution of problems involving partial differential equations often
revolves about an attempt to reduce the partial differential equation to one
or more ordinary differential equations . The solutions of the ordinary differential equations are then combined (if possible) so that the boundary
conditions and the original partial differential equation are simultaneously
satisfied . Three of these techniques are illustrated .
Similarity Variables The physical meaning of the term “similarity”
relates to internal similitude, or self-similitude . Thus, similar solutions in
boundary-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles
located at different coordinates x differ only by a scale factor . The mathematical interpretation of the term similarity is a transformation of variables
carried out so that a reduction in the number of independent variables is
achieved . There are essentially two methods for finding similarity variables,
“separation of variables” (not the classical concept) and the use of “continuous transformation groups .” The basic theory is available in Ames (1965) .
Example The equation ∂q/∂x = (A/y)(∂2q/∂y2) with the boundary conditions q = 0 at x = 0, y > 0; q = 0 at y = ∞, x > 0; q = 1 at y = 0, x > 0 represents
the nondimensional temperature q of a fluid moving past an infinitely wide
flat plate immersed in the fluid . Turbulent transfer is neglected, as is molecular transport except in the y direction . It is now assumed that the equation and the boundary conditions can be satisfied by a solution of the form
q = f (y/xn) = f (u), where q = 0 at u = ∞ and q = 1 at u = 0 . The purpose here is
to replace the independent variables x and y by the single variable u when
it is hoped that a value of n exists which will allow x and y to be completely
eliminated in the equation . In this case since u = y/xn, there results after
some calculation ∂q/∂x = -(nu/x)(dq/du), ∂2q/∂y2 = (1/x2n)(d2q/du2), and
when these are substituted in the equation, -(1/x)nu (dq/du) = (1/x3n)(A/u)
(d2q/du2) . For this to be a function of u only, choose n = ⅓ . There results
(d2q/du2) + (u2/3A)(dq/du) = 0 . Two integrations and use of the boundary
conditions for this ordinary differential equation give the solution
∞
∞
u
0
θ = ∫ exp(-u 3 /9 A ) du / ∫
exp (-u 3 /9 A ) du
Group Method The type of transformation can be deduced using
group theory . For a complete exposition, see Ames (1965) and Hill, J . M .,
Differential Equations and Group Methods for Scientists and Engineers, CRC
Press, New York, 1992; a shortened version can be found in Finlayson (1980) .
Basically, a similarity transformation should be considered when one of the
independent variables has no physical scale (perhaps it goes to infinity) . The
boundary conditions must also simplify (and combine) since each transformation leads to a differential equation with one fewer independent variable .
Example A similarity variable is found for the problem
∂c ∂ D (c ) ∂c
=
, c (0, t ) = 1, c (∞ , t ) = 0, c ( x , 0) = 0
∂t ∂ x D0 ∂ x
where a, b, and f depend on x, y, and u, with a2 + b2 ≠ 0 . This equation can
be solved using the method of characteristics, which writes the solution
in terms of a parameter s, which defines a path for the characteristic .
Note that the length dimension goes to infinity, so there is no length scale in
the problem statement; this is a clue to try a similarity transformation . The
transformation examined here is
du
dy
dx
= a,
= b,
= f
ds
ds
ds
t = a αt , x = a β x , c = a γ c
These equations are integrated from some initial conditions . For a specified
value of s, the value of x and y shows the location where the solution is u.
The equation is semilinear if a and b depend just on x and y (and not u),
and the equation is linear if a, b, and f all depend on x and y, but not u. Such
equations give rise to shock propagation, and conditions have been derived
to deduce the presence of shocks . Courant and Hilbert (1953, 1962); Rhee,
H . K ., R . Aris, and N . R . Amundson, First-Order Partial Differential Equations,
vol . 1, Theory and Applications of Single Equations, Prentice-Hall, Englewood
Cliffs, N .J ., 1986; and LeVeque (1992), ibid .
An example of a linear hyperbolic equation is the advection equation for
flow of contaminants when the x and y velocity components are u and v,
respectively .
∂c
∂c
∂c
=0
+v
+u
∂y
∂x
∂t
With this substitution, the equation becomes
a α−γ
∂ D ( a − γ c ) ∂c
∂c
= a 2β − γ
∂ x D0
∂x
∂t
Group theory says a system is conformally invariant if it has the same form
in the new variables; here, that is
γ=0
α - γ = 2b - γ
The invariants are
η=
β
x
, δ=
α
tδ
or α = 2b
DIFFEREnTIAL EQUATIOnS
and the solution is
Then u(x, t) satisfies
c(x, t) = f (h)t
γ/α
We can take γ = 0 and d = b/α = ½. Note that the boundary conditions combine because the point x = ∞ and t = 0 gives the same value of h and the conditions on c at x = ∞ and t = 0 are the same. We thus make the transformation
η=
x
∂2 u
∂u
= D 2 , u ( x , 0) = − 1, u (0, t ) = 0, u ( L , t ) = 0
L
∂x
∂t
Assume a solution of the form u(x, t) = X(x)T(t), which gives
1 dT 1 d 2 X
=
DT dt X dx 2
x
, c ( x , t ) = f ( η)
4 D0t
The use of the 4 and D0 makes the analysis below simpler. The result is
Since both sides are constant, this gives the following ordinary differential
equations to solve:
d D (c ) df
df
= 0, f (0) = 1, f (∞) = 0
+ 2η
d η D0 d η
dη
Thus, we solve a two-point boundary-value problem instead of a partial
differential equation. When the diffusivity is constant, the solution is the
error function, a tabulated function.
c ( x , t ) = 1 − erf η = erfc η
η
2
∞
1 dT
1 d2X
= −λ ,
= −λ
DT dt
X dx 2
The solution of these is
T = Ae − λDt
0
The combined solution for u(x, t) is
0
Separation of Variables This powerful, well-utilized method is applicable in certain circumstances. It consists of assuming that the solution
for a partial differential equation has the form U = f (x)g(y). If it is then possible to obtain an ordinary differential equation on one side of the equation
depending on only x and on the other side on only y, the partial differential
equation is said to be separable in the variables x and y. If this is the case, one
side of the equation is a function of x alone and the other of y alone. The two
can be equal only if each is a constant, say, l. Thus the problem has again
been reduced to the solution of ordinary differential equations.
Example Laplace’s equation ∂2V/∂x2 + ∂2V/∂y2 = 0 plus the boundary conditions V(0, y) = 0, V(l, y) = 0, V(x, ∞) = 0, V(x, 0) = f (x) represents
the steady-state potential in a thin plate (in the z direction) of infinite
extent in the y direction and of width l in the x direction . A potential f (x)
is impressed (at y = 0) from x = 0 to x = 1, and the sides are grounded . To
obtain a solution of this boundary-value problem, assume V(x, y) = f (x)g(y) .
Substitution in the differential equation yields f ′′( x ) g ( y ) + f ( x ) g ′′( y ) = 0 or
g ′′( y )/g ( y ) = − f ′′( x )/f ( x ) = λ 2 (say) . This system becomes g ′′( y ) − λ 2 g ( y ) = 0
and f ′′( y ) + λ 2 f ( y ) = 0 . The solutions of these ordinary differential equations are, respectively, g(y) = Aely + Be–ly and f (x) = C sin lx + D cos lx. Then
f (x)g(y) = (Aely + Be–ly) (C sin lx + D cos lx) . Now V(0, y) = 0 so that f (0)g(y) =
(Aely + Be-ly) D ≡ 0 for all y. Hence D = 0 . The solution then has the form
sin lx (Aely + Be-ly) where the multiplicative constant C has been eliminated .
Since V(l, y) = 0, sin ll(Aely + Be-ly) ≡ 0 . Clearly the bracketed function of y
is not zero, for the solution would then be the identically zero solution .
Hence sin ll = 0 or ln = nπ/l, n = 1, 2, …, where ln = nth eigenvalue .
The solution now has the form sin (nπx/l)(Aenπy/l + Be-nπy/l) . Since
V(x, ∞) = 0, A must be taken to be zero because ey becomes arbitrarily large
as y → ∞ . The solution then reads Bn sin (nπx/l)e-nπy/l, where Bn is the multiplicative constant . The differential equation is linear and homogeneous
∞
so that ∑ n=1 Bn e − nπy /l sin (nπx/l) is also a solution . Satisfaction of the last
boundary condition is ensured by taking
2 l
f ( x ) sin (nπx/l) dx = Fourier sine coefficients of f (x)
l ∫0
Further, convergence and differentiability of this series are established
quite easily . Thus the solution is
∞
V ( x , y ) = ∑ Bn e − nπy /l sin
n =1
nπx
l
Example The diffusion problem in a slab of thickness L
∂2 c
∂c
= D 2 , c (0, t ) = 1, c ( L , t ) = 0, c ( x , 0) = 0
∂x
∂t
can be solved by separation of variables . First transform the problem so that
the boundary conditions are homogeneous (having zeros on the right-hand
side) . Let
c(x , t ) = 1 −
X = B cos λ x + E sin λ x
2
erf η = ∫ e − ξ d ξ / ∫ e − ξ d ξ
Bn =
3-29
x
+ u( x , t )
L
u = A ( B cos λ x + E sin λ x ) e − λDt
Apply the boundary condition that u(0, t) = 0 to give B = 0 . Then the solution is
u = A (sin λ x )e − λDt
where the multiplicative constant E has been eliminated . Apply the boundary condition at x = L.
0 = A (sin λ L)e − λDt
This can be satisfied by choosing A = 0, which gives no solution . However, it
can also be satisfied by choosing l such that
sin λ L = 0, λ L = n π
Thus
λ=
n 2π2
L2
The combined solution can now be written as
sin nπx − n 2 π 2 Dt / L2
e
u= A
L
Since the initial condition must be satisfied, we use an infinite series of these
functions .
∞
sin nπx − n 2 π 2 Dt / L2
e
u = ∑ An
L
n =1
At t = 0, we satisfy the initial condition .
∞
x
sin nπ x
− 1 = ∑ An
L
L
n =1
This is done by multiplying the equation by
sin mπx
L
and integrating over x: 0 → L. (This is the same as minimizing the mean
square error of the initial condition .) This gives
L x
Am L
mπx
= ∫ − 1 sin
dx
0 L
2
L
which completes the solution .
Integral-Transform Method A number of integral transforms are used
in the solution of differential equations . Only one, the Laplace transform, is
discussed here [ for others, see Integral Transforms (Operational Methods)] .
3-30
MATHEMATICS
The one-sided Laplace transform indicated by L[ f (t)] is defined by the equation
∞
L[ f (t)] ∫ f (t )e − st dt . It has numerous important properties. The ones of
0
interest here are L[ f ′(t )] = sL[ f (t )] − f (0) L[ f ′′(t )] = s 2 L[ f (t )] − sf (0) − f ′(0);
L[ f (n)(t)] = snL[ f (t)] - sn -1f (0) - sn -2 f ′(0) - … - f (n -1)(0) for ordinary
derivatives. For partial derivatives an indication of which variable is being
transformed avoids confusion. Thus, if
∫
0
or
e − st
1 ∞
∂c
∂2 c
dt = ∫ e − st dt
∂t
D 0
∂x 2
sF
d 2F
= (1/D ) sF − c ( x ,0) =
D
dx 2
where F(x, s) = Lt[c(x, t)] . Hence
∂y
y = y ( x , t ), Lt = sL[ y ( x , t )] − y ( x , 0)
∂t
d 2F s
− F =0
dx 2 D
∂ y dL [ y ( x , t )]
Lt = t
dx
∂x
whereas
∞
since L[ y(x, t)] is “really” only a function of x. Otherwise the results are
similar. These facts coupled with the linearity of the transform, i.e., L[af (t) +
bg(t)] = aL[ f (t)] + bL[g(t)], make it a useful device in solving some linear
differential equations. Its use reduces the solution of ordinary differential
equations to the solution of algebraic equations for L[y]. the inverse transform must be obtained either from tables or by use of complex inversion
methods.
Example The equation ∂c/∂t = D(∂2c/∂x2) represents the diffusion in a
semi-infinite medium, x ≥ 0 . Under the boundary conditions c(0, t) = c0 and
c(x, 0) = 0, find a solution of the diffusion equation . By taking the Laplace
transform of both sides with respect to t,
The other boundary condition transforms into F(0, s) = c0/s. Finally the solution of the ordinary differential equation for F subject to F(0, s) = c0/s and F
remains finite as x → ∞ is F ( x , s ) = (c0 /s )e − s/ D x . Reference to a table shows
that the function having this as its Laplace transform is
2
c ( x , t ) = c0 1 −
π
∫
π/2 Dt
0
2
x
e − u du = C 0 erfc
4 Dt
This is the same solution obtained above by the group method .
Matched-Asymptotic Expansions Sometimes the coefficient in front of
the highest derivative is a small number . Special perturbation techniques can
then be used, provided the proper scaling laws are found . See Holmes, M . H .,
Introduction to Perturbation Methods, 2d ed ., Springer, New York, 2013 .
DIFFEREnCE EQUATIOnS
References: Elaydi, Saber, An Introduction to Difference Equations, 3d ed .,
Springer-Verlag, New York, 2005; Kelley, W . G ., and A . C . Peterson, Difference
Equations: An Introduction with Applications, 2d ed ., Harcourt/Academic,
San Diego, Calif ., 2001 .
Some models have independent variables that do not vary continuously,
but have meaning only for discrete values . Stagewise processes such as distillation, staged extraction systems, absorption columns, and continuous
stirred tank reactors (CSTRs) are such processes . The dependent variable
varies between stages, and the independent variable is the integral number
of the stage . Difference equations arise in discrete models of environmental problems (see Logan and Wolesensky) . Difference equations also arise
in the solution of partial differential equations using the finite difference
method, and those are treated below (Numerical Analysis and Approximate
Methods) . Examined here are solution methods applicable to the chemical
engineering problems; for more detailed information see the references . The
methods for difference equations mirror those for differential equations .
In particular, find complementary solution and then a particular solution .
The order of the difference equation is the difference between the largest
and smallest arguments .
Consider the countercurrent cascade shown in Fig . 3-45 . We let yi be the
ratio of the mass of solute to mass of solvent in the ith cell; xi is the ratio of
mass of solute to mass of carrier solvent in the ith cell . For illustration we
take the equilibrium relation as linear
yi = Kxi
A material balance on the ith stage gives
Lxi -1 + Vyi+1 - Lxi - Vyi = 0
Using the equilibrium relation transforms this equation to the form
(L/K) yi-1 + Vyi+1 - (L/K)yi - Vyi = 0
or
yi+1 - [(L/VK) + 1] yi + (L/VK)yi-1 = 0
With α = L/VK the final form of the difference equation is yi+1 - (α + 1)yi +
αyi-1 = 0 . The solution is obtained by trying the general form yi = r i . This gives
the characteristic equation r2 - (α + 1)r + α = 0 . One root is r = 1, and call the
other root b . The solution is then yi = A + B bi . This completes the complementary solution . The number of units is taken as N . The particular solution
is found by choosing A and B to fit boundary conditions . Here they are taken
as the inlet feed composition x0 and the inlet solvent composition yN+1 . Using
y0 = Kx0, we obtain two equations for A and B . The solutions are A = Kx0 - B
and B = (Kx0 - yN+1)/(1 - bN+1) . The exit concentration is y1 = A + B b .
Nonlinear Difference Equations: Riccati Difference Equation The
Riccati equation yi+1 yi + ayi+1 + byi + c = 0 is a nonlinear difference equation
which can be solved by reduction to linear form . Set y = z + h. The equation
becomes zi+1zi + (h + a)zi+1 + (h + b)zi + h2 + (a + b)h + c = 0 . If h is selected
as a root of h2 + (a + b)h + c = 0 and the equation is divided by zi+1zi, there
results (h + b)/zi+1 + (h + a)/zi + 1 = 0 . This is a linear equation with constant
coefficients for wi = 1/zi. The solution is
i
a+h
1
1
= K −
−
yi − h
b + h (a + h) + (b + h)
y1
y2
L
x0
FIG. 3-45
cell 1
y3
y2 = K2x2
y1 = K1x1
x1
cell 2
y4
V
y3 = K3x3
x2
cell 3
x3
Countercurrent cascade .
where K is a constant chosen to fit conditions at one point . This equation
is obtained in distillation problems, among others, in which the number of
theoretical plates is required . If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor
rates are constant, then a material balance around the nth plate of the
enriching section yields a Riccati difference equation .
InTEGRAL EQUATIOnS
References: Davis, H . T ., Introduction to Nonlinear Differential and
Integral Equations, Dover, New York, 2010; Statgold, I ., and M . J . Holst,
Green’s Functions and Boundary Value Problems, 3d ed ., Interscience,
New York, 2011 .
An integral equation is any equation in which the unknown function
appears under the sign of integration and possibly outside the sign of
integration . If derivatives of the dependent variable appear elsewhere in the
equation, the equation is said to be integrodifferential .
InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS)
CLASSIFICATIOn OF InTEGRAL EQUATIOnS
Volterra’s integral equations have an integral with a variable limit, whereas
Fredholm’s integral equations have a fixed limit. The Volterra equation of
the second kind is
Integral equations can arise from the formulation of a problem by using
Green’s function. The equation governing heat conduction with a variable
heat generation rate is represented in differential form as
d 2T Q ( x )
=
dx 2
k
x
u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt
a
3-31
T (0) = T (1) = 0
In integral form the same problem is
whereas a Volterra equation of the first kind is
1
T (x ) =
x
u ( x ) = λ ∫ K ( x , t )u (t ) dt
a
Equations of the first kind are very sensitive to solution errors so that they
present severe numerical problems. Volterra equations are similar to initialvalue problems.
A Fredholm equation of the second kind is
b
u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt
1
G ( x , y )Q ( y ) dy
k ∫0
− x (1 − y )
G(x , y ) =
− y (1 − x )
x≤y
y ≤x
The Poisson equation governs electric charges
a
∇ 2 Ψ = −4 πρ
whereas a Fredholm equation of the first kind is
b
u ( x ) = ∫ K ( x , t )u (t ) dt
and the formulation as an integral equation is
a
The limits of integration are fixed, and these problems are analogous to
boundary value problems.
An eigenvalue problem is a homogeneous equation of the second kind,
and solutions exist only for certain l.
Ψ (r) = ∫ ρ(r0 )G (r , r0 ) dV0
V
where Green’s function in three dimensions is
1
G (r , r0 ) = , r = ( x − x 0 )2 + ( y − y 0 )2 + ( z − z 0 )2
r
b
u ( x ) = λ ∫ K ( x , t )u (t ) dt
a
An example of a Volterra equation is the heat conduction problem in a
semi-infinite domain.
ρC p
∂2 T
∂T
=k 2
∂x
∂t
T ( x , 0) = 0
limT ( x , t ) = 0
x →0
G (r , r0 ) = −2 ln r , r = ( x − x 0 )2 + ( y − y 0 )2
0 ≤ x < ∞, t > 0
∂T
(0, t ) = − g (t )
∂x
∂T
lim
(x , t ) = 0
x →∞ ∂ x
If this is solved by using Fourier transforms [see Integral Transforms
(Operational Methods)], the solution is
1
T (x ) =
1
G ( x , y )Q ( y ) dy
k ∫0
1
T (x , t ) =
and in two dimensions is
2
1
1
e − x /4( t − s ) ds
g (s )
π ∫0
t−s
See the references for other examples.
Integral equations can be solved numerically, too. The methods are
analogous to the usual methods for integrating differential equations
(Runge-Kutta, predictor-corrector, Adams methods, etc.). Explicit methods
are fast and efficient until the time step is very small, to meet the stability requirements. Then implicit methods are used, even though sets
of simultaneous algebraic equations must be solved. The major part of
the calculation is the evaluation of integrals, however, so that the added
time to solve the algebraic equations is not excessive. Thus, implicit
methods tend to be preferred. Volterra equations of the first kind are
not well posed, and small errors in the solution can have disastrous consequences. The boundary element method uses Green’s functions and
integral equations to solve differential equations. See Brebbia, C. A.,
and J. Dominguez, Boundary Elements—An Introductory Course, 2d ed.,
Computational Mechanics Publications, Southhampton, UK, 1992; and
Mackerle, J., and C. A. Brebbia, eds., Boundary Element Reference Book,
Springer Verlag, Berlin, 1988.
InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS)
References: Davies, B., Integral Transforms and Their Applications, 3d ed.,
Springer, New York, 2002; Debnath, L., and D. Bhatta, Integral Transforms
and Their Applications, 3d ed., Chapman and Hall/CRC, New York, 2014;
Duffy, D. G., Transform Methods for Solving Partial Differential Equations,
Chapman & Hall/CRC, New York, 2nd ed., 2004; see also references for
Differential Equations.
The term operational method implies a procedure of solving differential
and difference equations by which the boundary or initial conditions are
automatically satisfied in the course of the solution. The technique offers
a very powerful tool in the applications of mathematics, but it is limited to
linear problems.
Most integral transforms are special cases of the equation g (s) =
∫
b
a
f (t ) K ( s , t )dt in which g(s) is said to be the transform of f (t) and K(s, t)
is called the kernel of the transform. A tabulation of the more important
kernels and the interval (a, b) of applicability follows.
Name of transform
(a, b)
K(s, t)
e-st
Laplace
(0, ∞)
Fourier
(–∞, ∞)
1 − ist
e
2π
Fourier cosine
(0, ∞)
2
cos st
π
Fourier sine
(0, ∞)
2
sin st
π
3-32
MATHEMATICS
LAPLACE TRAnSFORM
The Laplace transform of a function f (t) is defined by F(s) =
∞
L{ f (t )} = ∫ e − st f (t ) dt , where s is a complex variable. Note that the trans0
form is an improper integral and therefore may not exist for all continuous functions and all values of s. We restrict consideration to those values
of s and those functions f for which this improper integral converges. The
Laplace transform is used in process control (see Sec. 8).
The function L[ f (t)] = g(s) is called the direct transform, and L-1[g(s)] = f (t)
is called the inverse transform. Both the direct and the inverse transforms
are tabulated for many often recurring functions. In general,
L-1[ g ( s )] =
6. Transform of a derivative. Let f be a differentiable function such that
both f and f ¢ belong to the class L. Then L{ f ¢ (t)} = sF(s) - f (0).
7. Transform of a higher-order derivative. Let f be a function which has
continuous derivatives up to order n on (0, ∞), and suppose that f and its
derivatives up to order n belong to the class L. Then L{ f (j)(t)} = s jF(s) - s j-1
f (0) - s j -2f ¢(0) - … - sf ( j -2)(0) - f (j -1)(0) for j = 1, 2, …, k.
Example L{ f ″(t)} = s2L{ f (t)} - sf (0) - f¢ (0)
Example Solve y ″ + y = 2et, y(0) = y¢(0) = 2. L[y ″] = -y¢(0) - sy(0) + s2L[y] =
-2 - 2s + s2L[y]. Thus
−2 − 2 s + s 2 L[ y ] + L[ y ] = 2 L[e t ] =
1 α+i∞ st
e g ( s ) ds
2 πi ∫α−i∞
0
Laplace transform of f exists for all complex numbers s with a sufficiently
large real part.
Note that condition 3 is automatically satisfied if f is assumed to be piecewise continuous on every finite interval 0 ≤ t < T. The function f (t) = t-1/2 is
not piecewise continuous on 0 ≤ t < T but satisfies conditions 1 to 3.
Let L denote the class of all functions on 0 < t < ∞ which satisfy conditions 1 to 3.
Example Let f (t) be the Heaviside step function at t = t0; that is, f (t) = 0
for t ≤ t0 and f (t) = 1 for t > t0. Then
Hence y = et + cos t + sin t.
A short table (Table 3-2) of very common Laplace transforms and
inverse transforms follows. The references and computer programs
include more detailed tables. In Mathematica, the command∞ “Laplace
Transform[cosh[a*t],t,s]” returns s/(s2−a2). note: Γ (n + 1) = x n e − x dx
∫
0
(gamma function); Jn(t) = Bessel function of the first kind of order n.
t
1
1 0
8. L ∫a f (t ) dt = L[ f (t )] + ∫a f (t ) dt
s
s
TABLE 3-2 Laplace Transforms
f (t)
L{ f (t )} = ∫ e
− st
t0
∫
∞
0
dt = lim ∫ e
T →∞
− st
t0
e − st0
1
dt = lim (e − st0 − e − sT ) =
T →∞ s
s
provided s > 0
Example Let f (t) = eαt, t ≥ 0, where a is a real number. Then L{eαt} =
e − ( s −a ) t dt = 1/( s − a ) provided Re s > a.
Properties of the Laplace Transform
1. The Laplace transform is a linear operator: L{af (t) + bg(t)} = aL{ f (t)} +
bL{g(t)} for any constants a and b and any two functions f and g whose
Laplace transforms exist.
2. The Laplace transform of a real-valued function is real for real s. If f (t)
is a complex-valued function f (t) = u(t) + iu(t), where u and u are real, then
L{ f (t)} = L{u(t)} + iL{u(t)}. Thus L{u(t)} is the real part of L{ f (t)}, and L{u(t)}
is the imaginary part of L{ f (t)}.
3. The Laplace transform of a function in the class L has derivatives of
all orders, and L{t kf (t)} = (-1)k d kF(s)/dsk, k = 1, 2, 3, … , where F(s) is the
Laplace transform of f (t).
∞
a
st
Example ∫0 e sin at dt = 2 2 , s > 0.
s +a
∞
2 as
By property 3, L{t sin at } = ∫ e - st t sin at dt = 2
0
( s + a 2 )2
Example By applying property 3 with f (t) = 1 and using the preceding
results, we obtain
dk 1
k!
L{t k } = (−1) k k = k+1
ds s s
provided Re s > 0 for k = 1, 2, … . Similarly, we obtain
L{t k e at } = (−1) k
dk 1
k!
=
ds k s − a ( s − a ) k +1
4. Frequency-shift property (or, equivalently, the transform of an exponentially modulated function). If F (s) is the Laplace transform of a function
f (t) in class L, then for any constant a, L{eatf (t)} = F(s - a).
Example
L{te − at } =
1
( s + a )2
( s > 0).
5. Time-shift property. Let u(t - a) be the unit step function at t = a. Then
L{ f (t - a)u(t - a)} = e-asF(s).
f (t)
g(s)
1
1/s
e-at(1 - at)
tn, (n = + integer)
n!
s n +1
Γ (n + 1)
s n +1
s
s2 + a2
t sin at
2a
1
sin at sinh at
2a 2
cos at cosh at
tn, (n ≠ + integer)
cos at
T
∞
2s 2
1
1
s
=
+
+
( s − 1)( s 2 + 1) s − 1 s 2 + 1 s 2 + 1
L[ y ] =
and to evaluate this integral requires a knowledge of complex variables, the
theory of residues, and contour integration.
A function is said to be piecewise continuous on an interval if it has only a
finite number of finite (or jump) discontinuities. A function f on 0 < t < ∞ is
said to be of exponential growth at infinity if there exist constants M and α
such that | f (t)| ≤ Meat for sufficiently large t.
Sufficient Conditions for the Existence of the Laplace
Transform Suppose f is a function which is (1) piecewise continuous
on every finite interval 0 < t < T, (2) of exponential growth at infinity, and
δ
(3) for which ∫ | f (t )| dt exists ( finite) for every finite d > 0. Then the
2
s −1
a
s2 + a2
s
s2 − a2
sin at
cosh at
e-at
e
sin at
t
J0(at)
e-bt sin at
1 −k
e
s
k
2 t
s3
s 2 + 4a 4
s2
s4 − a4
s3
s4 − a4
a
tan −1
s
1
s2 + a2
s +b
( s + b)2 + a 2
a
( s + b)2 + a 2
cos at
erfc
½(cosh at + cos at)
a
s2 − a2
1
s+a
sinh at
-bt
1
(sinh at + sin at )
2a
g (s)
s
( s + a )2
s
( s 2 + a 2 )2
s
s 4 + 4a 4
na n
J n (at )
t
( s 2 + a 2 − s )n (n > 0)
1 − a/s
e
s
Γ (n)
(n > 0)
( s − a )n
J 0 (2 at )
t n −1e at
s
Example Find f (t) if L[ f (t )] =
1 1 1
1
. L sinh at = 2
.
s 2 s 2 − a 2 a
s − a2
t
t1
1 sinh at
Therefore f (t ) = ∫ ∫ sinh at dt dt = 2
− t .
0
a a
0a
∞
f (t )
= g ( s ) ds
9. L
t ∫s
∞
∞
f (t )
L k = ∫ ⋯∫ g ( s )(ds ) k
s
s
t
k integrals
Example
L
∞ a ds
sin at ∞
s
= L[sin at ] ds = ∫ 2
= cot −1
s s + a2
a
t ∫s
10. The unit step function
0 t < a
u (t − a ) =
1 t > a
L[u (t − a )] =
e − as
s
MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS
11. The unit impulse function is
∞ at t = a
δ(a ) = u ′(t − a ) =
0 elsewhere
The Fourier transform is given by
L[u ′(t − a )] = e − as
12. L-1[e-asg(s)] = f (t - a)u(t - a) (second shift theorem).
13. If f (t) is periodic of period b, that is, f (t + b) = f (t), then
F [ f (t )] =
F -1[ g ( s )] =
Example The partial differential equations relating gas composition to
position and time in a gas chromatograph are ∂y/∂n + ∂x/∂q = 0 and ∂y/∂n =
x - y, where x = mx′, n = (kGaP/Gm)h, θ = (mkGaP/ρB)t and GM = molar velocity,
y = mole fraction of the component in the gas phase, ρB = bulk density, h =
distance from entrance, P = pressure, kG = mass-transfer coefficient, and
m = slope of the equilibrium line . These equations are equivalent to ∂2y/∂n
∂θ + ∂y/∂n + ∂y/∂q = 0, where the boundary conditions considered here are
y(0, θ) = 0 and x(n, 0) = y(n, 0) + (∂y/∂n) (n, 0) = δ(0) (see property 11) . The
problem is conveniently solved
by using the Laplace transform of y with
∞
- ns
respect to n; write g ( s , θ) = ∫0 e y (n , θ) dn . Operating on the partial differential equation gives s(dg/dθ) - (∂y/∂q) (0, q) + sg - y(0, q) + dg/dq = 0
or (s + 1) (dg/dq) + sg = (∂y/∂θ) (0, θ) + y(0, q) = 0 . The second boundary
condition gives g(s, 0) + sg(s, 0) - y(0, 0) = 1 or g(s, 0) + sg(s, 0) = 1 (L[δ(0)] = 1) .
A solution of the ordinary differential equation for g consistent with this
second condition is
1 − sθ/( s +1)
g ( s , θ) =
e
s +1
Inversion of this transform gives the solution y (n , θ) = e − ( n+θ) I 0 (2 nθ ) where
I0 = zero-order Bessel function of an imaginary argument . For large u, In(u)
∼ e u / 2 πu . For large n,
exp[ −( θ − n )2 ]
2 π1/2 (nθ)1/4
or for sufficiently large n, the peak concentration occurs near θ = n.
Other applications of Laplace transforms are given under Differential
Equations .
∞
In brief, the condition for the Fourier transform to exist is that ∫ | f (t )| dt < ∞,
although certain functions may have a Fourier transform −∞
even if this is
violated .
1− a ≤ t ≤ a
a
Example The function f (t ) =
has F [ f (t )] = ∫ e − ist dt
−a
0 elsewhere
a
a
a
0
0
0
= ∫ e ist dt + ∫ e - ist dt = 2 ∫ cos st dt =
2 sin sa
s
Properties of the Fourier Transform Let F [ f (t)] = g(s); F -1[ g(s)] = f (t) .
1 . F [ f (n)(t)] = (is)nF [ f (t)] .
2 . F [a f (t) + bh(t)] = aF [ f (t)] + bF [h(t)] .
3 . F [ f (-t)] = g(-s) .
1 s
4 . F [ f (at )] = g , a > 0 .
a a
5 . F [e-iwtf (t)] = g(s + w) .
6 . F [ f (t + t1)] = eist1g(s) .
7 . F [ f (t)] = G(is) + G(-is) if f (t) = f (-t)
( f even)
F [ f (t)] = G(is) - G(-is) if f (t) = -f (-t) (f odd)
where G(s) = L[ f (t)] . This result allows the use of the Laplace transform
tables to obtain the Fourier transforms .
Example Find F [e-a|t|] by property 7 . Now e-a|t| is even . So L[e-at] = 1/(s + a) .
Therefore, F [e-a|t|] = 1/(is + a) + 1/(-is + a) = 2a/(s2 + a2) .
FOURIER COSInE TRAnSFORM
The
convolution integral of two functions f (t) and r(t) is x(t) = f (t)∗r(t) =
t
∫ f (τ)r (t − τ)d τ .
Example
1 ∞
g ( s )e ist dt = f (t )
2 π ∫−∞
The Fourier cosine transform is given by
COnVOLUTIOn InTEGRAL
0
1 ∞
f (t )- ist dt = g ( s )
2 π ∫−∞
and its inverse by
1 b − st
L[ f (t )] =
e f (t )dt
1 − e − bs ∫0
y (n , θ)
3-33
t
t ∗ sin t = ∫ τ sin(t − τ) d τ = t − sin t .
0
Fc [ f (t )] = g ( s ) =
2 ∞
f (t )cos st dt
π ∫0
Fc-1[ g ( s )] = f (t ) =
2 ∞
g ( s )cos st ds
π ∫0
and its inverse by
L[ f (t)]L[h(t)] = L[ f (t)∗h(t)]
FOURIER TRAnSFORM
References: https://en .wikipedia .org/wiki/Fourier_transform#Tables_
of_important_Fourier_transforms; Varma and Morbidelli (1997), see General
References .
The Fourier sine transform Fs is obtainable by replacing the cosine by
the sine in these integrals . They can be used to solve linear differential
equations; see the transform references .
MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS
References: Anton, H ., and C . Rorres, Elementary Linear Algebra
with Applications, 9th ed ., Wiley, New York, 2004; Bernstein, D . S ., Matrix
Mathematics: Theory, Facts, and Formulas with Application to Linear Systems
Theory, 2d ed ., Princeton University Press, Princeton, N .J ., 2009 .
MATRIX ALGEBRA
Matrices
n columns,
A rectangular array of mn quantities, arranged in m rows and
a11 ⋯ a1n
a ⋯ a
21
2n
A = (aij ) =
⋮
amn
am1
is called a matrix . The elements aij may be real or complex . The notation aij
means the element in the ith row and jth column; i is called the row index
and j the column index. If m = n, the matrix is said to be square and of order n.
A matrix, even if it is square, does not have a numerical value, as a determinant does . However, if the matrix A is square, a determinant can be formed
which has the same elements as matrix A. This is called the determinant
of the matrix and is written det (A) or |A| . If A is square and det (A) ≠ 0,
then A is said to be nonsingular; if det (A) = 0, then A is said to be singular .
A matrix A has rank r if and only if it has a nonvanishing determinant of
order r and no nonvanishing determinant of order > r.
Equality of Matrices Let A = (aij), B = (bij) . Two matrices A and B are
equal (=) if and only if they are identical; that is, they have the same number of rows and the same number of columns and equal corresponding
elements (aij = bij for all i and j) .
Addition and Subtraction The operations of addition (+) and
subtraction (-) of two or more matrices are possible if and only if the matrices
have the same number of rows and columns . Thus A ± B = (aij ± bij); i .e ., addition
and subtraction are of corresponding elements .
Transposition The matrix obtained from A by interchanging the rows
and columns of A is called the transpose of A, written A¢ or AT .
1 2
1 3 4
AT = 3 1
Example A =
2 1 6
4 6
Note that (AT)T = A .
3-34
MATHEMATICS
Multiplication Let A = (aij), i = 1, …, m1; j = 1, …, m2, and B = (bij),
i = 1, …, n1, j = 1, …, n2. The product AB is defined if and only if the number
of columns of A (m2) equals the number of rows of B (n1), that is, n1 = m2. For
two such matrices the product P = AB is defined by summing the elementby-element products of a row of A by a column of B.
This is the row-by-column rule. Thus
n1
Pij = ∑ aik bkj
k =1
The resulting matrix has m1 rows and n2 columns.
−4 3 17 24
3 2
1 1 0 1 5 6 = −2 1 6 9
Example
−2 0 1 3
−8 5 29 42
5 4
It is helpful to remember that the element Pij is formed from the ith row of
the first matrix and the jth column of the second matrix. The matrix product
is not commutative. That is, AB ≠ BA in general.
Inverse of a Matrix A square matrix A is said to have an inverse if there
exists a matrix B such that AB = BA = I, where I is the identity matrix of
order n.
The inverse B is a square matrix of the order of A, designated by A-1. Thus AA-1 =
A-1A = I. A square matrix A has an inverse if and only if A is nonsingular.
Certain relations are important:
(1)
(AB)-1 = B-1A-1
(2)
(AB)T = BTAT
(3)
(A-1)T = (AT )-1
(4)
(ABC)-1 = C-1B-1A-1
Scalar Multiplication Let c be any real or complex number. Then
cA = (caij).
Linear Equations in Matrix Form Every set of n nonhomogeneous
linear equations in n unknowns
a11 x 1 + a12 x 2 + ⋯ + a1n x n = b1
a21 x 1 + a22 x 2 + ⋯ + a2 n x n = b2
⋮
an1 x1 + an 2 x 2 + ⋯ + ann x n = bn
can be written in matrix form as AX = B, where A = (aij), XT = [x1 … xn], and
BT = [b1 … bn]. The solution for the unknowns is X = A-1B.
Special Square Matrices
1. A triangular matrix is a matrix all of whose elements above or below
the main diagonal (set of elements a11, …, ann) are zero.
If A is triangular, det (A) = a11a22 ann .
2. A diagonal matrix is one such that all elements both above and below
the main diagonal are zero (that is, aij = 0 for all i ≠ j). If all diagonal elements
are equal, the matrix is called scalar. If A is diagonal, A = (aij), A-1 = (1/aij).
3. If aij = aji for all i and j (that is, A = AT ), the matrix is symmetric.
4. If aij = -aji for i ≠ j but not all the aij are zero, the matrix is skew.
5. If aij = -aji for all i and j (that is, aii = 0), the matrix is skew symmetric.
6. If AT = A-1, the matrix A is orthogonal.
7. If the matrix A* = (aij )T and aij = complex conjugate of aij, then A* is the
hermitian transpose of A.
8. If A = A-1, then A is involutory.
9. If A = A*, then A is hermitian.
10. If A = -A*, then A is skew hermitian.
11. If A-1 = A*, then A is unitary.
If A is any matrix, then AAT and ATA are square symmetric matrices, usually of different order.
By using a program such as MATLAB, these are easily calculated.
Matrix Calculus
Differentiation Let the elements of A = [aij(t)] be differentiable funcdA daij (t )
tions of t. Then
.
=
dt dt
Example
sin t cos t
A=
− cos t sin t
t 2
A= 2 t
t e
Example
t 2/2 2t
.
3
e t
∫ Adt = t /3
The matrix B = A - lI is called the characteristic matrix or eigenmatrix
of A. Here A is square of order n, l is a scalar parameter, and I is the n × n
identity matrix. So det B = det (A - lI) = 0 is the characteristic equation
(or eigenequation) for A. The characteristic equation is always of the same
degree as the order of A. The roots of the characteristic equation are called
the eigenvalues of A or characteristic values of A.
1 2
A=
3 8
Example
1 2 λ 0 1 − λ 2 .
B=
=
−
3 8 0 λ 3 8 − λ
Above is the characteristic matrix and f (l) = det (B) = det (A - lI) = (1 - l)
(8 - l) - 6 = 2 − 9l + l2 = 0 is the characteristic equation. The eigenvalues of
A are the roots of l2 - 9l + 2 = 0, which are (9 ± 73)/2 .
A nonzero matrix Xi, which has one column and n rows, a column vector,
satisfying the equation
(A - lI)Xi = 0
1 0 ⋯⋅ 0
⋅⋅
0 1
⋮
1 0
0 ⋯⋅ 0 1
⋮
Integration The integral ∫ A dt = [ ∫ aij (t ) dt ].
dA cos t − sin t
=
dt sin t cos t
and associated with the ith characteristic root li is called an eigenvector.
Vector and Matrix Norms To carry out error analysis for approximate
and iterative methods for the solutions of linear systems, one needs notions
for vectors in Rn and for matrices that are analogous to the notion of length
of a geometric vector. Let Rn denote the set of all vectors with n components,
x = (x1, …, xn). In dealing with matrices it is convenient to treat vectors in Rn
as columns, and so x = (x1, …, xn)T; however, here we shall write them simply
as row vectors. A norm on Rn is a real-valued function f defined on Rn with
the following properties:
1. f (x) ≥ 0 for all x ∈ Rn.
2. f (x) = 0 if and only if x = (0, 0, …, 0).
3. f (ax) = |a| f (x) for all real numbers a and x ∈ Rn.
4. f (x + y) ≤ f (x) + f (y) for all x, y ∈ Rn.
The usual notation for a norm is f (x) = x .
The norm of a matrix is κ ( A ) ≡ A A −1
where
A sup x ≠0 =
n
Ax
= max k ∑ a jk
x
j =1
The norm is useful when doing numerical calculations. If the computer’s
floating-point precision is 10-6, then k = 106 indicates an ill-conditioned
matrix. If the floating-point precision is 10-12 (double precision), then a
matrix with k = 1012 may be ill-conditioned. Two other measures are useful
and are more easily calculated:
Ratio =
(k)
max k a kk
(k)
min k a kk
V=
det A
α 1α 2 α n
α1 = (α i21 + α i22 + + α in2 )1/2
where akk(k) are the diagonal elements of the LU decomposition.
MATRIX COMPUTATIOnS
The principal topics in linear algebra involve systems of linear equations,
matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, and least-squares problems. The calculations are routinely done on a
computer.
LU Factorization of a Matrix Let L be an n × n lower triangular matrix
with unit diagonal elements. Let U be an n × n upper triangular matrix. If
all the principal submatrices of an n × n matrix A are nonsingular, then it is
possible to represent A = LU. The Gauss elimination method is in essence an
algorithm to determine L and U.
Solution of Ax = b by Using LU Factorization Suppose that the indicated system is compatible and that A = LU. Let z = Ux. Then Ax = LUx = b
implies that Lz = b. Thus to solve Ax = b we first solve Lz = b for z and then
solve Ux = z for x. This procedure does not require that A be invertible and
can be used to determine all solutions of a compatible system Ax = b. Note
that the systems Lz = b and Ux = z are both in triangular form and thus can
be easily solved.
The LU decomposition is essentially a gaussian elimination, arranged for
maximum efficiency. The chief reason for doing an LU decomposition is
that it takes fewer multiplications than would be needed to find an inverse.
Also, once the LU decomposition has been found, it is possible to solve for
MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS
multiple right-hand sides with little increase in work. The multiplication
count for an n × n matrix and m right-hand sides is
1
1
Operation count = n 3 − n + mn 2
3
3
If an inverse is desired, it can be calculated by solving for the LU decomposition and then solving n problems with right-hand sides consisting of all
zeros except one entry. Thus 4n2/3 - n/3 multiplications are required for the
inverse. The determinant is given by
n
3-35
An m × m unitary matrix U is formed from the eigenvectors ui of the first
matrix.
U = [u1, u2, …, um]
An n × n unitary matrix V is formed from the eigenvectors vi of the second
matrix.
V = [v1, v2, …, vn]
Then matrix A can be decomposed into
Det A = ∏ aii( i )
i =1
where aii(i) are the diagonal elements obtained in the LU decomposition.
A tridiagonal matrix is one in which the only nonzero entries lie on the
main diagonal and on the diagonal just above and just below the main
diagonal. The set of equations can be written as
aixi-1 + bixi + cixi+1 = di
The LU decomposition is
b1 = b1
for k = 2, n do
a
a
ak′ = k , bk′ = bk − k c k−1
bk′−1
bk′−1
enddo
d1′ = d1
for k = 2, n do
d k′ = d k − ak′ d k′−1
A = U∑V*
where ∑ is a k × k diagonal matrix with diagonal elements dii = si > 0 for
1 ≤ i ≤ k. The eigenvalues of ∑*∑ are s2i. The vectors ui for k + 1 ≤ i ≤ m and
vi for k + 1 ≤ i ≤ n are eigenvectors associated with the eigenvalue zero;
the eigenvalues for 1 ≤ i ≤ k are s2i. The values of si are called the singular
values of matrix A. If A is real, then U and V are real and hence orthogonal
matrices. The value of the singular-value decomposition comes when a
process is represented by a linear transformation and the elements of A
and aij are the contribution to an output i for a particular variable as input
variable j. The input may be the size of a disturbance, and the output is the
gain (Seborg, D. E., T. F. Edgar, and D. A. Mellichamp, Process Dynamics and
Control, 2d ed., Wiley, New York, 2004). If the rank is less than n, not all the
variables are independent and they cannot all be controlled. Furthermore,
if the singular values are widely separated, the process is sensitive to small
changes in the elements of the matrix, and the process will be difficult to
control.
Example Consider the following example from Noble and Daniel
(Applied Linear Algebra, Prentice-Hall, Upper Saddle River, N.J., 1987) with
the MATLAB commands to do the analysis. Define the following real matrix
with m = 3 and n = 2 (whose rank k = 1).
>> a = [1 1
2 2
enddo
x n = dn′/bn′
2 2]
for k = n - 1,1 do
d′ − c x
x k = k k k+1
d k′
The following MATLAB commands are used.
a1 = a ∗ a
enddo
a 2 = a ∗ a′
The operation count for an n × n matrix with m right-hand sides is
[ v , d 1] = eig (a1)
2(n - 1) + m(3n - 2)
If |bi| > |ai| + |ci|, no pivoting is necessary, and this is true for many boundaryvalue problems and partial differential equations.
Sparse matrices are ones in which the majority of the elements are
zero. If the structure of the matrix is exploited, the solution time on a
computer is greatly reduced. See Duff, I. S., A. M. Erisman, and J. K. Reid,
Direct Methods for Sparse Matrices, Clarendon Press, Oxford, UK, 1986;
Davis, T. A., Direct Methods for Sparse Linear Systems, Society for Industrial
and Applied Mathematics, Philadelphia, Penn., 2006. The conjugate gradient method is one method for solving sparse matrix problems, since it
only involves multiplication of a matrix times a vector. Thus the sparseness of the matrix is easy to exploit. The conjugate gradient method is an
iterative method that converges for sure in n iterations where the matrix
is an n × n matrix.
Matrix methods, in particular finding the rank of the matrix, can be used
to find the number of independent reactions in a reaction set. If the
stoichiometric numbers for the reactions and molecules are put in the
form of a matrix, the rank of the matrix gives the number of independent reactions. See Amundson, N. R., Mathematical Methods in Chemical
Engineering, Prentice-Hall, Englewood Cliffs, N.J., 1966, p. 50. See also
Dimensional Analysis.
QR Factorization of a Matrix If A is an m × n matrix with m ≥ n,
there exists an m × m unitary matrix Q = [q1, q2, …, qm] and an m × n right
triangular matrix R such that A = QR. The QR factorization is frequently
used in the actual computations when the other transformations are
unstable.
Singular-Value Decomposition If A is an m × n matrix with m ≥ n and
rank k ≤ n, consider the two following matrices.
AA*
and
A*A
[u , d 2] = eig (a 2)
The results are
v = [ −0.7071 0.7071
0.7071 0.7071]
d 1 = [0 0
0 18]
u = [ 0.8944 0.2981 0.3333
− 0.4472 0.5963 0.6667
0 − 0.7454 0.6667]
d2 = 0 0 0
0 0 0
0 0 18
2
Thus, σ1 = 18 and the eigenfunctions are the rows of v and u. The second
column of v is associated with the eigenvalue σ12 = 18, and the third column
of u is associated with the eigenvalue σ12 = 18.
If A is square and nonsingular, the vector x that minimizes
||Ax - b||
is obtained by solving the linear equation
x = A-1b
(3-62)
3-36
MATHEMATICS
When A is not square, the solution to
mean by subtracting from each entry in the column the average of the column entries. Once this is done, the loadings are the vi and satisfy
Ax = b
cov(A) vi = σ i2 vi
is
and the score vector ui is given by
x = Vy
where yi = b′i/si for i = 1, …, k, b′ = UT b, and yk+1, yk+2, …, ym are arbitrary. The
matrices U and V are those obtained in the singular-value decomposition.
The solution which minimizes the norm, Eq. (3-62), is x with yk+1, yk+2, . . ., ym
zero. These techniques can be used to monitor process variables. See
Montgomery, D. C., Introduction to Statistical Quality Control, 6th ed.,
Wiley, New York, 2008; Piovos, M. J., and K. A. Hoo, “Multivariate Statistics
for Process Control,” IEEE Control Systems 22(5):8 (2002).
Principal Component Analysis (PCA) PCA is used to recognize patterns in data and reduce the dimensionality of the problem. Let the matrix A
now represent data with the columns of A representing different samples
and the rows representing different variables. The covariance matrix is
defined as
cov ( A ) =
AT A
m −1
This is just the same matrix discussed with singular-value decomposition.
For data analysis, however, it is necessary to adjust the columns to have zero
Avi = siui
In process analysis, the columns of A represent different measurement
techniques (temperatures, pressures, etc.), and the rows represent the
measurement output at different times. In that case the columns of A are
adjusted to have a zero mean and a variance of 1.0 (by dividing each entry
in the column by the variance of the column). The goal is to represent the
essential variation of the process with as few variables as possible. The ui, vi
pairs are arranged in descending order according to the associated si. The
si can be thought of as the variance, and the ui, vi pair captures the greatest
amount of variation in the data. Instead of having to deal with n variables,
one can capture most of the variation of the data by using only the first few
pairs. An excellent example of this is given by Wise, B. M., and B. R. Kowalski,
“Process Chemometrics,” Chap. 8 in Process Analytical Chemistry, eds.
F. McLennan and B. Kowalski, Blackie Academic & Professional, London,
1995. When modeling a slurry-fed ceramic melter, they were able to capture
97 percent of the variation by using only four eigenvalues and eigenvectors,
even though there were 16 variables (columns) measured.
nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS
APPROXIMATIOn IDEnTITIES
Approximation
For the following relationships the sign @ means approximately equal to,
when X is small. These equations are derived by using a Taylor’s series (see
Series Summation and Identities).
Approximation
1
≅1 X
1± X
Approximation
1± X ≅1±
X
2
Approximation
(1 ± X)n @ 1 ± nX
(1 ± X)-n @ 1 nX
(a ± X)2 = a2 ± 2aX
ex @ 1 + X
sin X @ X(X rad)
tan X @ X
2Y + X
Y (Y + X ) ≅
2
Stirling’s approximation
X2 X
small
2Y Y
In N! @ N ln N - N
Y 2 + X2 ≅Y +
nUMERICAL AnALYSIS AnD APPROXIMATE METHODS
References: Ascher, U. M., and C. Greif, A First Course in Numerical
Methods, SIAM-Soc. Ind. Appl. Math., 2011; Atkinson, K., W. Han, and D. E.
Stewart, Numerical Solution of Ordinary Differential Equations, Wiley, New
York, 2009; Burden, R. L., J. D. Faires, A. C. Reynolds, and A. M. Burden,
Numerical Analysis, 10th ed., Brookes/Cole, Pacific Grove, Calif., 2015;
Chapra, S. C., and R. P. Canal, Numerical Methods for Engineers, 5th ed.,
McGraw-Hill, New York, 2006; Heys, Jeffrey, J., Chemical and Biomedical
Engineering Calculations Using Python, Wiley, New York (2017); Johnson, C.,
Numerical Solution of Partial Differential Equations by the Finite Element
Method, Dover, New York, 2009; Lau, H. T., A Numerical Library in C for Scientists
and Engineers, CRC Press, Boca Raton, Fla., 3rd ed. 2007; LeVeque, R. J., Finite
Volume Methods for Hyperbolic Problems, Cambridge University Press,
Cambridge 2002; Morton, K. W., and D. F. Mayers, Numerical Solution of
Partial Differential Equations: An Introduction, 2d ed., Cambridge University
Press, Cambridge, 2005; Quarteroni, A., and A. Valli, Numerical Approximation
of Partial Differential Equations, 2d ed., Springer, New York, 2008; Reddy, J. N.,
and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid
Dynamics, 3d ed., CRC Press, Boca Raton, Fla., 2010; Zienkiewicz, O. C., R. L.
Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals,
7th ed., Butterworth-Heinemann Elsevier, Oxford, UK, 2013.
InTRODUCTIOn
The goal of approximate and numerical methods is to provide convenient
techniques for obtaining useful information from mathematical formulations of physical problems. Often this mathematical statement is not solvable by analytical means. Or perhaps analytic solutions are available but in
a form that is inconvenient for direct interpretation. In the first case, it is
necessary either to attempt to approximate the problem satisfactorily by
one that will be amenable to analysis, to obtain an approximate solution
to the original problem by numerical means, or to use the two techniques
in combination. Numerical methods have been used to model polymerization, yeast fermentation, chemical vapor deposition, catalytic converters,
pressure swing adsorption, insulin purification, ion exchange, and affinity
chromatography, plus many other chemical engineering applications.
Numerical techniques therefore do not yield exact results in the sense
of the mathematician. Since most numerical calculations are inexact, the
concept of error is an important feature.
The four sources of error are as follows:
1. Gross errors. These result from unpredictable human, mechanical, or
electrical mistakes.
2. Rounding errors. These are the consequence of using a number
specified by m correct digits to approximate a number which requires more
than m digits for its exact specification. For example, approximate the irrational number 2 by 1.414. Such errors are often present in experimental
data, in which case they may be called inherent errors, due either to empiricism or to the fact that the computer dictates the number of digits. Such
errors may be especially damaging in areas such as matrix inversion or the
numerical solution of partial differential equations when the number of
algebraic operations is extremely large.
3. Truncation errors. These errors arise from the substitution of a finite
number of steps for an infinite sequence of steps which would yield the exact
result. To illustrate this error, consider the infinite series for e-x: e-x = 1 - x +
x2/2 - x3/6 + ET(x), where ET is the truncation error, ET = (1/24)e-ex4, for
0 < e < x. If x is positive, e is also positive. Hence e-e < 1. The approximation
e-x ≈ 1 - x + x2/2 - x3/6 is in error by a positive amount smaller than (1/24)x4.
A variety of general-purpose computer programs are available commercially. Mathematica (http://www.wolfram.com/), Maple (http://www
.maplesoft.com/), and Mathcad (https://www.ptc.com/en/engineeringmath-software/mathcad) and MATLAB (http://www.mathworks.com/
nUMERICAL AnALYSIS AnD APPROXIMATE METHODS
product/symbolic) all have the capability of doing symbolic manipulation so
that algebraic solutions can be obtained. Different packages can solve some
ordinary and partial differential equations analytically, solve nonlinear algebraic equations, make simple graphs and do linear algebra, and combine the
symbolic manipulation with numerical techniques. In this section, examples
are given for the use of MATLAB (http://www.mathworks.com/), a package
of numerical analysis tools, some of which are accessed by simple commands
and others of which are accessed by writing programs in C. Spreadsheets can
also be used to solve certain problems, and these are described below too.
A popular program used in chemical engineering education is Polymath
(http://www.polymath-software.com/), which can numerically solve sets of
linear or nonlinear equations, ordinary differential equations as initial-value
problems, and perform data analysis and regression.
The Wegstein method is a secant method applied to g(x) ≡ x - F(x). In
Microsoft Excel, roots are found by using Goal Seek or Solver (an Add-In).
Assign one cell to be x, put the equation for f (x) in another cell, and let
Goal Seek or Solver find the value of x that makes the equation cell zero.
In MATLAB, the process is similar except that a function (m-file) is defined
and the command fzero (¢f ¢, x0) provides the solution x, starting from the
initial guess x0. The Wegstein method is sometimes used to promote convergence when solving a mass and energy balance problem for a chemical
process with recycle streams.
METHODS FOR MULTIPLE nOnLInEAR EQUATIOnS
Write a system of equations as
Method of Successive Substitutions
nUMERICAL SOLUTIOn OF LInEAR EQUATIOnS
See the section Matrix Algebra and Matrix Computation.
nUMERICAL SOLUTIOn OF nOnLInEAR EQUATIOnS
In OnE VARIABLE
Methods for Nonlinear Equations in One Variable
Successive Substitutions Let f (x) = 0 be the nonlinear equation to be
solved. If this is rewritten as x = F(x), then an iterative scheme can be set
up in the form xk+1 = F(xk). To start the iteration, an initial guess must be
obtained graphically or otherwise. The convergence or divergence of the
procedure depends upon the method of writing x = F(x), of which there will
usually be several forms. However, if a is a root of f (x) = 0, and if |F ′(a)| < 1,
then for any initial approximation sufficiently close to a, the method converges to a. This process is called first-order because the error in xk+1 is proportional to the first power of the error in xk for large k.
One way of writing the equation is xk+1 = xk + b f (xk). The choice of b is
made such that |1 + b df/dx(a)| < 1. Convergence is guaranteed by the theorem given for simultaneous equations.
Methods of Perturbation Let f (x) = 0 be the equation. In general, the
iterative relation is
αi = fi(`)
x 2 = x1 −
x1 − x 0
f ( x1 )
f ( x1 ) − f ( x 0 )
In each of the following steps αk is the slope of the line joining [xk, f (xk)] to
the most recently determined point where f (xj) has the opposite sign from
that of f (xk). This method is first-order. If one uses the most recently determined point (regardless of sign), the method is a secant method.
Method of Wegstein This is a variant of the method of successive
substitutions which forces and/or accelerates convergence. The iterative
procedure xk+1 = F(xk) is revised by setting xˆk+1 = F ( x k ) and then taking
x k+1 = qx k + (1 − q ) xˆk +1, where q is a suitably chosen number which may be
taken as constant throughout or may be adjusted at each step. Wegstein
found that suitable q’s are as follows:
Behavior of successive substitution process
Oscillatory divergence
without Wegstein
½<q<1
without Wegstein
1<q
q<0
Monotonic convergence
Monotonic divergence
Range of optimum q
0<q<½
Oscillatory convergence
At each step q may be calculated to give a locally optimum value by setting
q=
xˆk+1 − xˆk
xˆk+1 − 2 xˆk + xˆk−1
` = f(`)
or
The following theorem guarantees convergence. Let ` be the solution to
`i = fi(`). Assume that given h > 0, there exists a number 0 < m < 1 such that
∂ fi
n
∑ ∂x
j =1
x i − α i < h , i = 1,, n
for
≤µ
j
x ik +1 = f i ( x ik )
Then
x ik → α i
as k increases [see Finlayson (1980)].
Newton-Raphson Method To solve the set of equations
Fi(x1, x2, …, xn) = 0
Fi ({xj}) = 0
or
or
Fi(x) = 0
one uses a truncated Taylor series to get
∂ Fi
∂
j =1 x j
n
0 = Fi ({ x k }) + ∑
xk+1 = xk - [ f (xk)/αk]
where the iteration begins with x0 as an initial approximation and αk as
some functional, derived below.
Newton-Raphson Procedure This variant chooses αk = f ¢(xk) where
f ¢ = df/dx and geometrically consists of replacing the graph of f (x) by
the tangent line at x = xk in each successive step. If f ¢(x) and f ″ ≤(x) have the
same sign throughout an interval a ≤ x ≤ b containing the solution, with f (a)
and f (b) of opposite signs, then the process converges starting from any x0 in
the interval a ≤ x ≤ b. The process is second-order.
Method of False Position This variant is commenced by finding x0 and
x1 such that f (x0) and f (x1) are of opposite sign. Then α1 = slope of secant line
joining [x0, f (x0)] and [x1, f (x1)] so that
3-37
( x kj +1 + x kj )
xk
Thus one solves iteratively from one point to another.
n
∑A
( x kj +1 − x kj ) = − Fi ({ x k })
Aijk =
∂ Fi
∂x j
k
ij
j =1
where
xk
This method requires solution of sets of linear equations until either the
functions are zero to some tolerance or the changes of the solution between
iterations are small enough. Convergence is guaranteed provided the norm
of matrix A is bounded, F(x) is bounded for the initial guess, and the second
derivative of F(x) with respect to all variables is bounded. See Finlayson
(1980) in General References. Homotopy methods are also possible; see
Finlayson et al. (2006) in General References.
InTERPOLATIOn
When a function is known at several points, it is sometimes useful to have
a means to interpolate and assign a value between those points. The interpolation can be a global approximation, i.e., a function defined using all
the points, or piecewise approximation, i.e., a collection of functions, each
defined over several different subsets of the points.
Lagrange Interpolation Formulas A global polynomial is defined
over the entire region of space
m
Pm ( x ) = ∑ c j x j
j =0
This polynomial is of degree m (highest power is xm) and order m + 1 (m + 1
parameters {cj}). If we are given a set of m + 1 points
y1 = f (x1), y2 = f (x2), …, ym+1 = f (xm+1)
3-38
MATHEMATICS
then Lagrange’s formula gives a polynomial of degree m that goes through
the m + 1 points:
Pm ( x ) =
is approximately independent of x0 and x1 in the range. The linear approximation to the function f (x), x0 < x < x1 then leads to the interpolation formula
f ( x ) ≈ f ( x 0 ) + ( x − x 0 ) f [ x 0 − x1 ]
( x − x 2 )( x − x 3 )( x − x m +1 )
y1
( x 1 − x 2 )( x 1 − x 3 )( x 1 − x m +1 )
≈ f (x0 ) +
( x − x 1 )( x − x 3 )( x − x m +1 )
+
y 2 +
( x 2 − x 1 )( x 2 − x 3 )( x 2 − x m +1 )
( x − x 1 )( x − x 2 )( x − x m +1 )
+
y m +1
( x m +1 − x 1 )( x m +1 − x 2 )( x m +1 − x m )
Note that each coefficient of yj is a polynomial of degree m that vanishes at
the points {xj} (except for one value of j) and takes the value of 1.0 at that
point:
Pm(xj) = yj
m +1
x m +1 − x 1
(n + 2)!
max x1 ≤ x ≤ x m+1 | f ( n + 2) ( x )|
The evaluation of Pm(x) at a point other than at the defining points can be
made with Neville’s algorithm [Press et al. (2007) in General References].
Orthogonal Polynomials Another form of polynomials is obtained
by defining them so that they are orthogonal. It is required that Pm(x) be
orthogonal to Pk(x) for k = 0, …, m − 1.
1
[( x 1 − x ) f ( x 0 ) − ( x 0 − x ) f ( x 1 )]
x1 − x 0
Higher-order interpolation is also possible.
Equally Spaced Forward Differences If the ordinates are equally
spaced, that is, xj - xj -1 = Δx for all j, then the first differences are denoted by
Δf (x0) = f (x1) - f (x0) or Δy0 = y1 - y0, where y = f (x). The differences of these first
differences, called second differences, are denoted by Δ2y0, Δ2y1, …, Δ2yn. Thus
Δ2y0 = Δy1 - Δy0 = y2 - y1 - y1 + y0 = y2 - 2y1 + y0
j = 1, 2, …, m + 1
If the function f (x) is known, the error in the approximation is [www
.netliborg/lapack]
|error (x )|≤
≈
and in general
j
j
∆ j y 0 = ∑ (-1)n y j -n
n
n=0
j
j!
where =
= binomial coefficients
n n ! ( j − n )!
If the ordinates are equally spaced,
xn+1 - xn = Δx
yn = y(xn)
then the first and second differences are denoted by
b
∫ W (x )P (x )P
k
m
( x )dx = 0
x − x0
[ f ( x 1 ) − f ( x 0 )]
x1 − x 0
Δyn = yn+1 - yn
k = 0,1,, m − 1
a
Δ yn = Δyn+1 - Δyn = yn+2 - 2yn+1 + yn
2
The orthogonality includes a nonnegative weight function W(x) ≥ 0 for all
a ≤ x ≤ b. This procedure specifies the set of polynomials to within multiplicative constants, which are set by requiring the leading coefficient to be 1.0
or by requiring the norm to be 1.0.
b
∫W (x )P
2
m
A new variable is defined
α=
xa − x0
∆x
and the finite interpolation formula through the points y0, y1, …, yn is written as follows:
( x )dx = 1
a
The polynomial Pm(x) has m roots in the closed interval a to b.
The polynomial
p ( x ) = c 0 P0 ( x ) + c1 P1 ( x ) + c m P ( x )
minimizes
b
I = ∫ W ( x )[ f ( x ) − p ( x )]2 dx
yα = y 0 + α ∆ y 0 +
α (α − 1) 2
α (α + 1)(α − n + 1) n
∆ y 0 + +
∆ y0
2!
n!
(3-63)
Keeping only the first two terms gives a straight line through (x0, y0) and
(x1, y1); keeping the first three terms gives a quadratic function of position
going through those points plus (x2, y2). The value α = 0 gives x = x0; α = 1
gives x = x1; and so on.
Equally Spaced Backward Differences Backward differences are
defined by
∇yn = yn - yn-1
a
for a function f (x) when
∇2yn = ∇yn - ∇yn-1 = yn - 2yn-1 + yn-2
b
c j = ∫ W ( x ) f ( x ) Pj ( x ) dx / W j
a
b
W j = ∫ W ( x ) Pj2 ( x ) dx
The interpolation polynomial of order n through the points y0, y-1, …, y-n is
a
Note that each cj is independent of m, the number of terms retained in the
series. The minimum value of I is
b
n
a
j =0
I min = ∫ W ( x ) f 2 ( x ) dx − ∑W j c 2j
Such functions are useful for continuous data, i.e., when f (x) is known
for all x.
The types of orthogonal polynomials include Chebyshev (a = –1, b = 1,
W(x) = 1, used in spectral methods), Legendre (a = –1, b = 1, W(x) = 1/ 1 − x 2 ),
shifted Legendre (a = 0, b = 1, W(x) = 1), used in the orthogonal colloca2
tion method), Jacobi, Hermite (a = -∞, b = ∞, W ( x ) = e − x ), and Laguerre
polynomials.
Linear Interpolation The simplest piecewise continuous interpolation is a straight line between the points. If a function f (x) is approximately
linear in a certain range, then the ratio
f ( x1 ) − f ( x 0 )
= f [ x 0 , x1 ]
x1 − x 0
yα = y 0 + α ∇ y 0 +
α (α + 1) 2
α (α + 1)(α + n − 1) n
∇ y 0 + +
∇ y0
2!
n!
The value of α = 0 gives x = x0; α = -1 gives x = x-1, and so on. Alternatively,
the interpolation polynomial of order n through the points y1, y0, y-1, …, y−n is
y α = y 1 + (α − 1)∇y 1 +
(α − 1)α (α + 1)(α + n − 2) n
α (α − 1) 2
∇ y 1 + +
∇ y 1 (3-64)
2!
n!
Now α = 1 gives x = x1; α = 0 gives x = x0.
Central Differences The central difference denoted by
h
δf ( x ) = f x + −
2
h
f x −
2
h
h
δ 2 f ( x ) = δf x + − δf x − = f ( x + h) − 2 f ( x ) + f ( x − h)
2
2
h
h
δ n f ( x ) = δ n −1 f x + − δ n −1 f x −
2
2
is useful for calculating at the interior points of tabulated data.
nUMERICAL AnALYSIS AnD APPROXIMATE METHODS
Finite Element Method In the finite element method (see Ordinary
Differential Equations—Boundary Value Problems) the independent variable x is divided into regions called elements . The simplest approximation
is to use linear interpolation on each element, as described above. More
useful is to use a quadratic interpolation between the two endpoints of the
element and its midpoint. The points of an element are shown in Fig. 3-46.
FIG. 3-46
xi – 1
xi
xi + 1
u=0
12
1
Quadratic finite element.
The derivatives at all the points are
1
f 0′ = f1′= f 2′ = h[ y 2 − y 1 ]
2
Second-Degree Least Squares with Five Points For five evenly spaced
points x-2, x-1, x0, x1, and x2 (separated by distance h) and their ordinates f-2,
f-1, f0, f1, and f2, assume a parabola is fit by least squares. Then the derivative
at the center point is
f0′ = 1/10h [-2f-2 - f-1 + f1 + 2f2]
The derivatives at the other points are
f −′2 = 1/ 70 h[ −54 f −2 + 13 f −1 + 40 f 0 + 27 f1 − 26 f 2 ]
The element extends from xi-1 to xi+1. Define a new variable which takes the
values u = 0, 0.5, and 1 at the three points, respectively. The interpolation is then
f −′1 = 1/ 70 h[ −34 f −2 + 3 f −1 + 20 f 0 + 17 f1 − 6 f 2 ]
1
1
y = 2(u − 1) u − y i −1 + 4 u (1 − u ) y i + 2u u − y i +1
2
2
The interpolation clearly takes the correct values at u = 0, 0.5, and 1. Over
the whole domain in x the interpolated function is continuous, but the
first derivative is only piecewise continuous. Other types of finite elements
include cubic functions, which are also continuous but the derivatives are
only piecewise continuous. When Hermite cubic functions are used, however, the function and its first derivative are continuous throughout the
domain in x.
Spline Functions Splines are functions that match given values at the
points x1, …, xNT and have continuous derivatives up to some order at the
knots, or the points x2, …, xNT -1. Cubic splines are most common. The function is represented by a cubic polynomial within each interval (xi, xi+1) and
has continuous first and second derivatives at the knots. Two more conditions can be specified arbitrarily. These are usually the second derivatives at
the two endpoints, which are commonly taken as zero; this gives the natural
cubic splines. Spline functions are useful because the interpolation error can
be made small even with low-order polynomials. Some of the other methods
may oscillate wildly between the quadrature points. See Schumaker, L. L.,
Spline Functions: Computational Methods, Soc. Ind. Appl. Math. (SIAM), 2015.
nUMERICAL DIFFEREnTIATIOn
Numerical differentiation should be avoided whenever possible, particularly when data are empirical and subject to appreciable observation errors.
Errors in data can affect numerical derivatives quite strongly; i.e., differentiation is a roughening process. When such a calculation must be made, it is
usually desirable first to smooth the data to a certain extent.
Use of Interpolation Formula If the data are given over equidistant
values of the independent variable x, an interpolation formula such as the
Newton formula [Eq. (3-63) or (3-64)] may be used and the resulting formula
differentiated analytically. If the independent variable is not at equidistant
values, then Lagrange’s formulas must be used. By differentiating threepoint Lagrange interpolation formulas the following differentiation formulas result for equally spaced tabular points:
Three-Point Formulas Let x0, x1, and x2 be the three points.
1
h2
f ′( x 0 ) = [ −3 f ( x 0 ) + 4 f ( x 1 ) − f ( x 2 )] +
f ′′′(ε )
2h
3
2
h
1
f ′( x1 ) = [ − f ( x 0 ) + f ( x 2 )] −
f ′′′(ε )
2h
6
h2
1
f ′( x 2 ) = [ f ( x 0 ) − 4 f ( x1 ) + 3 f ( x 2 )] +
f ′′′(ε )
2h
3
where the last term is an error term min j x j < ε < max j x j .
Smoothing Techniques These techniques involve the approximation
of the tabular data by a least-squares fit of the data by using some known
functional form, usually a polynomial ( for the concept of least squares see
Statistics). In place of approximating f (x) by a single least-squares polynomial of degree n over the entire range of the tabulation, it is often desirable to replace each tabulated value by the value taken on by a least-squares
polynomial of degree n relevant to a subrange of 2M + 1 points centered,
when possible, at the point for which the entry is to be modified. Thus each
smoothed value replaces a tabulated value. Let fj = f (xj) be the tabular points
and yj = smoothed values.
First-Degree Least Squares with Three Points
y 0 = 1 6[5 f 0 + 2 f1 − f 2 ]
y 1 = 1 3[ f 0 + f 1 + f 2 ]
y 2 = 1 6[ − f 0 + 2 f 1 + 5 f 2 ]
3-39
f1′= 1/ 70 h[6 f −2 − 17 f −1 + 20 f 0 − 3 f1 + 34 f 2 ]
f 2′= 1/ 70 h[26 f −2 − 27 f −1 − 40 f 0 − 13 f1 + 54 f 2 ]
Numerical Derivatives The results given above can be used to obtain
numerical derivatives when solving problems on the computer, in particular
for the Newton-Raphson method and homotopy methods. Suppose one has
a program, subroutine, or other function evaluation device that will calculate f, given x . One can estimate the value of the first derivative at x0 using
df
f [ x 0 (1 + ε)] − f [ x 0 ]
≈
ε x0
dx x 0
(a first-order formula) or
df
f [ x 0 (1 + ε)] − f [ x 0 (1 − ε)]
≈
dx x 0
2 ε x0
(a second-order formula). The value of e is important; a value of 10-6 is typical, but smaller or larger values may be necessary depending on the computer precision and the application. One must also be sure that the value of
x0 is not zero and use a different increment in that case.
nUMERICAL InTEGRATIOn (QUADRATURE)
A multitude of formulas have been developed to accomplish numerical integration, which consists of computing the value of a definite integral from a
set of numerical values of the integrand.
Newton-Cotes Integration Formulas (Equally Spaced Ordinates)
b
for Functions of One Variable The definite integral ∫ f ( x ) dx is to be
a
evaluated.
Trapezoidal Rule This formula consists of subdividing the interval
a ≤ x ≤ b into n subintervals a to a + h, a + h to a + 2h, … and replacing the
graph of f (x) by the result of joining the ends of adjacent ordinates by line
segments. If fj = f (xj) = f (a + jh), f0 = f (a), and fn = f (b), the integration formula is
∫
b
a
h
f ( x ) dx = [ f 0 + 2 f1 + 2 f 2 + + 2 f n -1 + f n ] + En
2
where
En =
nh 3
(b − a )3
f ′′(ε)
f ′′(ε) =
12
12n 2
a <ε<b
This procedure is not of high accuracy. However, if f ″ ≤ (x) is continuous in
a < x < b, the error goes to zero as 1/n2, n → ∞. When the finite element
method is used with linear trial functions and equal-size elements, quadrature is the same as the trapezoid rule.
Parabolic Rule (Simpson’s Rule) This procedure consists of subdividing the interval a < x < b into n/2 subintervals, each of length 2h, where n is
an even integer. By using the notation as above the integration formula is
b
h
∫ f ( x ) dx = 3 [ f
0
+ 4 f 1 + 2 f 2 + 4 f 3 + 2 f 4 + + 4 f n - 3 + 2 f n - 2 + 4 f n -1 + f n ] + E n
a
where
En =
nh 5 (IV )
(b − a )5 (IV )
f (ε) =
f (ε)
180n 4
180
a <ε<b
3-40
MATHEMATICS
This method approximates f (x) by a parabola on each subinterval. This rule
is generally more accurate than the trapezoidal rule. It is the most widely
used integration formula. When the finite element method is used with
quadratic trial functions and equal-size elements, quadrature is the same
as Simpson’s rule.
Gaussian Quadrature Gaussian quadrature provides a highly accurate formula based on irregularly spaced points, but the integral needs to be
transformed onto the interval from 0 to 1.
x = a + (b - a)u
∫
∫
b
a
b
a
dx = (b - a)du
Replacing the ≈ by an equality (an approximation) and solving for c and
I0 give
I0 =
2m I 2 − I1
2m − 1
To obtain the most accurate value, first calculate I1, I2, …, by halving h
each time. Then calculate new estimates from each pair, calling them J1,
J2, … ; that is, in the formula above, replace I0 with J1. The formulas are reapplied for each pair of J to obtain K1, K2, … . The process continues until the
required tolerance is obtained.
1
f ( x ) dx = (b − a ) ∫ f (u ) du
I1 I 2 I 3 I 4
0
J1 J 2 J 3
m
f (u ) du = ∑Wi f (ui )
K1 K 2
L1
i =1
The quadrature is exact when f is a polynomial of degree 2m - 1 in x . Because
there are m weights and m Gauss points, we have 2m parameters that are
chosen to exactly represent a polynomial of degree 2m - 1, which has 2m
parameters. The Gauss points and weights are given in the table.
Romberg’s method is most useful for a low-order method (small m)
because significant improvement is then possible.
Example Evaluate the same integral by using the trapezoid rule and
then apply the Romberg method. Use 11, 21, 41, and 81 points with m = 2.
To achieve six-digit accuracy, any result from J2 through L1 is suitable, even
though the base results (I1 through I4) are not that accurate.
Gaussian Quadrature Points and Weights
m
ui
Wi
2
0.21132 48654
0.50000 00000
0.78867 51346
0.50000 00000
0.11270 16654
0.27777 77778
0.50000 00000
0.44444 44445
3
4
5
0.88729 83346
0.27777 77778
0.06943 18442
0.17392 74226
0.33000 94783
0.32607 25774
0.66999 05218
0.32607 25774
0.93056 81558
0.17392 74226
0.04691 00771
0.11846 34425
0.23076 53450
0.23931 43353
0.50000 00000
0.28444 44444
0.76923 46551
0.23931 43353
0.95308 99230
0.11846 34425
I1 = 0.24491 14823
I2 = 0.24560 56002
J1 = 0.24583 69728
I = ∫ e sin x dx
Using the gaussian quadrature formulas gives the following values for
various values of m . Clearly, three internal points, requiring evaluation of
the integrand at only three points, give excellent results.
m
I
2
0.24609 64306
3
0.24583 48774
4
0.24583 70044
5
0.24583 70070
Romberg’s Method Romberg’s method uses extrapolation techniques
to improve the answer [Press et al. (2007)]. If we let I1 be the value of the
integral obtained using interval size h = Δx, I2 be the value of I obtained
when using interval size h/2, I3 be the value obtained when using an interval
of size h/4, etc., and I0 is the true value of I, then the error in a method is
approximately hm, or
I ≈ I 0 + ch m
h
I 2 ≈ I 0 + c
2
m
J2 = 0.24583 70049
J3 = 0.24583 70069
K1 = 0.24583 70156
K2 = 0.24583 70075
Orthogonal Polynomials The quadrature formulas for orthogonal
polynomials are the same as for gaussian quadrature above, with different
points and different weights.
Cubic Splines The quadrature formula is
x NT
∫
y ( x ) dx =
x1
1 NT −1 3
1 NT −1
∆x i ( y i + y i +1 ) −
∑
∑ ∆x i ( y i′′+ y i′′+1 )
24 i =1
2 i =1
with y 1′ = 0, y ′′NT = 0 for natural cubic splines.
Computer Methods These methods are easily programmed in a spreadsheet program such as Microsoft Excel. In MATLAB, the trapezoid rule can
be calculated by using the command trapz(x,y), where x is a vector of x values xi and y is a vector of values y(xi). Alternatively, use the commands
F = @(x) exp(-x).*sin(x)
Q = quad(F,0,1)
−x
0
I4 = 0.24582 25436
L1 = 0.24583 70049
Example Calculate the value of the following integral.
1
I3 = 0.24577 91537
Monte Carlo methods can be used, too (see Monte Carlo Simulations).
Singularities When the integrand has singularities, a variety of techniques can be tried. The integral may be divided into one part that can be
integrated analytically near the singularity and another part that is integrated
numerically. Sometimes a change of argument allows analytical integration.
Series expansion might be helpful, too. When the domain is infinite, it is
possible to use Gauss-Legendre or Gauss-Hermite quadrature. Also a transformation can be made. For example, let u = 1/x and then
∫
b
f ( x ) dx = ∫
1/ a
1/b
a
1 1
f du
u2 u
ab > 0
Two-Dimensional Formula Two-dimensional integrals can be calculated by breaking down the integral into one-dimensional integrals.
b
g2 ( x )
a
g1 ( x )
∫∫
G(x ) = ∫
b
f ( x , y ) dx dy = ∫ G ( x ) dx
a
g2 ( x )
g1 ( x )
f ( x , y ) dy
Gaussian quadrature can also be used in two dimensions, provided the integration is on a square or can be transformed to one. (Domain transformations might be used to convert the domain to a square.)
1
1
0
0
∫∫
mx
my
i =1
i =1
f ( x , y )dx dy = ∑Wxi ∑W yi f ( x i , y j )
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS
3-41
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS
AS InITIAL-VALUE PROBLEMS
A differential equation for a function that depends on only one variable,
often the variable time, is called an ordinary differential equation. The general solution to the differential equation includes many possibilities; the
boundary or initial conditions are needed to specify which of those are
desired. If all conditions are at one point, then the problem is an initial-value
problem and can be integrated from that point on. If some of the conditions
are available at one point and others at another point, then the ordinary differential equations become two-point boundary-value problems, which are
treated in the next section. Initial-value problems as ordinary differential
equations arise in control of lumped-parameter models, transient models
of stirred tank reactors, and in all models where there are no spatial gradients in the unknowns. Many computer packages exist to solve initial-value
problems, but it is important to understand the choices one must make and
how to interpret the output (and change the choices) when the results are
anomalous. Furthermore, many problems can be solved using spreadsheets
(universally available) provided one understands the methods. It is important to know, too, when simple methods in spreadsheets won’t work.
A higher-order differential equation
z (n ) + F ( z (n−1) , z (n−2) , , z ) = 0
with initial conditions for z, and its first n - 1 derivatives can be converted
into a set of first-order equations using
y i ≡ z (i −1) =
( i − 1)
d
z d (i − 2) dy i −1
= z
=
dt (i − 1) dt
dt
The higher-order equation can be written as a set of first-order equations.
dy 1
dy
dy
dy
= y 2 , 2 = y 3 , 3 = y 4 ,, n = − F ( y n − 1 , y n − 2 ,, y 2 , y 1 )
dt
dt
dt
dt
The set of equations is then written as
dy
= f ( y , t ), y (0) = y 0
dt
The methods in this section are described for a single equation, but they all
apply to multiple equations.
The simplest method is Euler’s method, which is first-order.
y n + 1 = y n + Δt f ( y n )
and errors are proportional to Δt . The second-order Adams-Bashforth
method is
y n+1 = y n +
Δt
[3 f ( y n ) - f ( y n−1 )]
2
Errors are proportional to Δt2, and high-order methods are available. Notice
that the higher-order explicit methods require knowing the solution (or the
right-hand side) evaluated at times in the past. Since these were calculated
to get to the current time, this presents no problem except for starting the
problem. Then it may be necessary to use Euler’s method with a very small
step size for several steps in order to generate starting values at a succession of time points. The methods, error terms, order of the method, function
evaluations per step, and stability limitations are listed in Finlayson (1980)
in General References. The advantage of the high-order Adams-Bashforth
method is that it uses only one function evaluation per step, yet achieves
high-order accuracy. The disadvantage is the necessity of using another
method to start. In MATLAB the function ode113 uses a version of the
Adams-Bashforth method.
These methods can be used for simple problems when all the variables
change on the same time scale and precise results are not needed. Euler’s
method is easily done in a spreadsheet. Figure 3-47 shows the commands in
a spreadsheet for two differential equations, columns 1 to 3.
dy 1 /dt = y 2 − y 1 , dy 2 /dt = − y 2 , y 1 (0) = 1, y 2 (0) = 1
Once columns 4 to 6 are created, the formulas for the additional time steps
are created by copying down. The Richardson extrapolation (see below) can
be used to improve the accuracy.
Runge-Kutta methods are explicit methods that use several function evaluations for each time step. Runge-Kutta methods are traditionally written
Equations
Eq. time
0
=D3+$F$1
=D4+$F$1
=D5+$F$1
=D6+$F$1
=D7+$F$1
FIG. 3-47
Equations
Eq. 1
1
=E3+$F$1*(F3–E3)
=E4+$F$1*(F4–E4)
=E5+$F$1*(F5–E5)
=E6+$F$1*(F6–E6)
=E7+$F$1*(F7–E7)
Equations
Eq. 2
1
=F3–$F$1*F3
=F4–$F$1*F4
=F5–$F$1*F5
=F6–$F$1*F6
=F7–$F$1*F7
time
0
0.1
0.2
0.3
0.4
0.5
delta t
Results 1
1
1
0.99
0.972
0.9477
0.91854
0.1
Results 2
1
0.9
0.81
0.729
0.6561
0.59049
Spreadsheet for Euler’s method.
for f (t, y). The first-order Runge-Kutta method is Euler’s method. A secondorder Runge-Kutta method is
Δt n
[ f + f (t n + ∆t , y n + ∆t f n )]
2
while the midpoint scheme is also a second-order Runge-Kutta method
y n+1 = y n +
∆t
∆t n
y n + 1 = y n + ∆t f t n + , y n +
f
2
2
A popular fourth-order Runge-Kutta method uses the Runge-Kutta-Fehlberg
formulas, which have the property that the method is fourth-order but
achieves fifth-order accuracy. The coefficients are available at en.wikipedia
.org/wiki/Runge-Kutta-Fehlberg_method. An extension of this method is
ode45 in MATLAB.
Usually one would use a high-order method to achieve high accuracy.
The Runge-Kutta-Fehlberg method is popular because it is high-order and
does not require a starting method (as does an Adams-Bashforth method).
However, it does require four function evaluations per time step, or four
times as many as a fourth-order Adams-Bashforth method. For problems in
which the function evaluations are a significant portion of the calculation
time, this might be important. Given the speed and availability of desktop
computers, the efficiency of the methods is most important only for very
large problems that are going to be solved many times or for problems in
which some variables change rapidly while others change slowly. For other
problems, the most important criterion for choosing a method is probably
the time the user spends setting up the problem.
The stability limits for the explicit methods are based on the largest eigenvalue of the linearized system of equations
δf
dy i n
= ∑ Aij y j , Aij = i
δy j
dt j = 1
y
For linear problems, the eigenvalues do not change, so that the stability
and oscillation limits must be satisfied for every eigenvalue of matrix A.
In solving nonlinear problems, the equations are linearized about the solution at the local time, and the analysis applies for small changes in time,
after which a new analysis about the new solution must be made. Thus, for
nonlinear problems, the eigenvalues keep changing, and the largest stable
time step changes, too. The stability limits are as follows:
Euler method, l Δt ≤ 2
Runge-Kutta, second-order, l Δt < 2
Runge-Kutta-Fehlberg, l Δt < 3.0
Richardson extrapolation can be used to improve the accuracy of a
method. Suppose we step forward one step Δt with a pth-order method.
Then redo the problem, this time stepping forward from the same initial
point, but in two steps of length Δt/2, thus ending at the same point. Call
the solution of the one-step calculation y1 and the solution of the two-step
calculation y2. Then an improved solution at the new time is given by
y=
2 p y 2 − y1
2 p −1
This gives a good estimate provided Δt is small enough that the method is
truly convergent with order p . This process can also be repeated in the same
way Romberg’s method was used for quadrature.
The error term in the various methods can be used to deduce a step size
that will give a user-specified accuracy. Most packages today are based on a
user-specified tolerance; the step size is changed during the calculation to
3-42
MATHEMATICS
achieve that accuracy. The accuracy itself is not guaranteed, but it improves
as the tolerance is decreased.
Implicit Methods When some dependent variables change rapidly
while others change slowly, we say the problem is stiff and implicit methods
are needed. Implicit methods use different interpolation formulas involving
y n+1 and result in nonlinear equations to be solved for y n+1. Then iterative
methods must be used to solve the equations.
The backward Euler method is a first-order method:
y n+1 = y n + Δtf ( y n+1 )
Errors are proportional to Δt for small Δt . The trapezoid rule is a secondorder method.
y n +1 = y n +
Δt
[ f ( y n ) + f ( y n + 1 )]
2
Errors are proportional to Δt2 for small Δt . When the trapezoid rule is used
with the finite difference method for solving partial differential equations, it
is called the Crank-Nicolson method. The implicit methods are stable for any
step size but do require the solution of a set of nonlinear equations, which
must be solved iteratively. The set of equations can be solved using the successive substitution method or Newton-Raphson method. See Bogacki, M. B.,
K. Alejski, and J. Szymanewski, Comp . Chem . Eng . 13: 1081–1085 (1989) for an
application to dynamic distillation problems.
The best packages for stiff equations (see below) use backward-difference
formulas. Gear first developed these, and the first two orders are given
below (Gear, G. W., Numerical Initial Value Problems in Ordinary Differential
Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971).
1. y n+1 = y n + Δt f ( y n+1)
where e is the porosity of the catalyst, R is the catalyst radius, and De is the
effective diffusion coefficient inside the catalyst.
4. Time for heat transfer is
t internal heat transfer =
R 2 ρs C s R 2
=
ke
α
where rs is the catalyst density, Cs is the catalyst heat capacity per unit mass,
ke is the effective thermal conductivity of the catalyst, and α is the thermal
diffusivity. For example, in the model of a catalytic converter for an automobile [Ferguson, N. B., and B. A. Finlayson, AIChE J. 20: 539–550 (1974)], the
time constant for internal diffusion was 0.3 s; internal heat transfer, 21 s; and
device flow-through, 0.003 s. The device flow-through is so fast that it might
as well be instantaneous. The stiffness is approximately 7000, and implicit
methods must be used to integrate the equations. Alternatively, a quasistatic model can be developed. In this case the time derivative is deleted
for the variables that change rapidly on the grounds that those variables are
essentially in steady state with respect to the rest of the problem, even if the
steady state changes slowly.
Differential-Algebraic Systems Sometimes models involve ordinary
differential equations subject to some algebraic constraints. For example, the
equations governing one equilibrium stage (as in a distillation column) are
dx n
= V n + 1 y n + 1 − Ln x n − V n y n + Ln − 1 x x − 1
dt
x n − 1 − x n = E n ( x n −1 − x *,n )
M
N
∑x
i
=1
i =1
4
1
2
2. y n + 1 = y n + y n − 1 + ∆t f ( y n + 1 )
3
3
3
These methods require solving sets of nonlinear equations. By adroit
manipulation and estimation, a package will change the order to achieve
a required accuracy with a minimum number of time steps and iterations.
The programs ode15s and ode23s in MATLAB use these techniques.
Stiffness The concept of stiffness is described for a system of linear
equations.
dy
= Ay
dt
where x and y are the mole fraction in the liquid and vapor, respectively;
L and V are liquid and vapor flow rates, respectively; M is the holdup; and
the superscript is the stage number. The efficiency is E, and the concentration in equilibrium with the vapor is x*. The first equation is an ordinary
differential equation for the mass of one component on the stage, while the
third equation represents a constraint that the mass fractions add to 1. This
is a differential-algebraic system of equations.
Differential-algebraic equations can be written in the general notation
Let li be the eigenvalues of matrix A. The stiffness ratio SR is defined as
To solve the general problem by using the backward Euler method, replace
the nonlinear differential equation with the nonlinear algebraic equation for
one step.
max i | Re (λ i )|
SR =
max i | Re (λ i )|
(3-65)
SR = 20 is not stiff, SR = 103 is stiff, and SR = 106 is very stiff. If the problem is
nonlinear, then the solution is expanded about the current state.
n
∂f
dy i
= f i [ y (t n )] + ∑ i [ y j − y j (t n )]
dt
j =1 ∂ y j
The question of stiffness then depends on the solution at the current time.
Consequently nonlinear problems can be stiff during one time period and
not stiff during another. While the chemical engineer may not actually calculate the eigenvalues, it is useful to know that they determine the stability
and accuracy of the numerical scheme and the step size used.
Problems are stiff when the time constants for different phenomena have
very different magnitudes. Consider flow through a packed bed reactor. The
time constants for different phenomena are as follows:
1. Time for device flow-through
t flow =
L φAL
=
u
Q
where Q is the volumetric flow rate, A is the cross-sectional area, L is the
length of the packed bed, and f is the void fraction.
2. Time for reaction
tr × n =
1
k
where k is a rate constant (time-1).
3. Time for diffusion inside the catalyst
t internal diffusion =
εR 2
De
dy
F t , y , = 0
dt
y n +1 − y n
F t , y n + 1 ,
=0
∆t
This equation must be solved for y n+1. The Newton-Raphson method can
be used, and if convergence is not achieved within a few iterations, the time
step can be reduced and the step repeated. In actuality, the higher-order
backward-difference Gear methods are used in DASSL (Ascher, U. M., and
L. R. Petzold, Computer Methods for Ordinary Differential Equations and
Differential-Algebraic Equations, SIAM, Philadelphia, Penn., 1998). The program ode15s in MATLAB can be used to solve differential-algebraic equations.
Differential-algebraic systems are more complicated than differential
systems because the solution may not always be defined. See Pontelides et
al. [Comp . Chem . Eng. 12: 449–454 (1988)] for a model of a distillation column
in which the column pressure strongly affects the possible solutions and initial conditions. Byrne and Ponzi [Comp . Chem . Eng. 12: 377–382 (1988)] and
Chan, T. F. C., and H. B. Keller [SIAM J . Sci . Stat . Comput. 3: 173–194 (1982)]
also list several chemical engineering examples of differential-algebraic
systems and solve one involving two-phase flow.
Computer Software Efficient computer packages are available for
solving ordinary differential equations as initial-value problems. The packages are widely available and good enough that most chemical engineers
use them and do not write their own. On the NIST web page http://gams
.nist.gov/Problem.html insert “ordinary differential equations” to find packages that can be downloaded. On the Netlib website http://www.netlib.org/,
search the Netlib repository, and choose “ode” to find packages that can be
downloaded. Using Microsoft Excel to solve ordinary differential equations
is cumbersome, except for the simplest problems.
Stability, Bifurcations, and Limit Cycles Some aspects of this subject involve the solution of nonlinear equations; other aspects involve the
integration of ordinary differential equations; applications include chaos
and fractals as well as the unusual operation of some chemical engineering
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS
equipment. Kubicek, M., and M. Marek, Computational Methods in Bifurcation
Theory and Dissipative Structures, Springer-Verlag, Berlin (1983, 2012), give
an excellent introduction to the subject and the details needed to apply the
methods. A concise survey with some chemical engineering examples is
given in Doherty, M. F., and J. M. Ottino, Chem . Eng . Sci. 43: 139–183 (1988).
Bifurcation results are closely connected with the stability of the steady
states, which is essentially a transient phenomenon.
Sensitivity Analysis When one is solving differential equations, it is
frequently necessary to know the solution as well as the sensitivity of the
solution to the value of a parameter. Such information is useful when doing
parameter estimation (to find the best set of parameters for a model) and for
deciding if a parameter needs to be measured accurately. An added equation
is created by differentiating the ordinary differential equation with respect
to the parameter and solving that equation concurrently. See Finlayson et al.
(2006) in General References.
Molecular Dynamics Special integration methods have been developed for molecular dynamics calculations owing to the structure of the
equations. A very large number of equations are to be integrated, with the
following form based on molecular interactions between molecules.
mi
d 2 ri
= Fi ({ r })
dt 2
Fi ({ r }) = − ∇V
The symbol mi is the mass of the ith particle, ri is the position of the ith particle, Fi is the force acting on the ith particle, and V is the potential energy
that depends upon the location of all the particles (but not their velocities).
Since the major part of the calculation lies in the evaluation of the forces,
or potentials, a method must be used that minimizes the number of times
the forces are calculated to move from one time to another time. Rewrite
this equation in the form of an acceleration as
d 2 ri 1
= Fi ({ r }) ≡ a i
dt 2 m
In the Verlet method, this equation is written by using central finite differences (see Interpolation and Finite Differences). Note that the accelerations
do not depend upon the velocities.
ri(t + Δt) = 2ri (t) - ri (t - Δt) + ai(t)Δt2
The calculations are straightforward, and no explicit velocity is needed. The
storage requirement is modest, and the precision is modest (it is a secondorder method). Note that one must start the calculation with values of {r} at
times t and t - Δt.
In the Verlet velocity method, an equation is written for the velocity, too.
ORDInARY DIFFEREnTIAL EQUATIOnS—BOUnDARY-VALUE
PROBLEMS
Diffusion problems in one dimension lead to boundary-value problems.
The boundary conditions are applied at two different spatial locations: at
one side the concentration may be fixed and at the other side the flux may
be fixed. Because the conditions are specified at two different locations,
the problems are not initial-value in character. It is not possible to begin at
one position and integrate directly because at least one of the conditions is
specified somewhere else and there are not enough conditions to begin the
calculation. Thus, methods have been developed especially for boundaryvalue problems.
Boundary-value methods provide a description of the solution either
by providing values at specific locations or by an expansion in a series of
functions. Thus, the key issues are the method of representing the solution,
the number of points (i.e., the mesh) or the number of terms in the series,
and how the approximation converges to the exact answer, i.e., how the
error changes with the number of points or number of terms in the series.
In addition, boundary conditions and nonlinear transport coefficients are
handled differently in the various methods. These issues are discussed for
each of the methods: finite difference, orthogonal collocation, and Galerkin
finite element methods. Sometimes the solution has singularities or the
domain is semi-infinite, and these situations require special treatment.
The first approach is to try to find an analytical solution. Flow in a pipe is
governed by the equation
1 d du
∆P
µr = −
r dr dr
L
where u is the velocity, r is the radial position, m is the viscosity, and ΔP/L is
the pressure drop per length. The solution is finite at the origin, r = 0, and
takes the value zero at the radius of the pipe R . For a newtonian fluid, the
viscosity is constant. This equation can be integrated once to obtain
r
ΔP r 2
du
=−
+ c1
µL 2
dr
u=−
1
ri (t + ∆t ) = ri (t ) + v i ∆t + a i (t ) ∆t 2
2
Beginning with values of {r} and {v} at time 0, one calculates the new positions and then the new velocities. This method is second-order in Δt too.
Molecular dynamics is used in chemical engineering for a variety of applications, including drug design, protein folding, nucleation and growth processes, and the phase behavior of polymeric, colloidal, and self-assembled
systems [see Pamer, J. C., and P. G. Debenedettii, Recent Advances in
Molecular Simulation: A Chemical Engineering Perspective, AIChE J . 61,
370–383 (2015)]. For additional details about the method, see Hinchliffe,
A., Molecular Modelling for Beginners, 2d ed., Wiley, New York, 2008;
Jensen, J. H., Molecular Modeling Basics, CRC Press, Boca Raton, Fla., 2010;
Leach, A. R., Molecular Modelling: Principles and Applications, 2d ed.,
Prentice Hall, Upper Saddle River, N.J., 2001; Schlick, T., Molecular Modeling
and Simulations, 2d ed., Springer, New York, 2010. See https://en.wikipedia.
org/wiki/List_of_software_for_molecular_mechanics_modeling for computer packages, especially the free programs LAMMPS (lammps.sandia.
gov) and GROMACS (www.gromacs.org, especially for biological molecules).
See also Calvetti, D. E., and E. Somersalo, Computational Mathematical
Modeling: An Integrated Approach Across Scales, SIAM, 2012, for methods to
include phenomena that occur on different physical scales.
ΔP r c1
du
=−
+
µL 2 r
dr
ΔP r 2
+ c1 ln r + c2
µL 4
Since the velocity is finite at the origin, c1 is taken as zero; c2 is taken as
c2 =
∆P R 2
µL 4
so that the velocity is zero at r = R. The solution is then
1
v i (t + ∆t ) = v i (t ) + [a i (t ) + a i (t + ∆t )] ∆t
2
The position of the particles is expanded in a Taylor series.
or
and integrated again to get
dv i
= ai
dt
The trapezoid rule [see Numerical Integration (Quadrature)] is applied to
obtain
3-43
u=
∆P 2 2
(R - r )
4µL
This problem requires no numerical methods. But if the viscosity were
appropriate to a non-newtonian fluid and depended upon the shear rate,
e.g., for a Bird-Carreau fluid
µ=
η0
2 (1−n )/2
du
1 + λ
dr
then numerical methods would be required, as described in this subsection.
Finite Difference Method To apply the finite difference method, we
first spread grid points through the domain. Figure 3-48 shows a uniform
mesh of n points (nonuniform meshes are possible too). The unknown, here
c(x), at a grid point xi is assigned the symbol ci = c(xi). The finite difference
FIG. 3-48
Finite difference mesh; Δx uniform.
3-44
MATHEMATICS
method can be derived easily by using a Taylor expansion of the solution
about this point. Expressions for the derivatives are
ci + 1 − ci d 2 c Δ x
ci − ci − 1 d 2 c ∆ x
dc
dc
=
− 2
+ ,
=
+ 2
+
dx i
dx i 2
dx i
dx i 2
Δx
∆x
ci + 1 − ci −1 d 3c ∆ x 2
dc
=
− 3
+
dx i
dx i 3!
2∆ x
The truncation error in the first two expressions is proportional to Δx, and
the methods are said to be first-order. The truncation error in the third
expression is proportional to Δx2, and the method is said to be second-order.
Usually the last equation is used to ensure the best accuracy. The finite difference representation of the second derivative is
ci + 1 − 2 ci + ci − 1 d c 2 ∆ x
d c
=
− 4
+
dx 2 i
dx i 4!
∆x2
2
2
4
The truncation error is proportional to Δx2. To solve a differential equation,
it is evaluated at a point i and then these expressions are inserted for the
derivatives.
Example Consider the equation for convection, diffusion, and reaction
in a tubular reactor.
1 d 2c dc
−
= Da R (c )
Pe dx 2 dx
Pe is the Peclet number and Da is the Damköhler number. The finite difference
representation is
1 ci + 1 − 2ci + ci − 1 ci + 1 − ci − 1
−
= Da R (ci )
Pe
2 Δx
Δx 2
This equation is written for i = 2 to n - 1, or the internal points. The equations would then be coupled but would also involve the values of c1 and cn as
well. These are determined from the boundary conditions.
If the boundary condition involves a derivative, it is important that the
derivatives be evaluated using points that exist. Three possibilities exist;
the first two are
dc
dx
dc
dx
=
c2 − c1
∆x
=
−3c1 + 4 c2 − c3
2∆ x
1
1
The third alternative is to add a false point, outside the domain, as c0 =
c(x = -Δx).
c −c
dc
= 2 0
dx 1 2 Δ x
Since this equation introduces a new variable c0, another equation is
needed and is obtained by writing the finite difference equation for i = 1
too. The sets of equations can be solved by using the Newton-Raphson
method. The first form of the derivative gives a tridiagonal system of equations, and the standard routines for solving tridiagonal equations suffice.
For the other two options, some manipulation is necessary to put them
into a tridiagonal form.
Frequently, the transport coefficients, such as the diffusion coefficient or
thermal conductivity, depend on the dependent variable, concentration, or
temperature, respectively. Then the differential equation might look like
d
dc
D (c ) = 0
dx
dx
This could be written as two equations.
−
dJ
=0
dx
J = − D (c )
dc
dx
Because the coefficient depends on c, the equations are more complicated.
A finite difference method can be written in terms of the fluxes at the
midpoints i + 1/2.
J i + 1/2 − J i − 1/2
−
=0
∆x
ci + 1 − ci
J i + 1/2 = − D (ci + 1/2 )
∆x
These are combined to give the complete equation.
D (ci + 1/2 ) (ci + 1 − ci ) − D (ci − 1/2 ) (ci − ci − 1 )
=0
∆x2
This represents a set of nonlinear algebraic equations that can be solved
with the Newton-Raphson method. However, in this case, a viable iterative strategy is to evaluate the transport coefficients at the last value and
then solve
D (cik+ 1/2 ) (cik++11 − cik + 1 ) − D (cik− 1/2 ) (cik + 1 − cik−+11 )
=0
∆x 2
The advantage of this approach is that it is easier to program than a full
Newton-Raphson method. If the transport coefficients do not vary radically,
then the method converges. If the method does not converge, then it may be
necessary to use the full Newton-Raphson method.
There are two common ways to evaluate the transport coefficient at
the midpoint: Use the average value of the solution on each side to evaluate the diffusivity, or use the average value of the diffusivity on each side.
Both methods have truncation error Δx2. The spacing of the grid points need
not be uniform. See Finlayson (1980) and Finlayson et al. (2006) in General
References.
Example A reaction diffusion problem is solved with the finite difference method.
dc
d 2c
= φ2c ,
(0) = 0 c (1) = 1
dx
dx 2
The solution is derived for f = 2. It is solved several times, first with two
intervals and three points (at x = 0, 0.5, 1), then with four intervals, then
with eight intervals. The reason is that when an exact solution is not known,
one must use several Δx values and see that the solution converges as Δx
approaches zero. With two intervals, the equations are as follows. The
points are x1 = 0, x2 = 0.5, and x3 = 1.0; and the solutions at those points are c1,
c2, and c3, respectively. A false boundary is used at x0 = -0.5.
c0 − c2
c0 − 2c1 + c2
c1 − 2c2 + c3
= 0,
− φ2c1 = 0,
− φ2c2 = 0, c3 = 1
2∆ x
∆x2
∆x2
The solution is c1 = 0.2857, c2 = 0.4286, and c3 = 1.0. The problem is solved
again with four and then eight intervals. The value of concentration at x = 0
takes the following values for different Δx values . These values are extrapolated using the Richardson extrapolation technique to get c(0) = 0.265718.
Using this value as the best estimate of the exact solution, the errors in the
solution are tabulated versus Δx . Clearly the errors go as Δx2 (decreasing by
a factor of 4 when Δx decreases by a factor of 2), thus validating the solution.
The exact solution is 0.265802.
n-1
Δx
c(0)
2
4
8
0.5
0.25
0.125
0.285714
0.271043
0.267131
n-1
Δx
Error in c(0)
2
4
8
0.5
0.25
0.125
0.02000
0.00532
0.00141
Finite Difference Methods Solved with Spreadsheets A convenient
way to solve the finite difference equations for simple problems is to use a
computer spreadsheet. The equations for the problem solved in the example
can be cast into the following form:
c1 =
2c 2
2 + φ 2 ∆x 2
ci + 1 + ci − 1
2 + φ 2 ∆x 2
cn + 1 = 1
ci =
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS
3-45
This is the process that makes the method a Galerkin method. The basis for
the orthogonality condition is that any function that is orthogonal to each
member of a complete set is zero. The residual is being made orthogonal;
and if the basis functions are complete and you use infinitely many of them,
then the residual is zero. Once the residual is zero, the problem is solved.
This equation is integrated by parts to give the following equation:
NT
FIG. 3-49
−∑ ∫
i =1
Finite difference method using spreadsheets.
Let us solve the problem using 6 nodes, or 5 intervals. Then the connection
between the cell in the spreadsheet and the nodal value is shown in Fig. 3-49.
The following equations are placed into the various cells.
A1: = 2*B1/(2.+(phi*dx)**2)
B1: = (A1 + C1)/(2.+(phi*dx)**2)
F1: = 1.
The equation in cell B1 is copied into cells C1 through E1. Then turn on
the iteration scheme in the spreadsheet and watch the solution converge. Whether convergence is achieved can depend on how you write the
equations, so some experimentation may be necessary. Theorems for convergence of the successive substitution method are useful in this regard.
Orthogonal Collocation The orthogonal collocation method has
found widespread application in chemical engineering, particularly for
chemical reaction engineering. In the collocation method, the dependent
variable is expanded in a series of orthogonal polynomials. See Interpolation:
Lagrange Interpolation Formulas.
1
0
1
db j dbi
NT
dxai = φ2 ∫ b j ( x ) R ∑ ai bi ( x ) dx j = 1, , NT − 1
0
dx dx
i =1
(3-66)
This equation defines the Galerkin method, and a solution that satisfies this
equation ( for all j = 1, …, ∞) is called a weak solution. For an approximate
solution, the equation is written once for each member of the trial function,
j = 1, …, NT - 1, and the boundary condition is applied.
NT
∑a b (1) = c
i i
B
i =1
The Galerkin finite element method results when the Galerkin method
is combined with a finite element trial function. The domain is divided
into elements separated by nodes, as in the finite difference method. The
solution is approximated by a linear (or sometimes quadratic) function to
provide the Galerkin finite element equations. For example, with the grid
shown in Fig. 3-48, a linear interpolation would be used between points xi
and xi+1.
c ( x ) = ci (1 − u ) + ci + 1u
u≡
x − xi
x i +1 − x i
N
c ( x ) = ∑ am Pm ( x )
m=0
The differential equation is evaluated at certain collocation points. The
collocation points are the roots to an orthogonal polynomial, as first used
by Lanczos [Lanczos, C., J . Math . Phys. 17:123-199 (1938); and Lanczos, C.,
Applied Analysis, Prentice Hall, Upper Saddle River, N.J., 1956]. A major
improvement was proposed by Villadsen and Stewart [Villadsen, J. V., and
W. E. Stewart, Chem . Eng . Sci. 22:1483-1501 (1967)], who proposed that
the entire solution process be done in terms of the solution at the collocation points rather than the coefficients in the expansion. This method
is especially useful for reaction diffusion problems that frequently arise
when modeling chemical reactors. It is highly efficient when the solution
is smooth, but the finite difference method is preferred when the solution
changes steeply in some region of space. The error decreases very rapidly as
N is increased since it is proportional to [1/(1 - N)]N -1. See Finlayson (1980)
in General References.
Galerkin Finite Element Method In the finite element method, the
domain is divided into elements, and an expansion is made for the solution
on each finite element (see Interpolation: Finite Element Method). In the
Galerkin finite element method, an additional idea is introduced: the Galerkin
method is used to solve the equation. The Galerkin method is explained using
the equations for reaction and diffusion in a porous catalyst pellet.
d 2c
= φ2 R (c )
dx 2
dc
(0) = 0, c (1) = 1
dx
The unknown solution is expanded in a series of known functions {bi(x)}
with unknown coefficients {ai}.
NT
c ( x ) = ∑ai bi ( x )
i =1
The trial solution is substituted into the differential equation to obtain the
residual.
NT
Residual = ∑ ai
i =1
d 2bi
NT
− φ2 R ∑ ai bi ( x )
2
dx
1
=
i
The residual is then made orthogonal to the set of basis functions.
NT
1
∫ b ( x ) ∑ a
0
j
i =1
i
NT
d 2bi
− φ2 R ∑ ai bi ( x ) dx = 0
2
dx
i = 1
j = 1, , NT
A finite element method based on these functions would have an error proportional to Δ x2. The finite element representations for the first derivative
and second derivative are the same as in the finite difference method, but
this is not true for other functions or derivatives. With quadratic finite elements, take the region from xi-1 and xi+1 as one element with x = x i−1 at u = 0,
x = x i at u = ½, and x = x i+1 at u = 1. Then the interpolation would be
c ( x ) = ci − 1 N 1 (u ) + ci N 2 (u ) + ci +1 N 3 (u )
1
N 1 (u ) = 2(u − 1)u − N 2 (u ) = 4 u (1 − u )
2
1
N 3 (u ) = 2u u −
2
A finite element method based on these functions would have an error proportional to Δ x3. Thus, it would converge faster than one based on linear
interpolation.
Adaptive Meshes In many two-point boundary-value problems, the
difficulty in the problem lies in the formation of a boundary-layer region,
or a region in which the solution changes very dramatically. In such cases,
it is prudent to use small mesh spacing there, with either the finite difference method or the finite element method. If the region is known a priori,
small mesh spacings can be assumed at the boundary layer. If the region is
not known, however, other techniques must be used. These techniques are
known as adaptive mesh techniques. The mesh size is made small where
some property of the solution is large. For example, if the truncation error of
the method is nth-order, then the nth-order derivative of the solution is evaluated and a small mesh is used where it is large. Alternatively, the residual
(the differential equation with the numerical solution substituted into it) can
be used as a criterion. It is also possible to define the error that is expected
from a method one order higher and one order lower. Then a decision about
whether to increase or decrease the order of the method can be made, taking
into account the relative work of the different orders. This provides a method
of adjusting both the mesh spacing (Δ x, or sometimes called h) and the degree
of polynomial ( p). Such methods are called h-p methods. Many finite element
programs have the capability to do this mesh refinement automatically.
Singular Problems and Infinite Domains If the solution being
sought has a singularity, it may be difficult to find a good numerical solution.
Sometimes even the location of the singularity may not be known. One
method of solving such problems is to refine the mesh near the singularity,
relying on the better approximation due to a smaller Δx . Another approach
is to incorporate the singular trial function into the approximation. Thus,
if the solution approaches f (x) as x goes to zero and f (x) becomes infinite,
one may define a new variable u(x) = y(x) - f (x) and derive an equation for u .
The differential equation is more complicated, but the solution is better
near the singularity. See Press et al. (2007) in General References.
3-46
MATHEMATICS
Sometimes the domain is semi-infinite, as in boundary-layer flow. The
domain can be transformed from the x domain (0 - ∞) to the h domain
(1 - 0) using the transformation h = exp (-x). Another approach is to use
a variable mesh, perhaps with the same transformation. For example, use
h = exp (-bx) and a constant mesh size in h; the value of b is found experimentally. Still another approach is to solve on a finite mesh in which the last
point is far enough away that its location does not influence the solution.
A location that is far enough away must be found by trial and error.
Packages to solve boundary-value problems are available on the Internet. On the NIST web page http://gams.nist.gov/Problem.html insert “ordinary differential equations” to find packages for boundary-value problems.
On the Netlib website http://www.netlib.org/ search on “boundary-value
problem.” Any spreadsheet that has an iteration capability can be used with
the finite difference method. Some packages for partial differential equations also have a capability for solving one-dimensional boundary-value
problems (e.g., Comsol Multiphysics).
where the distribution function f (x) satisfies
f ( x ) ≥ 0,
b
a
(3-67)
f ( x ) dx = 1
The quantity GN is an estimation of G, and the fundamental theorem of
Monte Carlo guarantees that the expected value of GN is G, if G exists (Kalos,
M. H., and P. A. Whitlock, Monte Carlo Methods, vol. 1, Wiley, New York,
1986). The error in the calculation is given by
ε=
This subsection considers a method of solving numerically the Fredholm
integral equation of the second kind:
Ω0
The distribution function f (x) can be taken as constant, for example, 1/W0.
We choose variables x1, x2, …, xN randomly from f (x) and form the arithmetic mean
1
GN = ∑ g (xi )
N i
nUMERICAL SOLUTIOn OF InTEGRAL EQUATIOnS
u ( x ) = f ( x ) + λ ∫ k ( x , t ) u (t ) dt for u ( x )
∫
σ1
N 1/2
where σ 12 is calculated from
σ 12 =
∫
Ω0
g 2 ( x ) f ( x ) dx − G 2
The method discussed arises because a definite integral can be closely
approximated by any of several numerical integration formulas (each of
which arises by approximating the function by some polynomial over an
interval). Thus the definite integral in Eq. (3-67) can be replaced by an integration formula, and Eq. (3-67) may be written
Thus the number of terms needed to achieve a specified accuracy e can be
calculated once an estimate of σ 12 is known.
n
u ( x ) = f ( x ) + λ (b − a ) ∑ci k ( x , t i )u (ti )
i = 1
Various methods, such as influence sampling, can be used to reduce the
number of calculations needed. See also Lapeyre, B., Introduction to MonteCarlo Methods for Transport and Diffusion Equations, Oxford University
Press, London, 2003; Liu, J. S., Monte Carlo Strategies in Scientific Computing,
Springer, New York, 2008; and Thomopoulos, N. T., Essentials of Monte Carlo
Simulation: Statistical Methods for Building Simulation Models, Springer,
New York, 2013. Some computer programs are available that perform
simple Monte Carlo calculations using Microsoft Excel. Monte Carlo methods for molecular simulation lead to an equilibrium configuration of the
molecules. Thus, the approach to that equilibrium is not modeled, and this
is an advantage over molecular dynamics (see below) when the equilibrium
configuration is the desired result, since the Monte Carlo method is faster.
A good open-source Monte Carlo program is CASSANDRA at the University
of Notre Dame.
(3-68)
where t1, …, tn are points of subdivision of the t axis, a ≤ t ≤ b, and the c’s are
coefficients whose values depend upon the type of numerical integration
formula used. Now Eq. (3-68) must hold for all values of x, a ≤ x ≤ b; so it
must hold for x = t1, x = t2, …, x = tn. Substituting for x successively t1, t2, …, tn
and setting u(ti) = ui and f (ti) = fi, we get n linear algebraic equations for the
n unknowns u1, …, un. That is,
ui = fi + l(b - a)[c1k(ti , t1)u1 + c2k(ti , t2)u2 + … + cnk(ti , tn)un]
i = 1, 2, …, n
These uj may be solved for by the methods under Numerical Solution of
Linear Equations and Associated Problems and substituted into Eq. (3-68)
to yield an approximate solution for Eq. (3-67).
Because of the work involved in solving large systems of simultaneous
linear equations it is desirable that only a small number of u values be
computed. Thus the gaussian integration formulas are useful because of the
economy they offer.
Solutions for Volterra equations are done in a similar fashion, except that
the solution can proceed point by point or in small groups of points depending on the quadrature scheme. See Linz, P., Analytical and Numerical Methods
for Volterra Equations, SIAM, Philadelphia, Penn., 1985. There are methods
that are analogous to the usual methods for integrating differential equations (Runge-Kutta, predictor-corrector, Adams methods, etc.). Explicit
methods are fast and efficient until the time step is very small to meet the
stability requirements. Then implicit methods are used, even though sets
of simultaneous algebraic equations must be solved. The major part of the
calculation is the evaluation of integrals, however, so that the added time to
solve the algebraic equations is not excessive. Thus, implicit methods tend
to be preferred. Volterra equations of the first kind are not well posed, and
small errors in the solution can have disastrous consequences. The boundary
element method uses Green’s functions and integral equations to solve differential equations. See Brebbia, C. A., and J. Dominguez, Boundary Elements—
An Introductory Course, 2d ed., Computational Mechanics Publications,
Southhampton, UK, 1992; Poljak, D., and C. A. Brebbia, Boundary Element
Methods for Electrical Engineers, WIT Press, Ashurst, UK, 2005.
MOnTE CARLO SIMULATIOnS
Some physical problems, such as those involving the interaction of molecules,
are usually formulated as integral equations. Monte Carlo methods are especially well suited to their solution. This section cannot give a comprehensive
treatment of such methods, but their use in calculating the value of an integral will be illustrated. Suppose we wish to calculate the integral
G=
∫
Ω0
g ( x ) f ( x ) dx
N=
σ 12
ε2
nUMERICAL SOLUTIOn OF PARTIAL DIFFEREnTIAL
EQUATIOnS
The numerical methods for partial differential equations can be classified according to the type of equation (see Partial Differential Equations):
parabolic, elliptic, and hyperbolic. This section uses the finite difference
method to illustrate the ideas, and these results can be programmed for
simple problems. For more complicated problems, however, it is common
to rely on computer packages. Thus, some discussion is given to the issues
that arise in using computer packages. These methods are used in modeling microfluidics (with small Reynolds numbers) and turbulence (with large
Reynolds numbers).
Parabolic Equations in One Dimension By combining the techniques applied to initial-value problems and boundary-value problems, it is
possible to easily solve parabolic equations in one dimension. The method
is often called the method of lines. It is illustrated here using the finite difference method, but the Galerkin finite element method and the orthogonal collocation method can also be combined with initial-value methods in
similar ways. The analysis is done by example. The finite volume method is
described under Hyperbolic Equations.
Example Consider the diffusion equation, with boundary- and initialvalue conditions.
∂c
∂2 c
=D 2
∂t
∂x
c(x, 0) = 0,
c(0, t) = 1,
c(1, t) = 0
We denote by ci the value of c(xi , t) at any time. Thus, ci is a function of
time, and differential equations in ci are ordinary differential equations.
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS
3-47
Write a finite difference form for the time derivative and average the
right-hand sides, evaluated at the old and new times.
cin++11 − 2cin + 1 + cin−+11
cin+ 1 − 2cin + cin− 1
cin + 1 − cin
= D (1 − θ)
+ Dθ
∆x 2
∆t
∆x 2
Now the equations are of the form
−
D ∆ tθ n + 1 D ∆tθ n + 1
D ∆tθ n + 1
ci − 1
ci + 1 + 1 + 2
ci −
∆x 2
∆x 2
∆x 2
D∆t (1 − θ) n
(ci + 1 − 2cin + cin− 1 )
= cin +
∆x 2
and require solving a set of simultaneous equations, which have a tridiagonal structure. Using q = 0 gives the Euler method (as above), q = 0.5 gives the
Crank-Nicolson method, and q = 1 gives the backward Euler method. The
Crank-Nicolson method is also the same as applying the trapezoid rule to
do the integration. The stability limit is given by
∆t
FIG. 3-50
Computational molecules. h = Δx = Δy .
By evaluating the diffusion equation at the ith node and replacing the derivative with a finite difference equation, the following working equation is
derived for each node i, i = 2, …, n (see Fig. 3-50).
ci + 1 − 2ci + ci − 1
dci
=D
dt
∆x2
This can be written in the general form of a set of ordinary differential equations by defining matrix AA.
dc
= AAc
dt
This set of ordinary differential equations can be solved using any of the
standard methods, and the stability of the integration of these equations is
governed by the largest eigenvalue of AA. When Euler’s method is used to
integrate in time, the equations become
cin+ 1 − 2cin +cin− 1
cin + 1 − cin
=D
∆t
∆x 2
where cin = c(xi, tn). Notice that if the solution is known at every point at one
time n, then it is a straightforward calculation to find the solution at every
point at the new time n + 1.
If Euler’s method is used for integration, the time step is limited by
∆t ≤
2
| λ |max
n
≤ max ∑ AA ji =
max
2< j <n
i =2
4D
∆x2
This gives the well-known stability limit
∆t
The price of using implicit methods is that one now has a system of equations to solve at each time step, and the solution methods are more complicated (particularly for nonlinear problems) than the straightforward
explicit methods. Phenomena that happen quickly can also be obliterated
or smoothed over by using a large time step, so implicit methods are not
suitable in all cases. The engineer must decide if she or he wants to track
those fast phenomena, and choose an appropriate method that handles the
time scales that are important in the problem.
Other methods can be used in space, such as the finite element method, the
orthogonal collocation method, or the method of orthogonal collocation on
finite elements. One simply combines the methods for ordinary differential
equations (see Ordinary Differential Equations—Boundary-Value Problems)
with the methods for initial-value problems (see Numerical Solution of
Ordinary Differential Equations as Initial-Value Problems). Fast Fourier
transforms can also be used on regular grids (see Fast Fourier Transform).
Elliptic Equations Elliptic equations can be solved with both finite
difference and finite element methods. One-dimensional elliptic problems
are two-point boundary-value problems. Two- and three-dimensional elliptic problems are often solved with iterative methods when the finite difference method is used and with direct methods when the finite element
method is used. So there are two aspects to consider: how the equations are
discretized to form sets of algebraic equations and how the algebraic equations are then solved.
The prototype elliptic problem is steady-state heat conduction or diffusion
∂2 T ∂2 T
k 2 + 2 = Q
∂y
∂x
possibly with a heat generation term per unit volume Q . The boundary conditions taken here are T = f (x, y) on the boundary (S) with f a known function. Illustrations are given for constant thermal conductivity k while Q is a
known function of position. The finite difference formulation is given using
the following nomenclature:
Ti, j = T(i Δx, j Δy)
whereas if the Runge-Kutta-Fehlberg method is used, the 2 in the numerator
is replaced by 3.0. The largest eigenvalue of AA is bounded by Gerschgorin’s
theorem.
λ
0.25
D
≤
∆x 2 1 − 2 θ
1
D
≤
∆x2 2
The smallest eigenvalue is independent of Δx (it is Dπ2/L2) so that the ratio
of largest to smallest eigenvalue is proportional to 1/Δx2. Thus, the problem
becomes stiff as Δx approaches zero. See Eq. (3-65).
The effect of the increased stiffness is that a smaller and smaller time step
(Δt) must be taken as the mesh is refined (Δx2 → 0). At the same time, the
number of points is increasing, so the computation becomes very lengthy.
Implicit methods are used to overcome this problem.
The finite difference formulation is then (see Fig. 3-50)
Ti + 1, j − 2Ti , j + Ti − 1, j Ti , j + 1 − 2Ti , j + Ti , j − 1
+
= Qi , j
Δx 2
Δy 2
Ti , j = f ( x i , y j ) on S
(3-69)
If the boundary is parallel to a coordinate axis, any derivative is evaluated
as in the section on boundary-value problems, using either a one-sided,
centered difference or a false boundary. If the boundary is more irregular
and not parallel to a coordinate line, then more complicated expressions are
needed and the finite element method may be the better method.
Equation (3-69) provides a set of linear equations that must be solved. These
equations and their boundary conditions may be written in matrix form as
At = f
where t is the set of temperatures at all the points, f is the set of heat generation terms at all points, and A is formed from the coefficients of Tij in Eq. (3-69).
3-48
MATHEMATICS
The solution can be obtained simply by solving the set of linear equations. For
three-dimensional problems, the matrix A is sparse, and iterative methods are
used. These include Gauss-Seidel, alternating direction, overrelaxation methods, conjugate gradient, and multigrid methods. In Gauss-Seidel methods,
one writes the equation for Tij in terms of the other temperatures and cycles
through all the points over and over. In the alternating direction method, one
solves along one line (that is, x = constant), keeping the side values fixed, and
then repeats this for all lines, and then repeats the process. Multigrid methods
solve the problem on successively refined grids, which has advantages for both
convergence and error estimation. Conjugate gradient methods frequently
use a preconditioned matrix. The equation is multiplied by another matrix,
which is chosen so that the resulting problem is easier to solve than the original one. Finding such matrices is an art, but it can speed convergence. The
generalized minimal residual method is described in http://mathworld.wolfram.com/ GeneralizedMinimalResidualMethod.html. Additional resources
can be found at http://www.netlib.org/linalg/html_templates/Templates.
html. When the problem is nonlinear, the iterative methods may not converge,
or the mesh may have to be refined before they converge, so some experimentation is sometimes necessary.
Spreadsheets can be used to solve two-dimensional problems on rectangular grids. The equation for Tij is obtained by rearranging Eq. (3-69).
∆x 2
Qi , j
∆x 2
2 1 + 2 Ti , j = Ti + 1, j + Ti − 1, j + 2 (Ti , j + 1 + T1, j − 1 ) − ∆x 2
k
∆y
∆y
This equation is inserted into a cell and copied throughout the space represented by all the cells; when the iteration feature is turned on, the solution
is obtained.
The Galerkin finite element method (FEM) is useful for solving elliptic
problems and is particularly effective when the domain or geometry is
irregular. As an example, cover the domain with triangles and define a trial
function on each triangle. The trial function takes the value 1.0 at one corner
and the value 0.0 at the other corners and is linear in between. For a triangle
with corners at (x, y) = (0, 0.58), (0.66, 0), and (1, 0.66) one of three trial functions is shown in Fig. 3-51. These trial functions on each triangle are pieced
together to give a trial function on the whole domain. General treatments
of the finite element method are available (see references). The steps in the
solution method are similar to those described for boundary-value problems,
except now the problems are much bigger so that the numerical analysis
must be done very carefully to be efficient. Most engineers, however, just use
a finite element program without generating it. There are three major caveats that must be addressed. First, the solution is dependent on the mesh laid
down, and the only way to assess the accuracy of the solution is to solve the
problem with a more refined mesh. Second, the solution obeys the shape of
the trial function inside the element. Thus, if linear functions are used on triangles, a three-dimensional view of the solution, plotting the solution versus
x and y, consists of a series of triangular planes joined together at the edges,
as in a geodesic dome. Third, the Galerkin finite element method is applied
to both the differential equations and the boundary conditions. Computer
programs are usually quite general and may allow the user to specify boundary conditions that are not realistic. Also, natural boundary conditions are
satisfied if no other boundary condition (ones involving derivatives) is set at
a node. Thus, the user of finite element codes must be very clear what boundary conditions and differential equations are built into the computer code.
When the problem is nonlinear, the Newton-Raphson method is used to iterate from an initial guess. Nonlinear problems lead to complicated integrals to
evaluate, and they are usually evaluated using gaussian quadrature.
One nice feature of the finite element method is the use of natural boundary conditions. It may be possible to solve the problem on a domain that is
shorter than needed to reach some limiting condition (such as at an outflow
boundary). The externally applied flux is still applied at the shorter domain,
and the solution inside the truncated domain is still valid. Examples are given
in Chang, M. W., and B. A. Finlayson, Int . J . Num . Methods Eng . 15, 935–942
(1980), and Finlayson, B. A., Numerical Methods for Problems with Moving
Fronts, Ravenna Park Publishing, Seattle, Wash. (1992). The effect of this is
to allow solutions in domains that are smaller, thus saving computation time
and permitting the solution in semi-infinite domains.
The trial functions in the finite element method are not limited to linear
ones. Quadratic functions and even higher-order functions are frequently
used. The same considerations hold as for boundary-value problems: The
higher-order trial functions converge faster, but require more work. It is
possible to refine both the mesh h and the power of polynomial in the trial
function p in an h-p method. Some problems have constraints on some of
the variables. For flow problems, the pressure must usually be approximated
by using a trial function that is one order lower than the polynomial used to
approximate the velocity.
Hyperbolic Equations The most common situation yielding hyperbolic equations involves unsteady phenomena with convection. Two typical
equations are the convective diffusive equation
∂c
∂c
∂2 c
+u
=D 2
∂t
∂x
∂x
and the chromatography equation. (See Partial Differential Equations.) If the
diffusion coefficient is zero, the convective diffusion equation is hyperbolic.
If D is small, the phenomenon may be essentially hyperbolic, even though
the equations are parabolic. Thus the numerical methods for hyperbolic
equations may be useful even for special parabolic equations.
Equations for several methods are given here. If the convective term is
treated with a centered difference expression, the solution exhibits oscillations from node to node, and these go away only if a very fine grid is used.
The simplest way to avoid the oscillations with a hyperbolic equation is to
use upstream derivatives. If the flow is from left to right, this would give
ci − ci − 1
ci + 1 − 2c i + ci − 1
dci
=D
+u
Δx 2
Δx
dt
The effect of using upstream derivatives is to add artificial or numerical diffusion to the model. This can be ascertained by rearranging the finite difference form of the convective diffusion equation
ci +1 − ci − 1
dci
uΔx ci + 1 − 2c i + ci − 1
= D+
+u
Δx 2
2Δ x
2
dt
Thus the diffusion coefficient has been changed from
D to D +
1
u∆ x
2
Alternatively, the diffusion coefficient has been multiplied by the factor
Pecell
u∆ x
D ′ = D 1 +
= D 1 +
2
2D
0.5
∆x
u∆x uL ∆x
=
= Pe
is called the cell Peclet number. When
D
D L
L
the diffusion coefficient is very small (or diffusion is slow compared with
convection), the Peclet number will be large. In that case, extraneous diffusion will be included in the solution unless the mesh size (denoted by Δx)
is small compared with the characteristic length of the problem. To avoid
this problem (by keeping the factor small), very fine meshes must be
used, and the smaller the diffusion coefficient, the smaller the required
mesh size.
A variety of other methods are used to obtain a good solution without
using extremely fine meshes. The flux correction methods keep track of the
flux of material into and out of a cell ( from one node to another) and put
limits on the flux to make sure that no more material leaves the cell than
is there originally plus the input amount. See Finlayson, B. A., Numerical
where Pecell =
0
0.7
0.6
0.5
1
0.8
0.4
0.6
0.3
0.2
0.4
0.1
0
FIG. 3-51
a triangle.
0.2
0
Trial functions for Galerkin finite element method: a linear polynomial on
nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS
i –1st
cell
ith
cell
i−1 i−1/2 i
i+1/2
∆x
FIG. 3-52
Nomenclature for finite volume method.
Methods for Problems with Moving Fronts, Ravenna Park Publishing, Seattle,
Wash., 1992, for many examples.
All the methods have a limit to the time step that is set by the convection
term. Essentially, the time step should not be so big as to take the material
farther than it can go at its velocity. This is usually expressed as a Courant
number limitation.
Co =
u∆t
≤1
∆x
Some methods require a smaller limit, depending upon the amount of diffusion present (see Finlayson, 1992, Appendix).
In the finite element method, Petrov-Galerkin methods are used to
minimize the unphysical oscillations. The Petrov-Galerkin method essentially adds a small amount of diffusion in the flow direction to smooth the
unphysical oscillations. The amount of diffusion is usually proportional to
Δx so that it becomes negligible as the mesh size is reduced. The value of
the Petrov-Galerkin method lies in being able to obtain a smooth solution
when the mesh size is large, so that the computation is feasible. This is not
so crucial in one-dimensional problems, but it is essential in two- and threedimensional problems and purely hyperbolic problems.
Finite Volume Methods Finite volume methods are utilized extensively in computational fluid dynamics. An excellent presentation is by
LeVeque (2002). In this method, a mass balance is made over a cell, accounting for the change in what is in the cell, and the flow in and out. Figure 3-52
illustrates the geometry of the ith cell. A mass balance made on this cell
(with area A perpendicular to the paper) is
A ∆x (cin + 1 − cin ) = ∆t A ( J i − 1/2 − J i + 1/2 )
where J is the flux due to convection and diffusion, positive in the +x
direction.
J = uc − D
ci − ci − 1
∂c
, J i − 1/2 = ui − 1/2ci − 1/2 − D
∂x
∆x
The concentration at the edge of the cell is taken as
1
ci − 1/2 = (ci + ci − 1 )
2
Rearrangement for the case when the velocity u is the same for all nodes
gives
cin + 1 − c n i u (ci + 1 − ci − 1 ) D
= 2 (ci + 1 − 2ci + ci + 1 )
+
2 ∆x
∆x
∆t
This is the same equation obtained by using the finite difference method.
This coincidence occurs only when the velocity is constant, which isn’t usually true. In two and three dimensions, the mesh need not be rectangular,
as long as it is possible to compute the velocity normal to an edge of the cell.
The finite volume method is useful for applications involving filling, such as
injection molding, when only part of the cell is filled with fluid. Such applications do involve some approximations, since the interface is not tracked
precisely, but they are useful engineering approximations.
Parabolic Equations in Two or Three Dimensions Computations
become much more lengthy when there are two or more spatial dimensions.
For example, we may have the unsteady heat conduction equation
ρC p
∂2 T ∂2 T
∂T
=k 2 + 2 −Q
∂t
∂y
∂x
Most engineers use computer packages to solve such problems. If there
is both convection and diffusion in the problem, the same considerations
3-49
apply: A fine mesh is needed when the Peclet number is large. The upstream
weighting and Petrov-Galerkin methods can be used, but it is important to
apply the smoothing only in the direction of flow, since smoothing in the
direction transverse to the flow direction would be incorrect. Some transverse smoothing is unavoidable, but the engineer needs to be sure that
the smoothing is just enough to allow a good solution without creating
large errors. See Finlayson (1980) in General References; Kuzmin, D., and
J. Hämäläinen, Finite Element Methods for Computational Fluid Dynamics: A
Practical Guide, SIAM-Soc. Ind. Appl. Math., 2014; and Layton, W., Introduction
to the Numerical Analysis of Incompressible Viscous Flows, SIAM, 2008.
Computer Software When one is choosing computer software to
solve a problem, there are a number of important considerations. The first
decision is whether to use an approximate, engineering flow model, developed from correlations, or to solve the partial differential equations that
govern the problem. Correlations are quick and easy to apply, but they may
not be appropriate to the problem or give the needed detail. When one is
using a computer package to solve partial differential equations, the first
task is always to generate a mesh covering the problem domain. This is not
a trivial task, and special methods have been developed to permit importation of a geometry from a computer-aided design (CAD) program. Then the
mesh must be created automatically. If the boundary is irregular, the finite
element method is especially well suited, although special embedding
techniques can be used in finite difference methods (which are designed
to be solved on rectangular meshes). Another capability to consider is the
ability to track free surfaces that move during the computation. This phenomenon introduces the same complexity that occurs in problems with a
large Peclet number, with the added difficulty that the free surface moves
between mesh points and improper representation can lead to unphysical oscillations. The method used to solve the equations is important,
and both explicit and implicit methods (as described above) can be used.
Implicit methods may introduce unacceptable extra diffusion, so the engineer needs to examine the solution carefully. The methods used to smooth
unphysical oscillations from node to node are also important, and the engineer needs to verify that the added diffusion or smoothing does not give
inaccurate solutions. Since current-day problems are mostly nonlinear,
convergence is always an issue since the problems are solved iteratively.
Robust programs provide several methods for convergence, each of which
is best in some circumstance or other. It is wise to have a program that
includes many iterative methods. If the iterative solver is not very robust,
the only recourse to solving a steady-state problem may be to integrate the
time-dependent problem to steady state. The solution time may be long,
and the final result may be further from convergence than would be the
case if a robust iterative solver were used.
A variety of computer programs are available on the Internet, some free.
First consider general-purpose programs. The website http://www.netlib
.org/pdes/index.html lists programs for 2D elliptic partial differential equations as well as Clawpack for hyperbolic systems of equations from LeVeque
(2002). On the NIST website http://gams.nist.gov/ search on “partial
differential equations.” Lau (2007) provides many programs in C++ (also see
http://numerical.recipes /). The multiphysics program Comsol Multiphysics
also solves many standard equations arising in mathematical physics.
Computational fluid dynamics (CFD) programs are more specialized,
and most have been designed to solve sets of equations that are appropriate to specific industries. They can then include approximations and
correlations for some features that would be difficult to solve for directly.
ANSYS (http://www.ansys.com) is a major program having incorporated
both Fluent and CFX. Comsol Multiphysics (http://www.comsol.com) is
particularly useful because it incorporates many different types of physics
(and equations), has a convenient graphical-user interface, permits easy
mesh generation and refinement (including adaptive mesh refinement),
allows the user to add phenomena and equations easily, permits solution
by continuation methods (thus enhancing convergence), and has extensive
graphical output capabilities. Other packages are also available (see http://
cfd-online.com/), and these may contain features and correlations specific
to the engineer’s industry. One important point to note is that for turbulent
flow, all the programs contain approximations, using the k-epsilon models
of turbulence, or large eddy simulations; the direct numerical simulation of
turbulence is too slow to apply to very big problems, although it does give
insight (independent of any approximations) that is useful for interpreting
turbulent phenomena. Thus, the method used to include those turbulent
correlations is important, and the method also may affect convergence or
accuracy.
FAST FOURIER TRAnSFORM
The discrete Fourier transform can be used to differentiate a function, and
this is used in the spectral method for solving differential equations as well as
in modeling turbulent flow. Gottlieb, D., and S. A. Orszag, Numerical Analysis
3-50
MATHEMATICS
of Spectral Methods: Theory and Applications, SIAM, Philadelphia, Penn., 1977,
discusses why they work; Trefethen, L. N., Spectral Methods in Matlab, SIAM,
Philadelphia, Penn., 2000, shows how to use them in MATLAB. Suppose we
have a grid of equidistant points
x n = n∆x , n = 0,1, 2, , 2 N − 1, ∆x =
L
2N
Thus at the grid points
N
2 πik 2 ik π xn / L
dy
e
= ∑ Yk
dx n k = −N
L
The process works as follows. From the solution at all grid points the Fourier
transform is obtained by using the fast Fourier transform (FFT), {Yk}. Then
this is multiplied by 2πik/L to obtain the Fourier transform of the derivative.
The solution is known at each of these grid points {y(xn)}. First the discrete
Fourier transform is taken:
Yk =
1
2N
2 N −1
∑
y ( x n )e −2 ik π xn / L
k = − N , − N + 1, , 0, , N − 1, N
n=0
Yk′ = Yk
Then the inverse Fourier transform is taken using FFT, giving the value of
the derivative at each of the grid points.
1 N
dy
= ∑ Yk′e 2 ik π xn / L
dx n L k = − N
The inverse transformation is
y (x ) =
2 πik
L
1 N
∑ Yke 2ik π x /L
L k = −N
The spectral method is used for direct numerical simulation (DNS)
of turbulence. The Fourier transform is taken of the differential equation, and the resulting equation is solved. Then the inverse transformation gives the solution. When there are nonlinear terms, as in turbulent
flow, they are calculated at each node in physical space, and the Fourier
transform is taken of the result. This technique is especially suited to
time-dependent problems, and the major computational effort is in the
fast Fourier transform.
Differentiate this to get
2 πik 2 ik π x / L
dy 1 N
e
= ∑ Yk
dx L k = −N
L
OPTIMIZATIOn
References: General references include the following textbooks. For
nonlinear programming, see Nocedal, J., and S. J. Wright, Numerical Optimization, Springer, New York, 2006; Conn, A. R., N. Gould, and P. Toint, Trust
Region Methods, SIAM, Philadelphia, Penn., 2000; Biegler, L. T., Nonlinear
Programming: Concepts, Algorithms and Applications to Chemical Engineering, SIAM, Philadelphia, Penn., 2010; Edgar, T. F., D. M. Himmelblau, and
L. S. Lasdon, Optimization of Chemical Processes, McGraw-Hill, New York,
2002. For operations research and linear programming, Hillier, F. S., and G.
J. Lieberman, Introduction to Operations Research, McGraw-Hill, New York,
2015. For mixed integer programming, Nemhauser, G. L., and L. A. Wolsey,
Integer and Combinatorial Optimization, Wiley, New York, 1999. For global
optimization and mixed integer nonlinear programming, Floudas, C. A.,
Deterministic Global Optimization: Theory, Algorithms and Applications,
Kluwer, Norwell, Mass., 2000; Tawarmalani, M., and N. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer,
2002. Many useful resources including descriptions, trial software, and
examples can be found on the NEOS server maintained at Argonne National
Laboratory. Background material for this section includes the two previous
sections on matrix algebra and numerical analysis.
InTRODUCTIOn
Optimization is a key enabling tool for decision making in chemical
engineering. It has evolved from a methodology of academic interest into
a technology that continues to have a significant impact on engineering
research and practice. Optimization algorithms form the core tools for
(1) experimental design, parameter estimation, model development, and statistical analysis; (2) process synthesis analysis, design, and retrofit; (3) model
predictive control and real-time optimization; and (4) planning, scheduling,
and the integration of process operations into the supply chain.
As shown in Fig. 3-53, optimization problems that arise in chemical engineering can be classified in terms of continuous and discrete variables. For
the former, nonlinear programming (NLP) problems form the most general case, and widely applied specializations include linear programming
(LP) and quadratic programming (QP). An important distinction for NLP
is whether the optimization problem is convex or nonconvex. The latter
NLP problem may have multiple local optima, and an important question
is whether a global solution is required for the NLP. Another important distinction is whether the problem is assumed to be differentiable or not.
Mixed integer problems also include discrete variables. These can be
written as mixed integer nonlinear programs (MINLPs), or as mixed integer linear programs (MILP), if all variables appear linearly in the constraint
and objective functions. For the latter an important case occurs when all
the variables are integer; this gives rise to an integer programming (IP)
problem. IP problems can be further classified into many special problems (e.g., assignment, traveling salesperson, etc.), which are not shown in
Fig. 3-53. Similarly, the MINLP problem also gives rise to special problem
classes, although here the main distinction is whether its relaxation is convex or nonconvex.
The ingredients of formulating optimization problems include a mathematical model of the system, an objective function that quantifies a criterion to be extremized, variables that can serve as decisions, and, optionally,
inequality constraints on the system. When represented in algebraic form,
the general formulation of discrete and continuous optimization problems
can be written as the following mixed integer optimization problem:
Min f (x, y)
subject to h(x, y) = 0 g(x, y) ≤ 0 x ∈ n y ∈ {0, 1}t
(3-70)
where f (x, y) is the objective function (e.g., cost, energy consumption, etc.),
h(x, y) = 0 are the equations that describe the performance of the system
(e.g., material balances, production rates), and the inequality constraints
g(x, y) ≤ 0 may define process specifications or constraints for feasible
plans and schedules. Note that the operator max f (x, y) is equivalent to
Min[-f (x, y)] . We define the real n vector x to represent the continuous variables while the t vector y represents the discrete variables, which, without
loss of generality, are often restricted to take values of 0 or 1 to define logical
or discrete decisions, such as assignment of equipment and sequencing of
tasks. (These variables can also be formulated to take on other integer values
as well.) Problem (3-70) corresponds to a mixed integer nonlinear program
Optimization
Mixed Integer
(Discrete)
NLP
(Continuous)
MINLP
MILP
Nondifferentiable
Differentiable
Convex
Nonconvex
IP
LP
QP
Local
Global
FIG. 3-53 Classes of optimization problems and algorithms.
Direct
Search
OPTIMIZATIOn
For continuous variable optimization, we consider Eq. (3-70) without discrete variable y. The general NLP problem (3-71) is presented here:
subject to h(x) = 0, g(x) ≤ 0
9
8
7
100
6
5
50
4
3
10
2
GRADIEnT-BASED nOnLInEAR PROGRAMMInG
Min f (x)
10
x2
when any of the functions involved are nonlinear. If all functions are linear,
it corresponds to a mixed integer linear program (3-89). If there are no 0–1
variables, then problem (3-70) reduces to a nonlinear program (3-71) or linear program (3-78) depending on whether the functions are linear.
Following the road map in Fig. 3-53, we start with continuous variable
optimization and consider in the next section the solution of NLP problems
with differentiable objective and constraint functions. If only local solutions
are required for the NLP problem, then very efficient large-scale methods
can be considered. This is followed by methods that are not based on local
optimality criteria; we consider direct search optimization methods that
do not require derivatives as well as deterministic global optimization
methods. Following this, we consider the solution of mixed integer problems and outline the main characteristics of algorithms for their solution.
Finally, we conclude with a discussion of optimization modeling software
and its implementation on engineering models.
x*
−2
2
0
1
1
(3-71)
and we assume that the functions f (x), h(x), and g(x) have continuous first
and second derivatives. A key characteristic of Eq. (3-71) is whether the
problem is convex or not, i.e., whether it has a convex objective function
and a convex feasible region. A function f(x) of x in some domain X is convex
if and only if, for all points x1, x2 ∈ X,
3-51
3
2
4
5
x1
6
7
8
9
10
FIG. 3-54 Unconstrained minimum.
10
9
(3-72)
holds for all α ∈ (0, 1). [Strict convexity requires that the inequality Eq. (3-72)
be strict.] Convex feasible regions require g(x) to be a convex function and
h(x) to be linear. Referring to Fig. 3-53, problem (3-71) is convex if and only
if f (x) and g(x) are convex functions and h(x) is a linear function. Otherwise,
the problem is nonconvex. If Eq. (3-71) is a convex problem, then any local
solution is guaranteed to be a global solution to Eq. (3-71). Moreover, if the
objective function is strictly convex, then this solution x* is unique. On
the other hand, nonconvex problems may have multiple local solutions,
i.e., feasible solutions x* only within some nonvanishing neighborhood.
We first consider methods that find only local solutions to nonconvex
problems, as more difficult (and expensive) search procedures are required
to find a global solution. Local methods are currently very efficient and
have been developed to deal with very large NLP problems. Moreover, by
considering the structure of convex NLP problems (including LP and QP
problems), even more powerful methods can be applied. To study these
methods, we first consider conditions for local optimality.
Local Optimality Conditions: A Kinematic Interpretation Instead
of a formal development of conditions that define a local optimum, we present a more intuitive kinematic illustration. Consider the contour plot of the
objective function f (x), given in Fig. 3-54, as a smooth valley in space of variables x1 and x2. For the contour plot of this unconstrained problem, Min f (x),
consider a ball rolling in this valley to the lowest point of f (x), denoted by x*.
This point is at least a local minimum and is defined by a point with a zero
gradient and at least nonnegative curvature in all (nonzero) directions p.
We use the first-derivative (gradient) vector ∇f (x) and second-derivative
(hessian) matrix ∇xx f (x) to state the necessary first- and second-order conditions for unconstrained optimality:
∇x f (x*) = 0 p ∇xx f (x*)p ≥ 0
T
for all p ≠ 0
(3-73)
These necessary conditions for local optimality can be strengthened to sufficient conditions by making the inequality in Eq. (3-73) strict (i.e., positive
curvature in all directions). Equivalently, the sufficient (necessary) curvature conditions can be stated as follows: ∇xx f (x*) has all positive (nonnegative) eigenvalues and is therefore defined as a positive (semidefinite)
definite matrix.
Now consider the imposition of inequality g(x) ≤ 0 and equality constraints h(x) = 0 in Fig. 3-55. Continuing the kinematic interpretation, the
inequality constraints g(x) ≤ 0 act as “fences” in the valley, and equality constraints h(x) = 0 act as “rails.” Consider now a ball, constrained on a rail and
within fences, to roll to its lowest point. This stationary point occurs when
the normal forces exerted by the fences [-∇g(x*)] and rails [-∇h(x*)] on
the ball are balanced by the force of gravity [-∇f (x*)]. This condition can be
stated by the following Karush-Kuhn-Tucker (KKT) necessary conditions for
constrained optimality.
h(x*)=0
8
7
6
x2
f[αx1 + (1 - α)x2] ≤ αf[x1 + (1 - α)x2] + (1 - α)f(x2)
f (x*)
5
4
100
3
x*
2
50
−2
g(x*)
0
h(x* )
1
1
2
10
2
g(x)≤0
3
4
5
6
7
8
9
10
x1
FIG. 3-55
Constrained minimum.
Balance of Forces It is convenient to define the Lagrange function
L(x, l, n) = f (x) + g(x)Tl + h(x)Tn, along with “weights” or multipliers l and n
for the constraints. The stationarity condition (balance of forces acting on
the ball) is then given by
∇L(x, l, n) = ∇f (x) + ∇h(x) l + ∇g(x) n = 0
(3-74)
Feasibility Both inequality and equality constraints must be satisfied
(the ball must lie on the rail and within the fences):
h(x) = 0
g(x) ≤ 0
(3-75)
Complementarity Inequality constraints are either strictly satisfied
(active) or inactive, in which case they are irrelevant to the solution. In the
latter case the corresponding KKT multiplier must be zero. This is written as
nTg(x) = 0
n≥0
(3-76)
Constraint Qualification For a local optimum to satisfy the
KKT conditions, an additional regularity condition is required on the
constraints. This can be defined in several ways. A typical condition is
3-52
MATHEMATICS
that the active constraints at x* be linearly independent; i.e., the matrix
[∇h(x*)|∇gA(x*)] is full column rank, where gA is the vector of inequality
constraints with elements that satisfy gA,I (x*) = 0. With this constraint
qualification, the KKT multipliers (l, n) are guaranteed to be unique at
the optimal solution.
Second-Order Conditions As with unconstrained optimization, nonnegative (positive) curvature is necessary (sufficient) in all the allowable
(i.e., constrained) nonzero directions p. The necessary second-order conditions can be stated as
pT ∇xxL(x*)p ≥ 0
for all p ≠ 0 with ∇h(x*)Tp = 0, ∇gA (x*)Tp ≤ 0, ∇gA,i (x*)Tp = 0 for ni > 0
(3-77)
and the corresponding sufficient conditions require the first inequality
in Eq. (3-77) to be strict. Note that in Fig. 3-54, the allowable directions
p span the entire space for x while in Fig. 3-55 there are no allowable
directions p .
Convex Cases of NLP Problems Linear programs and quadratic
programs are special cases of Eq. (3-71) that allow for more efficient solution, based on application of KKT conditions Eq. (3-74) through Eq. (3-77).
Because these are convex problems, any locally optimal solution is a global
solution. In particular, if the objective and constraint functions in Eq. (3-71)
are linear, then the following linear program (LP)
Min cTx
subject to Ax = b and Cx ≤ d
(3-78)
can be solved in a finite number of steps, and the optimal solution lies
at a vertex of the polyhedron described by the linear constraints. This
is shown in Fig. 3-56, and in so-called primal degenerate cases, multiple
vertices can be alternate optimal solutions, with the same values of the
Min
objective function. The standard method to solve Eq. (3-78) is the simplex method, developed in the late 1940s, although since Karmarkar’s
discovery in 1984 interior point methods have also become quite
advanced and competitive for highly constrained problems. The simplex method proceeds by moving successively from vertex to vertex
with improved objective function values. Methods to solve Eq. (3-78) are
well implemented and widely used, especially in planning and logistical
applications. They also form the basis for MILP methods discussed later.
Currently, state-of-the-art LP solvers can handle millions of variables
and constraints, and the application of further decomposition methods
leads to the solution of problems that are two or three orders of magnitude larger than this. See the general references of Hillier and Lieberman
(2015) and Nocedal and Wright (2006) for more details. Also, the interior
point method is described below from the perspective of more general
NLP problems.
Quadratic programs (QPs) represent a slight modification of Eq. (3-78)
and can be stated as
Min cTx+1/2 xTQx
subject to
Ax = b
Cx ≤ d
If the matrix Q is positive semidefinite (positive definite) when projected
into the null space of the active constraints, then Eq. (3-79) is (strictly) convex and the QP is a global (and unique) minimum. Otherwise, local solutions
may exist for Eq. (3-79), and more extensive global optimization methods
are needed to obtain the global solution. Like LPs, convex QPs can be solved
in a finite number of steps. However, as seen in Fig. 3-57, these optimal solutions may lie on a vertex, on a constraint boundary, or in the interior. A number of active set strategies have been created that solve the KKT conditions
of the QP and incorporate efficient updates of active constraints. Popular
methods include null space algorithms, range space methods, and Schur
complement methods. As with LPs, QP problems can also be solved with
interior point methods.
Solving the General NLP Problem Solution techniques for Eq. (3-71)
deal with satisfaction of the KKT conditions, Eq. (3-74) through Eq. (3-77).
Many NLP solvers are based on successive quadratic programming (SQP)
as it allows the construction of a number of NLP algorithms based on the
Newton-Raphson method for equation solving (see the Numerical Analysis
section). SQP solvers have been shown to require the fewest function evaluations to solve NLP problems, and they can be tailored to a broad range of
process engineering problems with different structure.
Min
Min
Linear Program
Min
Min
Linear Program
(Alternate Optima)
FIG. 3-56 Contour plots of linear programs.
(3-79)
Convex Objective Functions
Linear Constraints
FIG. 3-57 Contour plots of convex quadratic programs.
OPTIMIZATIOn
3-53
where e = [1, 1, …, 1]T, S = diag{s}, and V = diag{n}. SQP methods find
solutions that satisfy Eq. (3-80) by generating Newton-like search directions at iteration k. However, Eq. (3-80d) and active bounds Eq. (3-80e)
are dependent at the solution and serve to make the KKT system ill conditioned near the solution. SQP algorithms treat these conditions in two
ways. In the active set strategy, discrete decisions are made regarding the
active constraint set i ∈ I = {i| gi(x*) = 0}, and Eq. (3-80d) is replaced by si = 0,
i ∈ I, and ni = 0, i ∉ I. Determining the active set is a combinatorial problem,
and a straightforward way to determine an estimate of the active set [and
to satisfy Eq. (3-80e)] is to formulate and solve, at a point xk, the following
QP at iteration k:
for various values of m, while active set methods require the solution of the
more expensive QP subproblem Eq. (3-81). Thus, if there are few inequality constraints or an active set is known (say from a good starting guess, or
a known QP solution from a previous iteration), then solving Eq. (3-81) is
not expensive and the active set method is favored. However, for problems
with many inequality constraints, interior point methods are often faster,
as they avoid the combinatorial problem of selecting the active set. This is
especially true for large-scale problems where a large number of bounds
are active. Examples that demonstrate the application of these approaches
include the solution of model predictive control (MPC) problems and the
solution of large optimal control problems using barrier NLP solvers. For
instance, IPOPT allows the solution of problems with more than 1,000,000
variables and up to 50,000 degrees of freedom [see Biegler et al., Chem . Eng .
Sci . 57(4): 575–593 (2002); Laird et al., ASCE J . Water Resource Management
and Planning 131(2):125 (2005)].
Other Gradient-Based NLP Solvers In addition to SQP methods, a
number of NLP solvers have been developed and adapted for large-scale
problems. Generally these methods require more function evaluations than
for SQP methods, but they perform very well when interfaced to optimization modeling platforms, where function evaluations are cheap. All these
can be derived from the perspective of applying Newton steps to portions
of the KKT conditions.
LANCELOT (Conn et al., 2000) is based on the solution of boundconstrained subproblems. Here an augmented lagrangian is formed from
Eq. (3-71), and the following subproblem is solved:
Min ∇f (xk)Tp + 1/2 pT ∇xxL(xk, lk, nk)p
Min f (x) + lTh(x) + nT[g(x) + s] + 1/2 r||h(x), g(x) + s||2 subject to s ≥ 0 (3-85)
The SQP strategy applies the equivalent of a Newton step to the KKT conditions of the nonlinear programming problem, and this leads to a fast rate
of convergence. By adding slack variables s, the first-order KKT conditions
can be rewritten as
∇f (x) + ∇h(x) l + ∇g(x) n = 0
h(x) = 0
g(x) + s = 0
SVe = 0
(s, n) ≥ 0
subject to: h(x ) + ∇h(x ) p = 0 g(x ) + ∇g(x ) p + s = 0
k
k T
k
k T
(3-80a)
(3-80b)
(3-80c)
(3-80d)
(3-80e)
s≥0
(3-81)
The KKT conditions of Eq. (3-81) are given by
∇f (xk) + ∇2L(xk, lk, nk)p + ∇h(xk) l + ∇g(xk) n = 0
(3-82a)
h(xk) + ∇h(xk) T p = 0
(3-82b)
g(x ) + ∇g(x ) p + s = 0
(3-82c)
SVe = 0
(3-82d)
(s, n) ≥ 0
(3-82e)
k
k T
where the hessian of the Lagrange function ∇xxL(x, l, n) = ∇xx[ f (x) +
h(x)Tl + g(x)Tn] is calculated directly or through a quasi-Newton approximation (created by differences of gradient vectors). If Eq. (3-81) is strictly
convex, it is easy to show that Eqs. (3-82a) through (3-82c) correspond to a
Newton-Raphson step for Eqs. (3-80a) through (3-80c) applied at iteration k.
Also, selection of the active set is now handled at the QP level by satisfying
the conditions of Eqs. (3-82d) and (3-82e). To evaluate and change candidate
active sets, QP algorithms apply inexpensive matrix updating strategies to
the KKT matrix associated with Eq. (3-82). Details of this approach can be
found in Nocedal and Wright (2006).
As alternatives that avoid the combinatorial problem of selecting the
active set, interior point (or barrier) methods modify the NLP problem
Eq. (3-71) to form
Min f (xk) - mΣI ln si subject to h(xk) = 0
g(xk) + s = 0
(3-83)
where the solution to Eq. (3-84) has s > 0 for the penalty parameter m > 0.
Decreasing m to 0 leads to solution of problem Eq. (3-71). The KKT conditions for this problem can be written as
∇f (x*) + ∇h(x*) l + ∇g(x*) n = 0
h(x*) = 0
g(x*) + s = 0
(3-84)
SVe = me
and for m > 0, s > 0, and n > 0, Newton steps generated to solve Eqs. (3-84) are
well behaved and analogous to Eq. (3-82), with a modification on the righthand side of Eq. (3-82d). A detailed description of a particular interior point
algorithm, called IPOPT, can be found in Wächter and Biegler [Math . Prog .
106(1): 25–57 (2006)].
Both active set and interior point methods possess clear trade-offs.
Interior point methods may require more iterations to solve Eqs. (3-84)
The above subproblem can be solved very efficiently for fixed values of the
multipliers l and n and penalty parameter r. Here a gradient projection
trust region method is applied. Once subproblem Eq. (3-85) is solved, the multipliers and penalty parameter are updated in an outer loop, and the cycle
repeats until the KKT conditions for Eq. (3-71) are satisfied. LANCELOT
works best when exact second derivatives are available. This promotes a
fast convergence rate in solving each subproblem and allows a bound-constrained trust region method to exploit directions of negative curvature in
the hessian matrix.
Reduced gradient methods are active set strategies that rely on partitioning the variables and solving Eq. (3-80) in a nested manner. Without loss of
generality, problem Eq. (3-71) can be rewritten as Min f (z) subject to c(z) = 0
and a ≤ z ≤ b . Variables are partitioned as nonbasic variables (those fixed to
their bounds), basic variables (those that can be solved from the equality
constraints), and superbasic variables (those remaining variables between
bounds that serve to drive the optimization); this leads to zT = [zNT, zBT, zST].
This partition is derived from local information and may change over the
course of the optimization iterations. The corresponding KKT conditions
can be written as
∇N f (z) + ∇N c(z)γ = ba - bb
(3-86a)
∇B f (z) + ∇Bc(z)γ = 0
(3-86b)
∇S f (z) + ∇Sc(z)γ = 0
(3-86c)
c(z) = 0
zN,j = aj or bj
ba,j ≥ 0
bb,j = 0
(3-86d)
or bb,j ≥ 0 ba,j = 0
(3-86e)
where γ and b are the KKT multipliers for the equality and bound
constraints, respectively, and Eq. (3-86e) replaces the complementarity conditions in Eq. (3-76). Reduced gradient methods work by nesting
equations Eqs. (3-86b and d) within Eqs. (3-86a and c). At iteration k, for
fixed values of zNk and zSk, we can solve for zB by using Eq. (3-86d) and for
γ by using Eq. (3-86b). Moreover, linearization of these equations leads to
sensitivity information (i.e., constrained derivatives or reduced gradients)
that indicates how zB changes with respect to zS and zN. The algorithm
then proceeds by updating zS by using reduced gradients derived from
Eq. (3-86b) and given by
df (z)/dzS = ∇S f (z) + ∇Sc(z) γ = ∇S f (z) - ∇Sc(z) ∇Bc(z)-1 ∇B f (z)
(3-87)
Driving df/dzS to zero, with quasi-Newton or Newton iterations, solves
Eq. (3-86c). Following this, bound multipliers b are calculated from
Eq. (3-86a). Over the course of the iterations, if the variable zB or zS exceeds
its bounds or if some bound multipliers b become negative, then the variable partition needs to be changed and Eqs. (3-86) are reconstructed. These
reduced gradient methods are embodied in the popular GRG2, CONOPT, and
SOLVER codes (Edgar et al., 2002). The SOLVER code has been incorporated
into Microsoft Excel.
3-54
MATHEMATICS
Algorithmic Details for NLP Methods All the above NLP methods
incorporate concepts from the Newton-Raphson method for equation
solving. Essential features of these methods are that they provide (1) accurate derivative information to solve for the KKT conditions, (2) stabilization
strategies to promote convergence of the Newton-like method from poor
starting points, and (3) regularization of the jacobian matrix in Newton’s
method (the so-called KKT matrix) if it becomes singular or ill conditioned.
1. NLP methods that use first and second derivatives . The KKT conditions
require first derivatives to define stationary points, so accurate first derivatives are essential to determine locally optimal solutions for differentiable
NLPs. Moreover, Newton-Raphson methods that are applied to the KKT
conditions, as well as the task of checking second-order KKT conditions,
necessarily require second-derivative information. (Note that second-order
conditions are not checked by methods that do not use second derivatives.)
With the recent development of automatic differentiation tools, many
modeling and simulation platforms can provide exact first and second
derivatives for optimization. When second derivatives are available for the
objective or constraint functions, they can be used directly in LANCELOT
as well as SQP and reduced gradient methods. Otherwise, on problems with
few superbasic variables, both reduced gradient methods and SQP methods
[with reduced gradient methods applied to the QP subproblem Eq. (3-81)]
can benefit from positive definite quasi-Newton approximations (Nocedal
and Wright, 2006) applied to reduced second-derivative quantities (the socalled reduced hessian). Finally, for problems with least squares functions
(see Statistics subsection), as in data reconciliation, parameter estimation,
and model predictive control, one often assumes that the values of the
objective function and its gradient at the solution are vanishingly small.
Under these conditions, one can show that the multipliers (l, n) also vanish
and ∇xxL(x, l, n) can be substituted by ∇xx f (x*). This Gauss-Newton approximation has been shown to be very efficient for the solution of least squares
problems (see Nocedal and Wright, 2006).
2. Line search and trust region methods promote convergence from poor
starting points. These are commonly used with the search directions calculated from NLP subproblems such as Eq. (3-81). In a trust region approach,
the constraint ||p|| ≤ Δ is added, and the iteration step is taken if there is
sufficient reduction of some merit function (e.g., the objective function
weighted with some measure of the constraint violations). The size of the
trust region Δ is adjusted based on the agreement of the reduction of the
actual merit function compared to its predicted reduction from the subproblem (see Conn et al., 2000). Such methods have strong global convergence
properties and are especially appropriate for ill-conditioned NLPs. This
approach has been applied in the KNITRO code (see Nocedal and Wright,
2006). Line search methods can be more efficient on problems with reasonably good starting points and well-conditioned subproblems, as in real-time
optimization. Typically, once a search direction is calculated from Eq. (3-81),
or other related subproblem, a step size α ∈ (0, 1) is chosen so that xk + α p
leads to a sufficient decrease of a merit function. As a recent alternative,
a novel filter stabilization strategy ( for both line search and trust region
approaches) has been developed based on a bicriterion minimization, with
the objective function and constraint infeasibility as competing objectives
[Fletcher et al., SIAM J . Optim . 13(3):635 (2002)]. This method often leads to
better performance than that based on merit functions.
3. Regularization of the KKT matrix for the NLP subproblem is essential for
good performance of general-purpose algorithms. For instance, to obtain a
unique solution to Eq. (3-81), active constraint gradients must be full rank
and the hessian matrix, when projected into the null space of the active constraint gradients, must be positive definite. These properties may not hold far
from the solution, and corrections to the hessian in SQP may be necessary.
Regularization methods ensure that subproblems such as Eq. (3-81) remain
well conditioned; they include addition of positive constants to the diagonal
of the hessian matrix to ensure its positive definiteness, judicious selection
of active constraint gradients to ensure that they are linearly independent,
and scaling the subproblem to reduce the propagation of numerical errors.
Often these strategies are heuristics built into particular NLP codes. While
quite effective, most of these heuristics do not provide convergence guarantees for general NLPs.
From the conceptual descriptions as well as algorithmic details given
above, it is clear that NLP solvers are complex algorithms that have required
considerable research and development to turn them into reliable and
efficient software tools. Practitioners who are confronted with engineering
optimization problems should therefore leverage these efforts, rather than
write their own codes. Table 3-3 presents a sampling of available NLP codes
that represent the above classifications.
OPTIMIZATIOn METHODS WITHOUT DERIVATIVES
A broad class of optimization strategies does not require derivative
information. These methods have the advantage of easy implementation
and little prior knowledge of the optimization problem. In particular, such
TABLE 3-3 Representative nLP Solvers
Method
Algorithm type
Stabilization
Second-order
information
CONOPT
(Drud, 1994)
Reduced gradient
Line search
Exact and
quasi-Newton
GRG2
(Edgar et al., 2002)
Reduced gradient
Line search
Quasi-Newton
IPOPT
SQP, barrier
Line search
Exact
KNITRO
(Byrd et al., 1997)
SQP, barrier
Trust region
Exact and
quasi-Newton
LANCELOT
Augmented
Lagrangian, bound
constrained
Trust region
Exact and
quasi-Newton
LOQO
SQP, barrier
Line search
Exact
MINOS
Reduced gradient,
augmented
Lagrangian
Line search
Quasi-Newton
NPSOL
SQP, active set
Line search
Quasi-Newton
SNOPT
Reduced space SQP,
active set
Line search
Quasi-Newton
SOCS
SQP, active set
Line search
Exact
SOLVER
Reduced gradient
Line search
Quasi-Newton
SRQP
Reduced space SQP,
active set
Line search
Quasi-Newton
methods are well suited for “quick and dirty” optimization studies that
explore the scope of optimization for new problems, prior to investing effort
for more sophisticated modeling and solution strategies. Most of these
methods are derived from heuristics that naturally spawn numerous variations. As a result, a very broad literature describes these methods. Here we
discuss only a few important trends in this area.
Classical Direct Search Methods Developed in the 1960s and 1970s,
these methods include one-at-a-time search and methods based on experimental designs (EVOP). At that time, direct search methods were the most
popular optimization methods in chemical engineering. Methods that fall
into this class include the pattern search of Hooke and Jeeves [J . ACM 8: 212
(1961)], the conjugate direction method of Powell (1964), the simplex search
of Nelder-Mead [Comput . J . 7: 308 (1965)], and the adaptive random search
methods of Luus-Jaakola [AIChE J. 19: 760 (1973)], Goulcher and Cesares
Long [Comp . Chem . Engr. 2: 23 (1978)], and Banga et al. [in State of the Art
in Global Optimization, C. Floudas and P. Pardalos, eds., Kluwer, Dordrecht,
1996, p. 563]. All these methods require only objective function values for
unconstrained minimization. Associated with these methods are numerous
studies on a wide range of process problems. Moreover, many of these methods include heuristics that prevent premature termination (e.g., directional
flexibility in the complex search as well as random restarts and direction
generation).
Simulated Annealing This strategy is related to random search methods and derives from a class of heuristics with analogies to the motion of
molecules in the cooling and solidification of metals (Laarhoven and Aarts,
Simulated Annealing: Theory and Applications, Reidel Publishing, Dordrecht,
1987). Here a temperature parameter q can be raised or lowered to influence
the probability of accepting points that do not improve the objective function.
The method starts with a base point x and objective value f (x) . The next point x′
is chosen at random from a distribution. If f (x′) < f (x), the move is accepted
with x′ as the new point. Otherwise, x′ is accepted with probability p(q, x′, x) .
Options include the Metropolis distribution p(q, x, x′) = exp{-[ f (x′) - f (x)]/q}
and the Glauber distribution, p(q, x, x′) = exp{-[ f (x′) - f (x)]/q}/(1 + exp{-[ f (x′) f (x)]/q}) . The q parameter is then reduced, and the method continues until no
further progress is made.
Genetic Algorithms This approach, described in Holland, J. H.,
Adaptations in Natural and Artificial Systems (University of Michigan
Press, Ann Arbor, 1975), is based on the analogy of improving a population of solutions through modifying their gene pool. It also has similar
performance characteristics as random search methods and simulated
annealing. Two forms of genetic modification, crossover or mutation, are
used, and the elements of the optimization vector x are represented as
binary strings. Crossover deals with random swapping of vector elements
(among parents with highest objective function values or other rankings
of population) or any linear combinations of two parents. Mutation deals
OPTIMIZATIOn
3-55
with the addition of a random variable to elements of the vector. Genetic
algorithms (GAs) have seen widespread use in process engineering, and a
number of codes are available. Edgar et al. (2002) describe a related GA
that is available in MS Excel.
Derivative-Free Optimization (DFO) Over the past two decades,
the availability of parallel computers and faster computing hardware and
the need to incorporate complex simulation models within optimization
studies have led a number of optimization researchers to reconsider classical direct search approaches. In particular, Dennis and Torczon [SIAM
J . Optim . 1: 448 (1991)] developed a multidimensional search algorithm
that extends the simplex approach of Nelder and Mead (1965). They note
that the Nelder-Mead algorithm fails as the number of variables increases,
even for very simple problems. To overcome this, their multidimensional
pattern search approach combines reflection, expansion, and contraction
steps that act as line search algorithms for a number of linearly independent search directions. This approach is easily adapted to parallel computation, and the method can be tailored to the number of processors
available. Moreover, this approach converges to locally optimal solutions
for unconstrained problems and observes an unexpected performance
synergy when multiple processors are used. The work of Dennis and
Torczon (1991) has spawned considerable research on the analysis and
code development for DFO methods. In addition, Conn et al. (Introduction to Derivative Free Optimization, SIAM, Philadelphia, Penn., 2009) constructed a multivariable DFO algorithm that uses a surrogate model for
the objective function within a trust region method. Here points are sampled to obtain a well-defined quadratic interpolation model, and descent
conditions from trust region methods enforce convergence properties.
A comprehensive overview and convergence analysis of pattern search,
surrogate, and trust region DFO methods is presented in Conn, Scheinberg,
and Vicente (2009). Moreover, several DFO codes have been developed that
lead to black box optimization implementations for large, complex simulation models [see Audet and Dennis, SIAM J . Optim. 13: 889 (2003); Kolda et al.,
SIAM Rev . 45(3): 385 (2003)].
Direct search methods are easy to apply to a wide variety of problem
types and optimization models. Moreover, because their termination criteria are not based on gradient information and stationary points, they are
more likely to favor the search for globally optimal rather than locally optimal solutions. These methods can also be adapted easily to include integer
variables. However, no rigorous convergence properties to globally optimal
solutions have yet been discovered. Also, these methods are best suited for
unconstrained problems or for problems with simple bounds. Otherwise,
they may have difficulties with constraints, as the only options open for handling constraints are equality constraint elimination and addition of penalty
functions for inequality constraints. Both approaches can be unreliable and
may lead to failure of the optimization algorithm. Finally, the performance
of direct search methods scales poorly (and often exponentially) with the
number of decision variables. While performance can be improved with
the use of parallel computing, these methods are rarely applied to problems
with more than a few dozen decision variables.
For simplicity, consider the problem Min f (x) subject to g(x) ≤ 0 where
each function can be defined by additive terms. Convex relaxations for f (x)
and g(x) can be derived in the following ways:
• Convex additive terms remain unmodified in these functions.
• Concave additive unary terms are replaced by linear underestimating
functions that match the terms at the boundaries of their subregions.
• Nonconvex polynomial terms can be replaced by a set of scalar bilinear
terms, with new variables introduced to define the higher-order polynomials.
• The scalar bilinear terms can be relaxed by using the McCormick underestimator; e.g., the bilinear term xz is replaced by a new variable w and
linear inequality constraints
GLOBAL OPTIMIZATIOn
MIXED InTEGER PROGRAMMInG
Deterministic optimization methods are available for nonconvex nonlinear
programming problems of the form of Eq. (3-71) that guarantee convergence to the global optimum. More specifically, one can show under mild
conditions that they converge to an e distance to the global optimum in a
finite number of steps. These methods are generally more expensive than
local NLP methods, and they require the exploitation of the structure of the
nonlinear program.
Because global optima cannot be characterized by properties analogous
to KKT conditions for local optima, global optimization methods work by
partitioning the problem domain (i.e., containing the feasible region) into
subregions. Upper bounds on the objective function are computed over
all subregions of the problem. In addition, lower bounds can be derived
from convex relaxations of the objective function and constraints for each
subregion. The algorithm then proceeds to eliminate all subregions that
have infeasible constraint relaxations or lower bounds that are greater than
the least upper bound. After this, the remaining regions are further partitioned to create new subregions, and the cycle continues until the upper
and lower bounds converge.
This basic concept leads to a wide variety of global algorithms, with the
following features that can exploit different problem classes. Bounding
strategies relate to the calculation of upper and lower bounds. For the former,
any feasible point or, preferably, a locally optimal point in the subregion can be
used. For the lower bound, convex relaxations of the objective and constraint
functions are derived. The refining step deals with the construction of partitions in the domain and further partitioning them during the search process.
Finally, the selection step decides on the order of exploring the open subregions.
Mixed integer programming deals with both discrete and continuous
decision variables. For this presentation we consider discrete decisions
as binary variables, that is, yi = 0 or 1, and we consider the mixed integer
problem (3-70). Unlike in local optimization methods, there are no optimality conditions, such as the KKT conditions, that can be applied directly.
Instead, as in global optimization methods, a systematic search of the solution space, coupled with upper and lower bounding information, is applied.
As with global optimization problems, large mixed integer programs can be
expensive to solve, and some care is needed in problem formulation.
Mixed Integer Linear Programming If the objective and constraint
functions are all linear, then Eq. (3-70) becomes a mixed integer linear programming problem given by
w ≥ xlz + zlx - xlzl
w ≥ xuz + zux - xuzu
w ≤ xuz + zlx - xuzl
w ≤ xlz + zux - xlzu
(3-88)
where the subregions are defined by xl ≤ x ≤ xu and zl ≤ z ≤ zu . Thus the feasible region and the objective function are replaced by convex envelopes to
form relaxed problems.
Solving these convex relaxed problems leads to global solutions that
are lower bounds to the NLP in the particular subregion. Finally, we see
that gradient-based NLP solvers play an important role in global optimization algorithms, as they often yield the lower and upper bounds for the
subregions. The spatial branch and bound global optimization algorithm
can therefore be given by the following steps:
0. Initialize algorithm. Calculate upper and lower bounds over the entire
(relaxed) feasible region.
For iteration k with a set of partitions Mkj and bounds in each subregion
fLj and fUj :
1. Bound . Define the best upper bound fU = Minj fUj and delete ( fathom)
all subregions j with lower bounds fLj ≥ fU. If the remaining subregions satisfy
fLj ≥ fU - e, stop.
2. Refine . Divide the remaining active subregions into partitions Mk,j1 and
Mk,j2. (Many branching rules are available for this step.)
3. Select . Solve the convex relaxed NLP in the new partitions to obtain fLj1
and fLj2. Delete the partition if there is no feasible solution.
4. Update . Obtain upper bounds fUj1 and fUj2 to new partitions, if present.
Set k = k + 1, update partition sets, and go to step 1.
Note that a number of improvements can be made to the bounding,
refinement, and selection strategies in the algorithm that accelerate the
convergence of this method. A comprehensive discussion of all these options
can be found in Floudas (2000) and Tawarlamani and Sahinidis (2002). Also,
a number of efficient global optimization codes have recently been developed, including αBB, BARON, LGO, and OQNLP . An interesting numerical
comparison of these and other codes can be found in Neumaier et al., Math .
Prog . B 103(2): 335 (2005).
Min aTx + cTy subject to Ax + By ≤ b
x ≥ 0 y ∈ {0, 1}t
(3-89)
Note that if we relax the t binary variables by the inequalities 0 ≤ y ≤ 1, then
Eq. (3-89) becomes a linear program with a (global) solution that is a lower
bound to the MILP Eq. (3-89). There are specific MILP classes where the LP
relaxation of Eq. (3-89) has the same solution as the MILP. Among these problems is the well-known assignment problem. Other MILPs that can be solved
with efficient special-purpose methods are the knapsack problem, the set
covering and set partitioning problems, and the traveling salesperson problem.
See Nemhauser and Wolsey (1999) for a detailed treatment of these problems.
More generally, MILPs are solved with branch and bound algorithms, similar to the spatial branch and bound method of the previous section, that
3-56
MATHEMATICS
explore the search space. As seen in Fig. 3-58, binary variables are used to
define the search tree, and a number of bounding properties can be noted
from the structure of Eq. (3-89).
Upper bounds on the objective function can be found from any feasible
solution to Eq. (3-89), with y set to integer values. These can be found at
the bottom or “leaf ” nodes of a branch and bound tree (and sometimes at
intermediate nodes as well). The top, or root, node in the tree is the solution
to the linear programming relaxation of Eq. (3-89); this is a lower bound to
Eq. (3-89). On the other hand, as one proceeds down the tree with a partial
assignment of the binary variables, a lower bound for any leaf node in that
branch can be found from solution of the linear program at this intermediate node with the remaining binary variables relaxed. This leads to the
following properties:
• Any intermediate node with an infeasible LP relaxation has infeasible leaf
nodes and can be fathomed (i.e., all remaining children of this node can
be eliminated).
• If the LP solution at an intermediate node is not less than an existing integer solution, then the node can be fathomed.
These properties lead to pruning of the search tree. Branching then continues in the tree until the upper and lower bounds converge.
This basic concept leads to a wide variety of MILP algorithms with the
following features. LP solutions at intermediate nodes are relatively easy
to calculate with the simplex method. If the solution of the parent node
is known, multiplier information from this solution can be used to calculate (via efficient pivoting operations) the LP solution at the child node.
Branching strategies to navigate the tree take a number of forms. More
common depth-first strategies expand the most recent node to a leaf node
or infeasible node and then backtrack to other branches in the tree. These
strategies are simple to program and require little storage of past nodes. On
the other hand, breadth-first strategies expand all the nodes at each level of
the tree, select the node with the lowest objective function, and then proceed until the leaf nodes are reached. Here more storage is required, but
generally fewer nodes are evaluated than in depth-first search. In addition,
selection of binary variable for branching is based on a number of criteria,
including choosing the variable with the relaxed value closest to 0 or 1, or
the one leading to the largest change in the objective. A number of improved
branching rules can accelerate the convergence of this method, and a number of efficient, large-scale MILP codes are widely used, including CPLEX,
OSL, XPRESS, and ZOOM. Additional description of these strategies can be
found in Nemhauser and Wolsey (1999).
Example To illustrate the branch and bound approach, we consider the
MILP:
Min Z = x + y 1 + 2 y 2 + 3 y 3
subject to − x + 3 y 1 + y 2 + 2 y 3 ≤ 0
− 4 y 1 − 8 y 2 − 3 y 3 ≤ −10
Min f (x) + cTy subject to g(x) + By ≤ b
Min f (x) + cTy- subject to g(x) + By- ≤ b
-7Inf.
(0,1,0)
-6Z=7.625
(0, 0.875, 1)
x≥0
f(x) ≥ f(xk) + ∇f(xk)T(x - xk)
(3-91)
(3-92)
Consequently, linearization of Eq. (3-90) at a point xk, to form the problem
Min
subject to
f (xk) + ∇f (xk)T(x - xk) + cTy
g(xk) + ∇g(xk)T(x - xk) + By ≤ b
x≥0
y ∈ {0, 1}t
(3-93)
leads to overapproximation of the feasible region and underapproximation
of the objective function in Eq. (3-90). Consequently, solution of Eq. (3-93) is
a lower bound to the solution of Eq. (3-90). Adding more linearizations from
other points does not change the bounding property, so for a set of points xl,
l = 1, …, k, the problem
-1Z=5
(0.5, 1, 0)
y1
-node#Z
(y1, y2, y3)
(3-90)
if feasible, leads to a solution that is an upper bound on the MINLP solution.
In addition, linearizations of a convex function f(x) leads to underestimation of the function itself, i.e.,
The solution to this problem is given by x = 4, y1 = 1, y2 = 1, y3 = 0, and Z = 7.
Here we use a depth-first strategy and branch on the variables closest to
0 or 1. Figure 3-58 shows the progress of the branch and bound algorithm
as the binary variables are selected and the bounds are updated. The
sequence numbers for each node in Fig. 3-58 show the order in which they
are processed. The grayed partitions correspond to the deleted nodes, and
at termination of the algorithm we see that Z = 7 and an integer solution is
obtained at an intermediate node where coincidentally y3 = 0.
y3
x ≥ 0 y ∈ {0, 1}t
where the binary variables are kept as separate linear terms. MINLP strategies can be classified into two types. The first deals with nonlinear extensions of the branch and bound method discussed above for MILPs. The
second deals with outer approximation decomposition strategies that provide lower and upper bounding information for convergence.
Nonlinear Branch and Bound The MINLP Eq. (3-90) can be solved in
a similar manner to Eq. (3-89). If the functions f (x) and g(x) in Eq. (3-90)
are convex, then direct extensions to the branch and bound method can
be made. A relaxed NLP can be solved at the root node, upper bounds
to the solution of Eq. (3-90) can be found at the leaf nodes, and the
bounding properties due to NLP solutions at intermediate nodes still
hold. However, this approach is more expensive than the corresponding
MILP method. First, NLPs are more expensive than LPs to solve. Second,
unlike with relaxed LP solutions, NLP solutions at child nodes cannot be
updated directly from solutions at parent nodes. Instead, the NLP needs
to be solved again (but one hopes with a better starting guess). The NLP
branch and bound method is used in the SBB code interfaced to GAMS.
In addition, Leyffer [Comput . Optim . Appl . 18: 295 (2001)] proposed a
hybrid MINLP strategy nested within an SQP algorithm. At each iteration,
a mixed integer quadratic program is formed, and a branch and bound
algorithm is executed to solve it.
If f (x) and g(x) are nonconvex, additional difficulties can occur. In this
case, nonunique, local solutions can be obtained at intermediate nodes,
and consequently lower bounding properties would be lost. In addition,
the nonconvexity in g(x) can lead to locally infeasible problems at intermediate nodes, even if feasible solutions can be found in the corresponding
leaf node. To overcome problems with nonconvexities, global solutions to
relaxed NLPs can be solved at the intermediate nodes. This preserves the
lower bounding information and allows nonlinear branch and bound to
inherit the convergence properties from the linear case. However, as noted
above, this leads to much more expensive solution strategies.
Outer Approximation Decomposition Methods Again, we consider
the MINLP Eq. (3-90) with convex f (x) and g(x). Note that the NLP with
binary variables fixed at y-
x ≥ 0 , y 1 , y 2 , y 3 ∈{0,1}
-5Z=6.33
(0,1,0.67)
Without loss of generality,
Mixed Integer Nonlinear Programming
we can rewrite the MINLP in Eq. (3-71) as
-2Z=6.25
(1, 0.75, 0)
y2
-4Inf.
(1,0,1)
FIG. 3-58 Branch and bound sequence for MILP example.
-3Z=7
(1,1,0)
Min α
subject to
α ≥ f ( x l ) + ∇f ( x l )T ( x − x l ) + c T y
l = 1,k
g ( x l ) + ∇g ( x l )T ( x − x l ) + By ≤ b
x ≥0
y ∈{0, 1}t
(3-94)
where α is a scalar variable, still has a solution that is a lower bound to
Eq. (3-90). The outer approximation strategy is depicted in Fig. 3-59.
OPTIMIZATIOn
Initialize
x 0, y 0
Upper bound
with y fixed
NLP (3-91)
Update y
Lower bound
MILP (3-94)
+ integer cuts
LB ≥ UB
FIG. 3-59 Outer approximation MINLP algorithm.
The outer approximation algorithm first initializes the process, either
with a predetermined starting guess or by solving a relaxed NLP based on
Eq. (3-90). An upper bound to the solution is then generated by fixing the
binary variables to their current values yk and solving the NLP Eq. (3-91).
This solution determines the continuous variable values xk for the MILP
Eq. (3-94). [If Eq. (3-94) is an infeasible problem, any point may be chosen for
xk, or the linearizations could be omitted.] Note that this MILP also contains
linearizations from previous solutions of Eq. (3-91). Finally, the integer cut
∑| y i − y ik | ≥ 1 is added to Eq. (3-94) to avoid revisiting previously encountered values of binary variables. Solution of Eq. (3-94) yields new values of
y and (without the integer cut) must lead to a lower bound to the solution
of Eq. (3-90). Consequently, if the objective function of the lower bounding MILP is greater than the least upper bound determined in solutions of
Eq. (3-91), then the algorithm terminates. Otherwise, the new values of y are
used to solve the next NLP Eq. (3-91).
Compared to nonlinear branch and bound, the outer approximation
algorithm usually requires very few solutions of the MILP and NLP subproblems. This is especially advantageous on problems where the NLPs are
large and expensive to solve. Moreover, there are three variations of outer
approximation that may be suitable for particular problem types:
In generalized benders decomposition (GBD) the lower bounding problem
Eq. (3-94) is replaced by the MILP
Min α subject to
x ≥ 0, y ∈{0, 1}t
α ≥ f ( x l ) + c T y + [ g ( x l ) + By ]T νl
∑| y i − y il | ≥ 1 l = 1,, k
i
(3-95)
where nl is the vector of KKT multipliers from the solution of Eq. (3-91) at
iteration l. This MILP can be derived through a reformulation of the MILP
used in Fig. 3-59 with the inactive constraints from Eq. (3-91) dropped. Solution of Eq. (3-95) leads to a weaker lower bound than Eq. (3-94), and consequently, more solutions of the NLP and MILP subproblems are needed to
converge to the solution. However, Eq. (3-95) contains only a single continuous variable and far fewer inequality constraints and is much less expensive
to solve than Eq. (3-94). Thus, GBD is favored over outer approximation if
Eq. (3-91) is relatively inexpensive to solve or solution of Eq. (3-94) is too
expensive.
The extended cutting plane (ECP) algorithm is complementary to GBD.
While the lower bounding problem in Fig. 3-59 remains essentially the same,
the continuous variables xk are chosen from the MILP solution and the
NLP Eq. (3-91) is replaced by a simple evaluation of the objective and constraint functions. As a result, only MILP problems [Eq. (3-94) plus integer
cuts] need to be solved. Consequently, the ECP approach has weaker upper
bounds than outer approximation and requires more MILP solutions. It has
advantages over outer approximation when the NLP Eq. (3-91) is expensive
to solve.
The third extension to the outer approximation approach is based on a
branch-and-cut algorithm, which solves a continuous linear program at each
node of the search tree, and therefore improves the lower bounds while
branching on integer variables. BONMIN, a comprehensive MINLP code
described in Bonami et al. [“An Algorithmic Framework for Convex Mixed
Integer Nonlinear Programs,” Discrete Optimization 5(2): 186–204 (2008)]
3-57
incorporates NLP branch and bound, branch and cut, and outer approximation as options, along with hybrids of these strategies.
Additional difficulties arise for the outer approximation algorithm and
its GBD, ECP, and branch and cut extensions when either f (x) or g(x) is nonconvex. Under these circumstances, the lower bounding properties resulting from the linearization and formulation of the MILP subproblem are
lost, and the MILP solution may actually exclude the solution of Eq. (3-90).
Hence, these algorithms need to be applied with care to nonconvex problems. To deal with nonconvexities, one can relax the linearizations in
Eq. (3-94) through the introduction of additional deviation variables that
can be penalized in the objective function. Alternately, the linearizations in
Eq. (3-94) can be replaced by valid underestimating functions, such as those
derived for global optimization [e.g., Eq. (3-86)]. However, this requires specific structural knowledge of Eq. (3-90) and may lead to weak lower bounds
for the resulting MILP.
Finally, the performance of both MILP and MINLP algorithms is strongly
dependent on the problem formulations Eq. (3-89) and Eq. (3-90). In particular, the efficiency of the approach is impacted by the lower bounds produced by the relaxation of the binary variables and subsequent solution of
the linear program in the branch and bound tree. A number of approaches
have been proposed to improve the quality of the lower bounds, including
these:
• Logic-based methods such as generalized disjunctive programming (GDP)
can be used to formulate MINLPs with fewer discrete variables that have
tighter relaxations. The imposition of logic-based constraints prevents the
generation of unsuitable alternatives, leading to less expensive searches.
In addition, constrained logic programming (CLP) methods offer efficient
alternatives to MILP solvers for highly combinatorial problems. See Jain
and Grossmann, INFORMS Journal of Computing, 13: 258–276 (2001) for
more details.
• Convex hull formulations of MILPs and MINLPs lead to relaxed problems
that have much tighter lower bounds. This leads to the examination of far
fewer nodes in the branch and bound tree. See Grossmann and Lee, Comput . Optim . Applic . 26: 83 (2003) for more details.
• Reformulation and preprocessing strategies including bound tightening
of the variables, coefficient reduction, lifting facets, and special ordered
set constraints frequently lead to improved lower bounds and significant
performance improvements in mixed integer programming algorithms.
See Bixby, R., and E. Rothberg, Annals of Operations Research, 49(1): 37–41
(2007) for more details.
A number of efficient codes are available for the solution of MINLPs,
including AlphaECP, BARON, BONMIN, DICOPT, MINLP, and SBB. All are
available within the GAMS modeling platform.
DEVELOPMEnT OF OPTIMIZATIOn MODELS
The most important aspect to a successful optimization study is the formulation of the optimization model. These models must reflect the real-world
problem so that meaningful optimization results are obtained; they also
must satisfy the properties of the problem classes in Fig. 3-53. For instance,
NLPs addressed by gradient-based methods need to have functions that
are defined in the variable domain and have bounded and continuous first
and second derivatives. In mixed integer problems, proper formulations are
also needed to yield good lower bounds for efficient search. With increased
understanding of optimization methods and the development of efficient
and reliable optimization codes, optimization practitioners now focus on
the formulation of optimization models that are realistic, well posed, and
inexpensive to solve. Finally, convergence properties of NLP, MILP, and
MINLP solvers require accurate first (and often second) derivatives from the
optimization model. If these contain numerical errors (say, through finite
difference approximations), then the performance of these solvers can deteriorate considerably. As a result of these characteristics, modeling platforms
are essential for the formulation task. These are classified into two broad
areas: optimization modeling platforms and simulation platforms with
optimization.
Optimization modeling platforms provide general-purpose interfaces for
optimization algorithms and remove the need for the user to interface to the
solver directly. These platforms allow the general formulation for all problem classes discussed above with direct interfaces to state-of-the-art optimization codes. Three representative platforms are GAMS (General Algebraic
Modeling Systems), AMPL (A Mathematical Programming Language), and
AIMMS (Advanced Integrated Multidimensional Modeling Software). All
three require problem model input via a declarative modeling language
and provide exact gradient and hessian information through automatic
differentiation strategies. Although it is possible, these platforms were not
designed to handle externally added procedural models. As a result, these
platforms are best applied on optimization models that can be developed
entirely within their modeling framework. Nevertheless, these platforms are
3-58
MATHEMATICS
widely used for large-scale research and industrial applications. In addition,
the MATLAB platform allows for flexible formulation of optimization models as well, although it currently has only limited capabilities for automatic
differentiation and limited optimization solvers.
Simulation platforms with optimization are often dedicated, applicationspecific modeling tools to which optimization solvers have been interfaced.
These lead to very useful optimization studies, but because they were not
originally designed for optimization models, they need to be used with some
caution. In particular, most of these platforms do not provide exact derivatives to the optimization solver; often they are approximated through finite
differences. In addition, the models themselves are constructed and calculated through numerical procedures, instead of through an open declarative
language. Examples of these include widely used process simulators such as
Aspen/Plus, PRO/II, and Hysys . Also note that more recent platforms such
as Aspen Custom Modeler, GPROMS, and MOSAIC include declarative models and exact first derivatives .
Finally, for optimization tools that must be linked to procedural models,
reliable and efficient automatic differentiation (AD) tools that provide exact
first (often second) derivatives are available that link to models written in C,
C++, FORTRAN, Python, and other modeling platforms. Example AD tools
include ADIC, ADOL-C, CasADi, CppAD, and TAPENADE. When used with
care, these can be applied to existing procedural models and, when linked
to modern NLP and MINLP algorithms, can lead to powerful optimization
capabilities.
STATISTICS
References: Box, G. P., J. S. Hunter, and W. G. Hunter, Statistics for
Experimenters: Design, Innovation, and Discovery, 2d ed., Wiley, New
York, 2005; Cropley, J. B., “Heuristic Approach to Complex Kinetics,”
pp. 292–302 in Chemical Reaction Engineering—Houston, ACS Symposium
Series 65, American Chemical Society, Washington, D.C., 1978; Schiller, Jr.,
J. J., R. A. Srinivasan, and M. Spiegel, Schaum’s Outline of Probability and
Statistics, 4th ed., McGraw-Hill, New York, 2012; Mendenhall, W., and
T. Sincich, Statistics for Engineering and the Sciences, 5th ed., Pearson,
Boston, 2006; Moore, D. S., G. P. McCabe, and B. Craig, Introduction to the
Practice of Statistics, 8th ed., Freeman, San Francisco, 2014; Montgomery,
D. C., and G. C. Runger, Applied Statistics and Probability for Engineers,
6th ed., Wiley, New York, 2013; see also Logan and Wolesensky (2009) in
General References and https://cloud.r-project.org/ for Statistics in R.
InTRODUCTIOn
Statistics represents a body of knowledge that enables one to deal with
quantitative data reflecting any degree of uncertainty. There are six basic
aspects of applied statistics:
1. Type of data
2. Random variables
3. Models
4. Parameters
5. Sample statistics
6. Characterization of chance occurrences
From these can be developed strategies and procedures for dealing with
(1) estimation and (2) inferential statistics. The following has been directed
more toward inferential statistics because of its broader utility.
Detailed illustrations and examples are used throughout to develop basic
statistical methodology for dealing with a broad area of applications. If you
are new to statistics, look first at the examples and find one that is appropriate to your application. In addition to this material, there are many specialized topics as well as some very subtle areas that have not been discussed.
The references should be used for more detailed information. Section 8
discusses the use of statistics in statistical process control (SPC).
Type of Data In general, statistics deals with two types of data: counts
and measurements. Counts represent the number of discrete outcomes,
such as the number of defective parts in a shipment, the number of losttime accidents, and so forth. Measurement data are treated as a continuum.
For example, the tensile strength of a synthetic yarn theoretically could be
measured to any degree of precision. A subtle aspect associated with count
and measurement data is that some types of count data can be dealt with
through the application of techniques that have been developed for measurement data alone. This ability is due to the fact that some simplified
measurement statistics serve as an excellent approximation for the more
tedious count statistics.
Random Variables Applied statistics deals with quantitative data. In
tossing a fair coin the successive outcomes would tend to be different, with
heads and tails occurring randomly over time. Given a long strand of synthetic fiber, the tensile strength of successive samples would tend to vary
significantly from sample to sample. Counts and measurements are characterized as random variables, that is, observations which are susceptible
to chance. Virtually all quantitative data are susceptible to chance in one
way or another.
Models Part of the foundation of statistics consists of the mathematical models that characterize an experiment. The models themselves are
mathematical ways of describing the probability, or relative likelihood, of
observing specified values of random variables. For example, in tossing a
coin once, a random variable x could be defined by assigning to x the value 1
for a head and 0 for a tail. Given a fair coin, the probability of observing a
head on a toss would be .5, and similarly for a tail. Therefore, the mathematical
model governing this experiment can be written as
x
P(x)
0
1
.5
.5
where P(x) stands for what is called a probability function . This term is
reserved for count data, in that probabilities can be defined for particular
outcomes. The probability function that has been displayed is a very special case of the more general case, which is called the binomial probability
distribution .
For measurement data which are considered continuous, the term probability density is used. For example, consider a spinner wheel which conceptually can be thought of as being marked off on the circumference infinitely
precisely from 0 up to, but not including, 1. In spinning the wheel, the probability of the wheel’s stopping at a specified marking point at any particular
x value, where 0 ≤ x < 1, is 0, for example, stopping at the value x = .5 . For
the spinning wheel, the probability density function would be defined by
f (x .) = 1 for 0 ≤ x < 1. Graphically, this is shown in Fig. 3-60. The relative probability concept refers to the fact that density reflects the relative likelihood
of occurrence; in this case, each number between 0 and 1 is equally likely.
For measurement data, probability is defined by the area under the curve
between specified limits. A density function always must have a total area
of 1.
Example For the density of Fig. 3-60
P[0 ≤ x ≤ .4] = .4
P[.2 ≤ x ≤ .9] = .7
P[.6 ≤ x < 1] = .4
and so forth. Since the probability associated with any particular point
value is zero, it makes no difference whether the limit point is defined by a
closed interval (≤ or ≥) or an open interval (< or >).
Many different types of models are used as the foundation for statistical
analysis. These models are also referred to as populations.
Parameters As a way of characterizing probability functions and
densities, certain types of quantities called parameters can be defined.
For example, the center of gravity of the distribution is defined to be the
population mean, which is designated as m. For the coin toss m = .5, which
corresponds to the average value of x; i.e., for one-half of the time x will take
on a value 0 and for the other half a value 1. The average would be .5. For the
spinning wheel, the average value would also be .5.
FIG. 3-60
Density function.
STATISTICS
Another parameter is called the standard deviation, which is designated
as s. The square of the standard deviation is used frequently and is called
the variance s2. Basically, the standard deviation is a quantity which measures the spread or dispersion of the distribution from its mean m. If the
spread is broad, then the standard deviation will be larger than if it were
more constrained.
For specified probability and density functions, the respective mean, or
expected value E(x), variance Var(x), and standard deviation s are defined
by the following:
Probability functions
(discrete variables and counts)
Probability density functions
(continuous variables)
E ( x ) = µ = ∑ x p( x )
E ( x ) = µ = ∫ x f ( x ) dx
x
x
Var( x ) = σ = ∑ ( x − µ) P ( x )
2
2
Var( x ) = σ = ∫ ( x − µ)2 f ( x ) dx
2
x
x
Sample Statistics Many types of sample statistics will be defined.
Two very special types are the sample mean, designated as x, and the sample standard deviation, designated as s . These are, by definition, random
variables. Parameters such as m and s are not random variables; they are
fixed constants corresponding to a probability function or distribution.
Example In an experiment, six random numbers (rounded to four decimal places) were observed from the uniform distribution f (x) = 1 for 0 ≤ x < 1:
0.1009, 0.3754, 0.0842, 0.9901, 0.1280, 0.6606
The sample mean corresponds to the arithmetic average of the observations,
which will be designated as x1 through x6, where
x=
1 n
∑ x i with n = 6 x = 0.3899
n i =1
(3-96)
The sample standard deviation s is defined by the computation
s=
∑( x
i
− x )2
n −1
=
n ∑ x i2 − (∑ x i )2
n (n − 1)
(3-97)
In effect, this represents the root of a statistical average of the squares. The
divisor quantity n - 1 will be referred to as the degrees of freedom. The sample value of the standard deviation for the data given is .3686.
The value of n - 1 is used in the denominator because the deviations from
the sample average must total zero, or
∑( x
i
− x)= 0
Thus knowing n - 1 values of xi - x permits calculation of the nth value of
xi - x.
The sample mean and sample standard deviation are obtained by using
Microsoft Excel with the commands AVERAGE(B2:B7) and STDEV(B2:B7)
when the observations are in cells B2 to B7.
In effect, the standard deviation quantifies the relative magnitude of the
deviation numbers, i.e., a special type of “average” of the distance of points
from their center. In statistical theory, it turns out that the corresponding
variance quantities s2 have remarkable properties which make possible
broad generalities for sample statistics and therefore also their counterparts, the standard deviations.
For the corresponding population, the parameter values are m = .50 and
s = .2887, which are obtained by calculating the integrals defined above with
f (x) = 1 and integrating x from 0 to 1. If, instead of using individual observations only, averages of 6 were reported, then the corresponding population
parameter values would be m = .50 and σ x = σ / 6 = .1179. The corresponding variance for an average will be written occasionally as Var (x) = var (x)/n .
In effect, the variance of an average is inversely proportional to the sample
size n, which reflects the fact that sample averages will tend to cluster much
more closely than individual observations. This is illustrated in greater
detail under Measurement Data and Sampling Densities.
Characterization of Chance Occurrences To deal with a broad area
of statistical applications, it is necessary to characterize the way in which
random variables will vary by chance alone. The basic foundation for this
characteristic is laid through a density called the gaussian, or normal,
distribution.
3-59
Determining the area under the normal curve is a very tedious procedure.
However, by standardizing a random variable that is normally distributed, it
is possible to relate all normally distributed random variables to one table.
The standardization is defined by the identity z = (x - m)/s, where z is called
the unit normal. Further, it is possible to standardize the sampling distribution of averages x by the identity z = ( x − µ)/(σ / n ).
A remarkable property of the normal distribution is that, almost regardless of the distribution of x, sample averages x will approach the gaussian
distribution as n gets large. Even for relatively small values of n, of about
10, the approximation in most cases is quite close. For example, sample
averages of size 10 from the uniform distribution will have essentially a
gaussian distribution. Also, in many applications involving count data, the
normal distribution can be used as a close approximation. In particular,
the approximation is quite close for the binomial distribution within certain guidelines.
The normal probability distribution function can be obtained in
Microsoft Excel by using the NORM.DIST function and supplying the desired
mean and standard deviation. The cumulative value can also be determined. In the MATLAB Statistics Toolbox the corresponding command is
normcdf(x, m, s).
EnUMERATIOn DATA AnD PROBABILITY DISTRIBUTIOnS
Introduction Many types of statistical applications are characterized
by enumeration data in the form of counts. Examples are the number of losttime accidents in a plant, the number of defective items in a sample, and the
number of items in a sample that fall within several specified categories.
The sampling distribution of count data can be characterized through
probability distributions. In many cases, count data are appropriately
interpreted through their corresponding distributions. However, in other
situations analysis is greatly facilitated through distributions which have
been developed for measurement data. Examples of each will be illustrated
in the following subsections.
Binomial Probability Distribution
Nature Consider an experiment in which each outcome is classified
into one of two categories, one of which will be defined as a success and the
other as a failure. Given that the probability of success p is constant from
trial to trial, then the probability of observing a specified number of successes x in n trials is defined by the binomial distribution. The sequence of
outcomes is called a Bernoulli process .
Nomenclature Let p̂ = x/n be the proportion of successes in n trials.
Probability Law
n
x
p ( x ) = p = p x (1 − p )n− x x = 0,1, 2, , n
n x
n
n!
where =
x n !(n − x )!
Properties
E ( x ) = np
E ( pˆ ) = p
Var( x ) = np (1 − p )
Var( pˆ ) = p (1 − p )/n
Example In three tosses of a coin, what is the probability of seeing
three heads? This problem uses the binomial probability distribution
because each toss is independent of the previous ones. Assuming the coins
are “fair” and the probability of heads is ½, then the probability of 3 heads
in 3 tosses is
3
P=
0
3! 1 1 1
=
3!0! 2 2 8
Likewise, the probability of 2 heads and 1 tail in 3 tosses is
2
P=
1
3! 1 1 3